Author name code: toomre
ADS astronomy entries on 2022-09-14
author:"Toomre, Juri" 
------------------------------------------------------------------------  

Title: Confinement of the Solar Tachocline by Dynamo Action in the
    Radiative Interior
Authors: Matilsky, Loren I.; Hindman, Bradley W.; Featherstone,
   Nicholas A.; Blume, Catherine C.; Toomre, Juri
Bibcode: 2022arXiv220612920M
Altcode:
  A major outstanding problem in solar physics is the confinement
  of the solar tachocline, the thin shear layer that separates nearly
  solid-body rotation in the radiative interior from strong differential
  rotation in the convection zone. Here, we present the first 3-D, global
  solar simulation in which a tachocline is confined by a self-excited
  dynamo. The non-axisymmetric magnetism is initially built in the
  convection zone and then diffusively imprints downward. Additionally,
  the field is locally amplified throughout the radiative interior by
  vigorous horizontal motions that arise from equatorial Rossby waves and
  possibly shear instabilities. Our work thus challenges the long-held
  notion that the Sun's dynamo magnetic field is amplified only as deep
  as the tachocline and stored in a quiescent radiative interior.

Title: Longitudinally Modulated Dynamo Action in Simulated M-dwarf
    Stars
Authors: Bice, Connor P.; Toomre, Juri
Bibcode: 2022ApJ...928...51B
Altcode: 2022arXiv220202869B
  M-dwarf stars are well known for the intense magnetic activity that many
  of them exhibit. In cool stars with near-surface convection zones, this
  magnetic activity is thought to be driven largely by the interplay of
  convection and the large-scale differential rotation and circulations
  it establishes. The highly nonlinear nature of these flows yields
  a fascinatingly sensitive and diverse parameter space, with a wide
  range of possible dynamics. We report here on a set of three global MHD
  simulations of rapidly rotating M2 (0.4 M <SUB>⊙</SUB>) stars. Each of
  these three models established nests of vigorous convection that were
  highly modulated in longitude at low latitudes. Slight differences in
  their magnetic parameters led each model to disparate dynamo states,
  but the effect of the convective nest was a unifying feature. In each
  case, the action of longitudinally modulated convection led to localized
  (and in one case, global) reversals of the toroidal magnetic field,
  as well as the formation of an active longitude, with enhanced poloidal
  field amplitudes and flux emergence.

Title: Powering Stellar Magnetism: Energy Transfers in Cyclic Dynamos
    of Sun-like Stars
Authors: Brun, Allan Sacha; Strugarek, Antoine; Noraz, Quentin;
   Perri, Barbara; Varela, Jacobo; Augustson, Kyle; Charbonneau, Paul;
   Toomre, Juri
Bibcode: 2022ApJ...926...21B
Altcode: 2022arXiv220113218B
  We use the anelastic spherical harmonic code to model the convective
  dynamo of solar-type stars. Based on a series of 15 3D MHD simulations
  spanning four bins in rotation and mass, we show what mechanisms are
  at work in these stellar dynamos with and without magnetic cycles
  and how global stellar parameters affect the outcome. We also derive
  scaling laws for the differential rotation and magnetic field based
  on these simulations. We find a weaker trend between differential
  rotation and stellar rotation rate, ( ${\rm{\Delta }}{\rm{\Omega
  }}\propto {(| {\rm{\Omega }}| /{{\rm{\Omega }}}_{\odot })}^{0.46}$ )
  in the MHD solutions than in their HD counterpart ${\left(| {\rm{\Omega
  }}| /{{\rm{\Omega }}}_{\odot }\right)}^{0.66}$ ), yielding a better
  agreement with the observational trends based on power laws. We find
  that for a fluid Rossby number between 0.15 ≲ Ro <SUB>f</SUB> ≲
  0.65, the solutions possess long magnetic cycle, if Ro <SUB>f</SUB>
  ≲ 0.42 a short cycle and if Ro <SUB>f</SUB> ≳ 1 (antisolar-like
  differential rotation), a statistically steady state. We show that
  short-cycle dynamos follow the classical Parker-Yoshimura rule
  whereas the long-cycle period ones do not. We also find efficient
  energy transfer between reservoirs, leading to the conversion of
  several percent of the star's luminosity into magnetic energy that
  could provide enough free energy to sustain intense eruptive behavior
  at the star's surface. We further demonstrate that the Rossby number
  dependency of the large-scale surface magnetic field in the simulation
  ( ${B}_{{\rm{L}},\mathrm{surf}}\sim {{Ro}}_{{\rm{f}}}^{-1.26}$ ) agrees
  better with observations ( ${B}_{V}\sim {{Ro}}_{{\rm{s}}}^{-1.4\pm 0.1}$
  ) and differs from dynamo scaling based on the global magnetic energy
  ( ${B}_{\mathrm{bulk}}\sim {{Ro}}_{{\rm{f}}}^{-0.5}$ ).

Title: Global Confinement Of The Solar Tachocline By A Convective
    Dynamo
Authors: Matilsky, L.; Hindman, B.; Toomre, J.
Bibcode: 2021AAS...23830401M
Altcode:
  After more than thirty years, the most striking feature of the internal
  rotation profile of the Sun as revealed by helioseismology­—the
  tachocline of shear at the base of the convection zone (CZ)—remains
  poorly understood. Here we present rotating, 3D, spherical-shell
  simulations of a CZ overlying a stable radiative zone (RZ) that
  confine the tachocline against inward diffusive spreading via a
  convective dynamo. In particular, the viscous imprinting of the
  differential rotation from the CZ onto the RZ is prevented by the
  non-axisymmetric Lorentz torque, producing a tachocline-like shear
  layer at all latitudes. The balance remains stable on centuries-long
  timescales and overall resembles a more complex (non-axisymmetric)
  version of Ferraro's Law of Isorotation, in which isorotation contours
  are forced to fall along poloidal magnetic field lines. These results
  add an unexpected path toward solving the tachocline confinement
  problem. Namely, a dynamo operating mostly in the CZ (and notably
  in the absence of a primordial magnetic field confined beneath the
  tachocline in the RZ, as suggested in Gough and McIntyre 1998) can by
  itself stop the inward burrowing of the differential rotation.

Title: Neural network to analyze rising magnetic flux ropes in
    M-dwarf stellar convective dynamo simulations
Authors: Bice, C. P.; Toomre, J.
Bibcode: 2021AAS...23820805B
Altcode:
  Despite the central role that rising magnetic flux ropes are thought
  to play in the formation of active regions on the surfaces of the
  Sun and other stars, global MHD simulations of stellar interiors have
  struggled to self-consistently capture their dynamics. By their nature,
  these structures tend to be short-lived or wholly absent in all but
  the most turbulent high-resolution convective dynamo simulations
  — environments which make their hand-identification and study
  prohibitively time-consuming. We present here an analysis of hundreds
  of self-consistent, rising flux ropes identified autonomously in
  global simulations of M-dwarf convective dynamos with the help of
  a novel machine-learning pipeline developed for the task. We report
  on the details of the neural network models employed, as well as the
  variation of flux rope formation rates, locations, and trajectories
  across differing stellar parameters.

Title: Building and Maintaining a Solar Tachocline through Convective
    Dynamo Action
Authors: Matilsky, Loren I.; Toomre, Juri
Bibcode: 2021arXiv210505412M
Altcode:
  For more than thirty years, the dynamical maintenance of the thin
  solar tachocline has remained one of the central outstanding problems
  of stellar astrophysics. Three main theories have been developed to
  explain the tachocline's thinness, but so far none of them has been
  shown to work convincingly in the extreme parameter regime of the solar
  interior. Here, we present a rotating, 3D, spherical-shell simulation of
  a combined solar-like convection zone and radiative zone that achieves
  a tachocline built and maintained by convective dynamo action. Because
  of numerical constraints, the dynamo prevents the viscous spread of the
  tachocline instead of the Eddington-Sweet-time-scale radiative spread
  believed to occur in the Sun. Nonetheless, our simulation supports
  the scenario of tachocline confinement via the cyclic solar dynamo,
  and is the first time one of the main confinement scenarios has been
  realized in a global, 3D, spherical-shell geometry including nonlinear
  fluid motions and a self-consistently generated dynamo.

Title: Machine Learning analysis of self-consistent magnetic flux
    ropes realized in M-dwarf dynamo simulations
Authors: Bice, Connor P.; Toomre, Juri
Bibcode: 2021csss.confE.300B
Altcode:
  The dynamical origins of the intense magnetic activity exhibited
  by most M-dwarf stars remains an unanswered question in stellar
  astrophysics. Despite the central role magnetic flux ropes are
  thought to play in the formation of sun and star spots, global MHD
  simulations of stellar interiors have historically struggled to
  self-consistently capture their dynamics. By their nature, these
  structures tend to be short-lived or wholly absent in all but the
  most turbulent high-resolution simulations -- environments which make
  their hand-identification and study prohibitively time-consuming. We
  present here a novel machine learning approach for the identification
  and dynamical analysis of the hundreds of self-consistent, rising flux
  ropes in our simulations of M-dwarf interiors. We report on the details
  of the models developed, as well as the prospects for their continued
  use with not only our own simulations, but those of the entire stellar
  convection community.

Title: Machine Learning Analysis of Self-Consistent Magnetic Flux
    Ropes Realized In M-Dwarf Dynamo Simulations
Authors: Bice, Connor; Toomre, Juri
Bibcode: 2021csss.confE.327B
Altcode:
  The dynamical origins of the intense magnetic activity exhibited
  by most M-dwarf stars must be tied to their internal convective
  dynamos, and yet there remain many unanswered questions concerning
  its details. Despite the central role magnetic flux ropes are thought
  to play in the formation of solar and stellar starspots, global
  MHD simulations of stellar interiors have historically struggled
  to self-consistently capture their dynamics. By their nature, these
  structures tend to be short-lived or wholly absent in all but the most
  turbulent high-resolution simulations -- environments which make their
  hand-identification and study prohibitively time-consuming. We present
  here a novel machine-learning pipeline for the autonomous identification
  and analysis of self-consistent, rising flux ropes found in our global
  3D MHD simulations of M-dwarf convective interiors. We report on the
  details of the models developed, as well as early results from the
  project and its prospects moving forward.

Title: Building and maintaining a solar tachocline through convective
    dynamo action
Authors: Matilsky, Loren Isaac; Toomre, Juri
Bibcode: 2021csss.confE.331M
Altcode:
  For more than thirty years, the dynamical maintenance of the thin
  solar tachocline has remained one of the central outstanding problems
  of stellar astrophysics. Three main theories have been developed to
  explain the tachocline's thinness, but so far none of them has been
  shown to work convincingly in the extreme parameter regime of the solar
  interior. Here, we present a rotating, 3D, spherical-shell simulation of
  a combined solar-like convection zone and radiative zone that achieves
  a tachocline built and maintained by convective dynamo action. Because
  of numerical constraints, the dynamo prevents the viscous spread of the
  tachocline instead of the Eddington-Sweet-time-scale radiative spread
  believed to occur in the Sun. Nonetheless, our simulation supports
  the scenario of tachocline confinement via the cyclic solar dynamo,
  and is the first time one of the main confinement scenarios has been
  realized in a global, 3D, spherical-shell geometry including nonlinear
  fluid motions and a self-consistently generated dynamo.

Title: Revisiting the Sun's Strong Differential Rotation along
    Radial Lines
Authors: Matilsky, Loren I.; Hindman, Bradley W.; Toomre, Juri
Bibcode: 2020ApJ...898..111M
Altcode: 2020arXiv200400208M
  Current state-of-the-art models of the solar convection zone consist
  of solutions to the Navier-Stokes equations in rotating, 3D spherical
  shells. Such models are highly sensitive to the choice of boundary
  conditions. Here we present two suites of simulations differing only in
  their outer thermal boundary condition, which is either one of fixed
  entropy (FE) or fixed flux (FF; corresponding to a fixed gradient
  in the entropy). We find that the resulting differential rotation is
  markedly different between the two sets. The FF simulations have strong
  differential rotation contrast and isocontours tilted along radial
  lines (in good agreement with the Sun's interior rotation revealed by
  helioseismology), whereas the FE simulations have weaker contrast and
  contours tilted in the opposite sense. We examine in detail the force
  balances in our models and find that the poleward transport of heat
  by Busse columns drives a thermal wind responsible for the different
  rotation profiles. We conclude that the Sun's strong differential
  rotation along radial lines may result from the solar emissivity being
  invariant with latitude (which is similar to the FF condition in our
  models) and the poleward transport of heat by Busse columns. In future
  work on convection in the solar context, we strongly advise modelers
  to use an FF outer boundary condition.

Title: Exploring Bistability in the Cycles of the Solar Dynamo
    through Global Simulations
Authors: Matilsky, Loren I.; Toomre, Juri
Bibcode: 2020ApJ...892..106M
Altcode: 2019arXiv191208158M
  The calling card of solar magnetism is the sunspot cycle, during which
  sunspots regularly reverse their polarity sense every 11 yr. However,
  a number of more complicated time-dependent behaviors have also been
  identified. In particular, there are temporal modulations associated
  with active longitudes and hemispheric asymmetry, when sunspots appear
  at certain solar longitudes or else in one hemisphere preferentially. So
  far, a direct link between this asymmetric temporal behavior and the
  underlying solar dynamo has remained elusive. In this work, we present
  results from global 3D magnetohydrodynamic simulations, which display
  both behavior reminiscent of the sunspot cycle (regular polarity
  reversals and equatorward migration of internal magnetic field) and
  asymmetric, irregular behavior which we interpret as active longitudes
  and hemispheric asymmetry in the simulations. The simulations are
  thus bistable, in that the turbulent convection can stably support two
  distinct flavors of magnetism at different times, in superposition or
  with smooth transitions from one state to the other. We discuss this new
  family of dynamo models in the context of the extensive observations
  of the Sun's surface magnetic field with the Solar and Heliospheric
  Observatory and the Solar Dynamics Observatory, as well as earlier
  observations of sunspot number and synoptic maps. We suggest that the
  solar dynamo itself may be bistable in nature, exhibiting two types
  of temporal behavior in the magnetic field.

Title: Probing the Influence of a Tachocline in Simulated M-dwarf
    Dynamos
Authors: Bice, C. P.; Toomre, J.
Bibcode: 2020ApJ...893..107B
Altcode: 2020arXiv200105555B
  M-type stars are among the best candidates in searches for habitable
  Earth-like exoplanets, and yet many M-dwarfs exhibit extraordinary
  flaring that would bombard otherwise habitable planets with ionizing
  radiation. Observers have found that the fraction of M-stars
  demonstrating significant activity transitions from roughly 10% for
  main-sequence stars more massive than 0.35 M<SUB>⊙</SUB> to nearly
  90% for less massive stars. The latter are typically rotating quite
  rapidly, suggesting differing spin-down histories. It is also below
  0.35 M<SUB>⊙</SUB> when main-sequence stars become fully convective
  and may no longer contain a tachocline. We turn here to the more
  massive M-stars to study the impact such a layer may have on their
  internal dynamics. Using the global MHD code Rayleigh, we compare the
  properties of convective dynamos generated within rapidly rotating 0.4
  M<SUB>⊙</SUB> stars, with the computational domain either terminating
  at the base of the convection zone or permitting overshoot into the
  underlying stable region. We find that a tachocline is not necessary
  for the organization of strong toroidal wreaths of magnetism in these
  stars, though it can increase the coupling of mean field amplitudes to
  the stellar rotation rate. Additionally, we note that the presence of a
  tachocline tends to make magnetic cycles more regular than they would
  otherwise have been, and can permit alternative field configurations
  with much longer cycles. Finally, we find that the tachocline helps
  enhance the emergent fields and organize them into larger spatial
  scales, providing favorable conditions for more rapid spin-down via
  the stellar wind.

Title: Dynamo States with Strikingly Different Symmetries Coexisting
    in Global Solar Simulations
Authors: Matilsky, Loren I.; Toomre, Juri
Bibcode: 2020ASSP...57..197M
Altcode:
  We present new global 3D MHD simulations of the solar convection
  zone that exhibit two distinct states of the dynamo coexisting
  simultaneously. We discuss our results in terms of the solar active
  longitudes and hemispheric asymmetry.

Title: Touching the Interior Structure and Dynamics of Our Nearest
    Star
Authors: Toomre, Juri
Bibcode: 2020ASSP...57...37T
Altcode:
  Michael Thompson has had a pivotal and continuing role in developing
  and refining inversion techniques to be applied to the great blossoming
  of helioseismic data forthcoming from the GONG, MDI (on SOHO) and HMI
  (on SDO) observational projects. This has enabled major discoveries
  about the internal differential rotation of the Sun, revealing
  both a tachocline of shear at the base of its convection zone and
  a near-surface shear layer near its surface, and of its temporal
  variations. It has also guided efforts to map subsurface flows of many
  scales in the convection zone. In parallel with his abiding interests
  in helioseismology, Michael was very enthusiastic about recent efforts
  in solar convection and dynamo theory to address what he saw as the
  outstanding questions about the dynamics proceeding deep within our
  nearest star, and thus we touch briefly upon some of these here.

Title: Exploring the Origins of Intense Magnetism in Early M-Dwarf
    Stars
Authors: Bice, Connor; Toomre, Juri
Bibcode: 2020ASSP...57..285B
Altcode:
  We present the results of new global 3D MHD simulations of early M-Dwarf
  stars, exploring the influence that a tachocline of shear has on their
  instantaneous and long-term magnetic activity.

Title: Probing the Origins of Intense Magnetism in Early M-Dwarf Stars
Authors: Bice, Connor; Toomre, Juri
Bibcode: 2019AAS...23412203B
Altcode:
  M-type stars are quickly stepping into the forefront as some of the
  best candidates in searches for habitable Earth-like exoplanets, and
  yet many M-dwarfs exhibit extraordinary flaring events which would
  bombard otherwise habitable planets with ionizing radiation. In
  recent years, observers have found that the fraction of M-stars
  demonstrating significant magnetic activity transitions sharply from
  roughly 10% for main-sequence stars earlier (more massive) than
  spectral type M3.5 (0.35 M<SUB>⊙</SUB>) to nearly 90% for stars
  later than M3.5. Stellar dynamos are are driven primarily by fluid
  motions in the convection zone, the base of which migrates inward with
  decreasing stellar mass. Suggestively, it is also later than M3.5 at
  which main-sequence stars become fully convective, and may no longer
  contain a tachocline. This layer of rotational shear separating the
  convection and radiative zones is thought to play a significant role
  in solar magnetism, and so we here investigate its influence on M-dwarf
  dynamos. Using the spherical 3D MHD simulation code Rayleigh, we compare
  the convective flows, magnetic field configurations and generation,
  and time dependencies of dynamos operating within quickly rotating
  M2 (0.4 M<SUB>⊙</SUB>) stars spanning a range of rotation rates
  and diffusivities, with the computational domain either terminating
  at the base of the convection zone or permitting overshoot into the
  underlying stable region. We find that a tachocline is not necessary for
  the organization of strong (10-20 kG) toroidal wreaths of magnetism in
  these stars, though its presence can increase the coupling of mean field
  amplitudes to the stellar rotation rate and in some cases drastically
  alter the character of the fields produced. Additionally, in stars
  that undergo periodic magnetic cycles, we find that the presence of a
  tachocline makes these cycles both longer and more regular than they
  would have otherwise been. Finally, we find that the tachocline helps
  to enhance the surface poloidal fields and organize them into larger
  spatial scales, both of which provide favorable conditions for more
  rapid angular momentum loss through a magnetized stellar wind.

Title: The Relationship Between Differential Rotation and Constant
    Effective Temperature in the Sun
Authors: Matilsky, Loren; Hindman, Bradley W.; Toomre, Juri
Bibcode: 2019AAS...23431806M
Altcode:
  Helioseismology has shown that the rotation rate of the solar
  interior is constant along radial lines (conical rotation contours)
  and has a mostly uniform gradient from equator to pole, facts which
  are still not completely understood. Conical rotation contours and
  uniform rotation gradients have been reproduced in previous global,
  3D, hydrodynamic simulations of the solar convective envelope by
  imposing a small temperature gradient at the base of the convective
  layer, consistent with thermal wind balance in the tachocline. Here
  we show that similar results can be obtained in global simulations
  by demanding that the conductive flux through the outer boundary of
  the convective layer (corresponding physically to the solar effective
  temperature) be constant with latitude. For the Sun, this is in line
  with observations that show no significant dependence of the effective
  temperature with latitude. By contrast, if instead the entropy at
  the outer boundary is fixed (keeping all other simulation parameters
  constant), the outward conductive flux is allowed to vary with latitude
  and a markedly different rotation profile emerges, namely one that has
  cylindrical contours and strong rotation gradients confined mainly to
  low latitudes. We discuss in detail how the outer boundary condition
  on the entropy (fixed flux vs. fixed entropy) affects the dynamics
  responsible for the differential rotation achieved in our simulations.

Title: Exploring the Coexistence of Two Distinct Dynamo States in
    the Sun through Global Simulations
Authors: Matilsky, Loren; Toomre, Juri
Bibcode: 2019AAS...23431803M
Altcode:
  The origin of the Sun's magnetism remains one of the most pressing
  outstanding problems in solar physics. The number of sunspots
  (eruptions of magnetic flux through the photosphere) rises and falls
  over a regular 11-year cycle. Within each cycle, the sunspots emerge
  at mid-latitudes near solar maximum and then closer to the equator
  as the cycle progresses. Furthermore, the polarity sense of sunspot
  pairs is opposite in the Northern hemisphere compared to the Southern
  hemisphere, and this polarity sense flips from one 11-year cycle to the
  next. Recently, 3D, global, MHD dynamo simulations have made substantial
  contact with observations, yielding regular cycling, polarity reversals,
  and in a few cases, equatorward propagation of interior magnetic
  field. Here we present a new class of 3D, global simulations of a
  solar convection zone that remarkably achieve two distinct states
  of the dynamo coexisting simultaneously. One state consists of two
  opposite-polarity reservoirs of magnetism in each hemisphere that cycle,
  flip polarity, and exhibit equatorward propagation, in remarkable
  agreement with the observed solar cycle. Superimposed is another
  state, asymmetric about the equator, that consists of one reservoir of
  strong toroidal field in a single hemisphere that flips polarity and
  migrates poleward with the cycle, in agreement with many other dynamo
  simulations. We describe theoretically how our simulated dynamos might
  be achieved and whether such processes could be at work in the solar
  dynamo. We also investigate the possible observable signatures of two
  distinct dynamo states if they were present in the solar interior.

Title: Some travels in the land of nonlinear convection and magnetism
Authors: Toomre, J.
Bibcode: 2019EAS....82..273T
Altcode:
  Rotating stars with convection zones are the great builders of magnetism
  in our universe. Seeking to understand how turbulent convection actually
  operates, and so too the dynamo action that it can achieve, has advanced
  through distinctive stages in which Jean-Paul Zahn was often a central
  player, or joined by his former students. Some of the opening steps in
  dealing with the basic nonlinearity in such dynamics involved modal
  equations (with specified horizontal structure) to study convective
  amplitudes and heat transports achieved as solutions equilibrated by
  feeding back on the mean stratification. These dealt in turn with
  laboratory convection, with penetrative convection in Boussinesq
  settings, then with compressible penetration via anelastic equations in
  simple geometries, and finally with stellar penetrative convection in
  A-type stars that coupled two convection zones. Advances in computation
  power allowed 2-D fully compressible simulations, and then 3-D modeling
  including rotation, to revisit some of these convection and penetration
  settings within planar layers. With externally imposed magnetic fields
  threading the 2-D layers, magnetoconvection could then be studied to
  see how the flows concentrated the fields into complex sheets, or how
  new classes of traveling waves could result. The era of considering
  turbulent convection in rotating spherical shells had also arrived,
  using 3-D MHD codes such as ASH to evaluate how the solar differential
  rotation is achieved and maintained. Similarly the manner in which
  global magnetic fields could be built by dynamo action within the solar
  convection zone took center stage, finding that coherent wreaths of
  strong magnetism could be built, and also cycling solutions with field
  reversals. The coupling of convection and magnetism continues as a
  vibrant research subject. It is also clear that stars like the Sun do
  not give up their dynamical mysteries readily when highly turbulent
  systems are at play.

Title: Rossby and Magnetic Prandtl Number Scaling of Stellar Dynamos
Authors: Augustson, K. C.; Brun, A. S.; Toomre, J.
Bibcode: 2019ApJ...876...83A
Altcode:
  Rotational scaling relationships are examined for the degree of
  equipartition between magnetic and kinetic energies in stellar
  convection zones. These scaling relationships are approached from two
  paradigms, with first a glance at scaling relationship built on an
  energy-balance argument and second a look at a force-based scaling. The
  latter implies a transition between a nearly constant inertial scaling
  when in the asymptotic limit of minimal diffusion and magnetostrophy,
  whereas the former implies a weaker scaling with convective Rossby
  number. Both scaling relationships are then compared to a suite of 3D
  convective dynamo simulations with a wide variety of domain geometries,
  stratifications, and range of convective Rossby numbers.

Title: Rossby and Magnetic Prandtl Number Scaling of Stellar Dynamos
Authors: ~C. Augustson, K.; ~S. Brun, A.; Toomre, J.
Bibcode: 2019arXiv190400225C
Altcode:
  Rotational scaling relationships are examined for the degree of
  equipartition between magnetic and kinetic energies in stellar
  convection zones. These scaling relationships are approached from two
  paradigms, with first a glance at scaling relationship built upon an
  energy-balance argument and second a look at a force-based scaling. The
  latter implies a transition between a nearly-constant inertial scaling
  when in the asymptotic limit of minimal diffusion and magnetostrophy,
  whereas the former implies a weaker scaling with convective Rossby
  number. Both scaling relationships are then compared to a suite of 3D
  convective dynamo simulations with a wide variety of domain geometries,
  stratifications, and range of convective Rossby numbers.

Title: The Role of Downflows in Establishing Solar Near-surface Shear
Authors: Matilsky, Loren I.; Hindman, Bradley W.; Toomre, Juri
Bibcode: 2019ApJ...871..217M
Altcode: 2018arXiv181000115M
  The dynamical origins of the Sun’s tachocline and near-surface
  shear layer (NSSL) are still not well understood. We have attempted
  to self-consistently reproduce an NSSL in numerical simulations of a
  solar-like convection zone by increasing the density contrast across
  rotating 3D spherical shells. We explore the hypothesis that high
  density contrast leads to near-surface shear by creating a rotationally
  unconstrained layer of fast flows near the outer surface. Although
  our high-contrast models do have near-surface shear, it is confined
  primarily to low latitudes (between ±15°). Two distinct types of flow
  structures maintain the shear dynamically: rotationally constrained
  Busse columns aligned with the rotation axis and fast, rotationally
  unconstrained downflow plumes that deplete angular momentum from
  the outer fluid layers. The plumes form at all latitudes and, in
  fact, are more efficient at transporting angular momentum inward at
  high latitudes. The presence of Busse columns at low latitudes thus
  appears essential to creating near-surface shear in our models. We
  conclude that a solar-like NSSL is unobtainable from a rotationally
  unconstrained outer fluid layer alone. In numerical models, the shear is
  eliminated through the advection of angular momentum by the meridional
  circulation. Therefore, a detailed understanding of how the solar
  meridional circulation is dynamically achieved will be necessary to
  elucidate the origin of the Sun’s NSSL.

Title: Exploring the Role of a Tachocline in M-Dwarf Magnetism
Authors: Bice, Connor; Toomre, Juri
Bibcode: 2018csss.confE..27B
Altcode: 2018arXiv180902238B
  M-type stars are quickly stepping into the forefront as some of the
  best candidates in searches for habitable Earth-like exoplanets, and
  yet many M-dwarfs exhibit extraordinary flaring events which would
  bombard otherwise habitable planets with ionizing radiation. In recent
  years, observers have found that the fraction of M-stars demonstrating
  significant magnetic activity transitions sharply from roughly 10%
  for main-sequence stars earlier (more massive) than spectral type M3.5
  (0.35 M_⊙) to nearly 90% for stars later than M3.5. Suggestively,
  it is also later than M3.5 at which main-sequence stars become
  fully convective, and may no longer contain a tachocline. Using the
  spherical 3D MHD simulation code Rayleigh, we compare the peak field
  strengths, topologies, and time dependencies of convective dynamos
  generated within a quickly rotating (2 Omega_⊙) M2 (0.4 M_⊙) star,
  with the computational domain either terminating at the base of the
  convection zone or including the tachocline. We find that while both
  models generate strong (∼10kG), wreathlike toroidal fields exhibiting
  polarity reversals, the tachocline model provided a further reservoir
  for the toroidal field, which slowed the average reversal period from
  100 rotations to more than 220 rotations and increased the spectral
  power of the low-order modes of the near-surface radial field by a
  factor of 4.

Title: Exploring the Influence of Density Contrast on Solar
    Near-Surface Shear
Authors: Matilsky, Loren I.; Hindman, Bradley W.; Toomre, Juri
Bibcode: 2018csss.confE..49M
Altcode: 2018arXiv181100665M
  The advent of helioseismology has determined in detail the average
  rotation rate of the Sun as a function of radius and latitude. These
  data immediately reveal two striking boundary layers of shear in
  the solar convection zone (CZ): a tachocline at the base, where the
  differential rotation of the CZ transitions to solid-body rotation in
  the radiative zone, and a 35-Mm-thick near-surface shear layer (NSSL)
  at the top, where the rotation rate slows by about 5% with increasing
  radius. Though asteroseismology cannot probe the differential rotation
  of distant stars to the same level of detail that helioseismology
  can achieve for the Sun, it is possible that many cool stars with
  outer convective envelopes possess similar differential rotation
  characteristics, including both a tachocline and a NSSL. Here we present
  the results of 3D global hydrodynamic simulations of spherical-shell
  convection for a Sun-like star at different levels of density contrast
  across the shell. The simulations with high stratification possess
  characteristics of near-surface shear, especially at low latitudes. We
  discuss in detail the dynamical balance of torques giving rise to the
  NSSL in our models and interpret what these balances imply for the
  real Sun. We further discuss the dynamical causes that may serve to
  wipe out near-surface shear at high latitudes, and conclude by offering
  some theories as to how this problem might be tackled in future work.

Title: Driving Solar Giant Cells through the Self-organization of
    Near-surface Plumes
Authors: Nelson, Nicholas J.; Featherstone, Nicholas A.; Miesch,
   Mark S.; Toomre, Juri
Bibcode: 2018ApJ...859..117N
Altcode: 2018arXiv180401166N
  Global 3D simulations of solar giant-cell convection have provided
  significant insight into the processes which yield the Sun’s observed
  differential rotation and cyclic dynamo action. However, as we move
  to higher-resolution simulations a variety of codes have encountered
  what has been termed the convection conundrum. As these simulations
  increase in resolution and hence the level of turbulence achieved,
  they tend to produce weak or even anti-solar differential rotation
  patterns associated with a weak rotational influence (high Rossby
  number) due to large convective velocities. One potential culprit for
  this convection conundrum is the upper boundary condition applied in
  most simulations, which is generally impenetrable. Here we present
  an alternative stochastic plume boundary condition which imposes
  small-scale convective plumes designed to mimic near-surface convective
  downflows, thus allowing convection to carry the majority of the outward
  solar energy flux up to and through our simulated upper boundary. The
  use of a plume boundary condition leads to significant changes in
  the convective driving realized in the simulated domain and thus to
  the convective energy transport, the dominant scale of the convective
  enthalpy flux, and the relative strength of the strongest downflows, the
  downflow network, and the convective upflows. These changes are present
  even far from the upper boundary layer. Additionally, we demonstrate
  that, in spite of significant changes, giant cell morphology in the
  convective patterns is still achieved with self-organization of the
  imposed boundary plumes into downflow lanes, cellular patterns, and
  even rotationally aligned banana cells in equatorial regions. This
  plume boundary presents an alternative pathway for 3D global convection
  simulations where driving is non-local and may provide a new approach
  toward addressing the convection conundrum.

Title: The Role of Rotation in Convective Heat Transport: an
    Application to Low-Mass Stars
Authors: Matilsky, Loren; Hindman, Bradley W.; Toomre, Juri;
   Featherstone, Nicholas
Bibcode: 2018AAS...23230603M
Altcode:
  It is often supposed that the convection zones (CZs) of low-mass stars
  are purely adiabatically stratified. This is thought to be because
  convective motions are extremely efficient at homogenizing entropy
  within the CZ. For a purely adiabatic fluid layer, only very small
  temperature variations are required to drive convection, making the
  amplitude and overall character of the convection highly sensitive
  to the degree of adiabaticity established in the CZ. The presence
  of rotation, however, fundamentally changes the dynamics of the CZ;
  the strong downflow plumes that are required to homogenize entropy
  are unable to penetrate through the entire fluid layer if they are
  deflected too soon by the Coriolis force. This talk discusses 3D
  global models of spherical-shell convection subject to different
  rotation rates. The simulation results emphasize the possibility
  that for stars with a high enough rotation rate, large fractions of
  their CZs are not in fact adiabatically stratified; rather, there is a
  finite superadiabatic gradient that varies in magnitude with radius,
  being at a minimum in the CZ’s middle layers. Two consequences of
  the varying superadiabatic gradient are that the convective amplitudes
  at the largest length scales are effectively suppressed and that there
  is a strong latitudinal temperature gradient from a cold equator to a
  hot pole, which self-consistently drives a thermal wind. A connection
  is naturally drawn to the Sun’s CZ, which has supergranulation
  as an upper limit to its convective length scales and isorotational
  contours along radial lines, which can be explained by the presence
  of a thermal wind.

Title: Dynamo Scaling Relationships
Authors: Augustson, Kyle; Mathis, Stéphane; Brun, Sacha; Toomre, Juri
Bibcode: 2017IAUS..329..233A
Altcode: 2017arXiv170204227A
  This paper provides a brief look at dynamo scaling relationships for
  the degree of equipartition between magnetic and kinetic energies. Two
  simple models are examined, where one that assumes magnetostrophy
  and another that includes the effects of inertia. These models are
  then compared to a suite of convective dynamo simulations of the
  convective core of a main-sequence B-type star and applied to its
  later evolutionary stages.

Title: On Differential Rotation and Overshooting in Solar-like Stars
Authors: Brun, Allan Sacha; Strugarek, Antoine; Varela, Jacobo; Matt,
   Sean P.; Augustson, Kyle C.; Emeriau, Constance; DoCao, Olivier Long;
   Brown, Benjamin; Toomre, Juri
Bibcode: 2017ApJ...836..192B
Altcode: 2017arXiv170206598B
  We seek to characterize how the change of global rotation rate
  influences the overall dynamics and large-scale flows arising in the
  convective envelopes of stars covering stellar spectral types from
  early G to late K. We do so through numerical simulations with the
  ASH code, where we consider stellar convective envelopes coupled to
  a radiative interior with various global properties. As solar-like
  stars spin down over the course of their main sequence evolution,
  such a change must have a direct impact on their dynamics and rotation
  state. We indeed find that three main states of rotation may exist for
  a given star: anti-solar-like (fast poles, slow equator), solar-like
  (fast equator, slow poles), or a cylindrical rotation profile. Under
  increasingly strict rotational constraints, the last profile can
  further evolve into a Jupiter-like profile, with alternating prograde
  and retrograde zonal jets. We have further assessed how far the
  convection and meridional flows overshoot into the radiative zone
  and investigated the morphology of the established tachocline. Using
  simple mixing length arguments, we are able to construct a scaling of
  the fluid Rossby number {R}<SUB>{of</SUB>}=\tilde{ω }/2{{{Ω }}}<SUB>*
  </SUB>∼ \tilde{v}/2{{{Ω }}}<SUB>* </SUB>{R}<SUB>* </SUB>, which we
  calibrate based on our 3D ASH simulations. We can use this scaling to
  map the behavior of differential rotation versus the global parameters
  of stellar mass and rotation rate. Finally, we isolate a region on
  this map (R <SUB> of </SUB> ≳ 1.5-2) where we posit that stars with
  an anti-solar differential rotation may exist in order to encourage
  observers to hunt for such targets.

Title: Prospects and Challenges for Helioseismology
Authors: Toomre, J.; Thompson, M. J.
Bibcode: 2017hdsi.book....7T
Altcode:
  No abstract at ADS

Title: The Magnetic Furnace: Intense Core Dynamos in B Stars
Authors: Augustson, Kyle C.; Brun, Allan Sacha; Toomre, Juri
Bibcode: 2016ApJ...829...92A
Altcode: 2016arXiv160303659A
  The dynamo action achieved in the convective cores of main-sequence
  massive stars is explored here through three-dimensional (3D) global
  simulations of convective core dynamos operating within a young
  10 {M}<SUB>⊙ </SUB> B-type star, using the anelastic spherical
  harmonic code. These simulations capture the inner 65% of this star by
  radius, encompassing the convective nuclear-burning core (about 23%
  by radius) and a portion of the overlying radiative envelope. Eight
  rotation rates are considered, ranging from 0.05% to 16% of the surface
  breakup velocity, thereby capturing both convection that barely senses
  the effects of rotation and other situations in which the Coriolis
  forces are prominent. The vigorous dynamo action realized within all
  of these turbulent convective cores builds magnetic fields with peak
  strengths exceeding a megagauss, with the overall magnetic energy (ME)
  in the faster rotators reaching super-equipartition levels compared
  to the convective kinetic energy (KE). The core convection typically
  involves turbulent columnar velocity structures roughly aligned with
  the rotation axis, with magnetic fields threading through these rolls
  and possessing complex linkages throughout the core. The very strong
  fields are able to coexist with the flows without quenching them
  through Lorentz forces. The velocity and magnetic fields achieve such
  a state by being nearly co-aligned, and with peak magnetic islands
  being somewhat displaced from the fastest flows as the intricate
  evolution proceeds. As the rotation rate is increased, the primary
  force balance shifts from nonlinear advection balancing Lorentz forces
  to a magnetostrophic balance between Coriolis and Lorentz forces.

Title: Magnetoconvection
Authors: Toomre, Juri
Bibcode: 2016GApFD.110..458T
Altcode:
  No abstract at ADS

Title: The Magnetic Furnace: Examining Fully Convective Dynamos And
    The Influence Of Rotation
Authors: Augustson, Kyle; Mathis, S.; Brun, A. S.; Toomre, J.
Bibcode: 2016csss.confE..29A
Altcode:
  The dynamo action likely present within fully convective regions
  is explored through global-scale 3-D simulations. These simulations
  provide a contextual analog for the convective dynamos that are likely
  operating deep within the interiors of fully convective low mass
  stars. A logarithmic range of rotation rates is considered, thereby
  capturing both convection barely sensing the effects of rotation
  to others in which the Coriolis forces are prominent. The vigorous
  dynamo action realized within all of these turbulent convective cores
  builds magnetic fields with peak strengths exceeding a megagauss,
  with the overall magnetic energy (ME) in the faster rotators reaching
  super-equipartition levels compared to the convective kinetic energy
  (KE). Such strong fields are able to coexist with the flows without
  quenching them through Lorentz forces. This state is achieved due to
  the velocity and magnetic fields being nearly co-aligned, and with
  peak magnetic islands being somewhat displaced from the fastest flows
  as the intricate evolution of these MHD structures proceeds. As the
  rotation rate is increased, the primary force balance shifts from
  nonlinear advection balancing Lorentz forces to a magnetostrophic
  balance between Coriolis and Lorentz forces.

Title: Helioseismic Imaging of Supergranulation throughout the
    Sun’s Near-Surface Shear Layer
Authors: Greer, Benjamin J.; Hindman, Bradley W.; Toomre, Juri
Bibcode: 2016ApJ...824..128G
Altcode:
  We present measurements of the Sun’s sub-surface convective flows
  and provide evidence that the pattern of supergranulation is driven
  at the surface. The pattern subsequently descends slowly throughout
  the near-surface shear layer in a manner that is inconsistent with
  a 3D cellular structure. The flow measurements are obtained through
  the application of a new helioseismic technique based on traditional
  ring analysis. We measure the flow field over the course of eleven
  days and perform a correlation analysis between all possible pairs of
  depths and temporal separations. In congruence with previous studies,
  we find that the supergranulation pattern remains coherent at the
  surface for slightly less than two days and the instantaneous surface
  pattern is imprinted to a depth of 7 Mm. However, these correlation
  times and depths are deceptive. When we admit a potential time lag
  in the correlation, we find that peak correlation in the convective
  flows descends at a rate of 10-40 m s<SUP>-1</SUP> (or equivalently
  1-3 Mm per day). Furthermore, the correlation extends throughout all
  depths of the near-surface shear layer. This pattern-propagation rate
  is well matched by estimates of the speed of downflows obtained through
  the anelastic approximation. Direct integration of the measured speed
  indicates that the supergranulation pattern that first appears at the
  surface eventually reaches the bottom of the near-surface shear layer
  a month later. Thus, the downflows have a Rossby radius of deformation
  equal to the depth of the shear layer and we suggest that this equality
  may not be coincidental.

Title: Helioseismic Measurements of the Rossby Number in the Sun's
    Near-surface Shear Layer
Authors: Greer, Benjamin J.; Hindman, Bradley W.; Toomre, Juri
Bibcode: 2016ApJ...824....4G
Altcode:
  Through helioseismic measurement of the Sun’s subsurface flows, we
  assess the Rossby number associated with the convective motions. The
  helioseismic procedure is a new form of the ring-analysis technique
  that is capable of resolving supergranulation. The extremely fine
  spatial resolution is achieved by deconvolving the set of p-mode
  Doppler shifts measured separately within a multitude of densely
  overlapping analysis regions. We find that just below the photosphere,
  the Rossby number is large ({Ro}≈ 5) and the convective flows are
  only weakly influenced by rotation. Below a depth of 10 {Mm}, the flows
  become rotationally constrained and the concomitant Rossby number is
  small ({Ro}≈ 0.2). These results support the supposition that the
  near-surface shear layer is a transition region for the degree of
  rotational impact on convective motions.

Title: Global Solar Convective Dynamo with Cycles, Equatorward
    Propagation and Grand Minima
Authors: Toomre, Juri; Augustson, Kyle C.; Brun, Allan Sacha; Miesch,
   Mark S.
Bibcode: 2016SPD....47.1013T
Altcode:
  The 3-D MHD Anelastic Spherical Harmonic (ASH) code, using slope-limited
  diffusion, is used to study the interaction of turbulent convection,
  rotation and magnetism in a full spherical shell comparable to the solar
  convection zone. Here a star of one solar mass, with a solar luminosity,
  is considered that is rotating at three times the solar rate. The
  dynamo generated magnetic field forms large-scale toroidal wreaths,
  whose formation is tied to the low Rossby number of the convection in
  this simulation which we have labeled K3S. This case displays prominent
  polarity cycles with regular reversals occurring roughly every 6.2
  years. These reversals are linked to the weakened differential rotation
  and a resistive collapse of the large-scale magnetic field. Distinctive
  equatorial migration of the strong magnetic wreaths is seen, arising
  from modulation of the differential rotation rather than a dynamo
  wave. As the wreaths approach the equator, cross-equatorial magnetic
  flux is achieved that permits the low-latitude convection to generate
  poloidal magnetic field with opposite polarity. Poleward migration of
  such magnetic flux from the equator eventually leads to the reversal of
  the polarity of the high-latitude magnetic field. This K3S simulation
  also enters an interval with reduced magnetic energy at low latitudes
  lasting roughly 16 years (about 2.5 polarity cycles), during which the
  polarity cycles are disrupted and after which the dynamo recovers its
  regular polarity cycles. An analysis of this striking grand minimum
  reveals that it likely arises through the interplay of symmetric and
  antisymmetric dynamo families.

Title: Helioseismic Imaging of Supergranulation throughout the Sun's
    Near-Surface Shear Layer
Authors: Hindman, Bradley; Greer, Benjamin; Toomre, Juri
Bibcode: 2016SPD....4720304H
Altcode:
  We present measurements of the Sun's sub-surface convective flows
  and provide evidence that the pattern of supergranulation is driven
  at the surface. The pattern subsequently descends slowly throughout
  the near-surface shear layer in a manner that is inconsistent with
  a 3-D cellular structure. The flow measurements are obtained through
  the application of a new helioseismic technique based on traditional
  ring analysis. We measure the flow field over the course of eleven
  days and perform a correlation analysis between all possible pairs of
  depths and temporal separations. In congruence with previous studies,
  we find that the supergranulation pattern remains coherent at the
  surface for slightly less than two days and the instantaneous surface
  pattern is imprinted to a depth of 7 Mm. However, these correlation
  times and depths are deceptive. When we admit a potential time lag
  in the correlation, we find that peak correlation in the convective
  flows descends at a rate of 10 - 30 m s<SUP>-1</SUP> (or equivalently
  1 - 3 Mm per day). Furthermore, the correlation extends throughout
  all depths of the near-surface shear layer. This pattern-propagation
  rate is well matched by estimates of the speed of down flows obtained
  through the anelastic approximation. Direct integration of the measured
  speed indicates that the supergranulation pattern that first appears
  at the surface eventually reaches the bottom of the near-surface shear
  layer a month later. Thus, the transit time is roughly equal to a solar
  rotation period and we suggest this equality may not be coincidental.

Title: Tiny Stars, Strong Fields: Exploring the Origin of Intense
    Magnetism in M Stars
Authors: Toomre, Juri
Bibcode: 2016atp..prop...15T
Altcode:
  The M-type stars are becoming dominant targets in searches for
  Earth-like planets that could occupy their habitable zones. The
  low masses and luminosities of M-dwarf central stars make them
  very attractive for such exoplanetary hunts. The habitable zone
  of M dwarfs is close to the star due to their low luminosity. Thus
  possibly habitable planets will have short orbital periods, making
  their detection feasible both with the transit method (used by Kepler,
  K2 and soon with TESS) and with the radial velocity approaches. Yet
  habitability on a planet likely requires both solid surfaces and
  atmospheres, but also a favorable radiation environment. It is here
  that the M-dwarf central stars raise major theoretical puzzles, for
  many of them exhibit remarkably intense and frequent flaring, despite
  their modest intrinsic luminosities. The super-flares release their
  energy both in white light and in X-rays, and can be thousands of times
  brighter than the strongest solar flares. Such striking events must
  have magnetic origins, likely from fields built by convective dynamos
  operating in their interiors. Further, recent observations suggest that
  the surface of some M stars is carpeted with magnetic fields of 3 kG
  or more. Such field strengths are reminiscent of a sunspot, but here
  instead cover much of the stellar surface. With M stars now taking
  center stage in the search for Earthlike planets, it is crucial to
  begin to understand how convective dynamos may be able to build intense
  magnetic fields involved with super-flares and vast star spots, and how
  they depend upon the mass and rotation rate of these stars. We propose
  to use major 3-D MHD simulations with our Anelastic Spherical Harmonic
  (ASH) code to study the coupling of turbulent convection, rotation,
  and magnetism within full spherical domains such as the interior of
  an M dwarf. This permits the exploration of the magnetic dynamos that
  must be responsible for the evolving magnetism and intense activity
  of many M dwarfs. We bring to this our prior experience with studying
  dynamo processes in the outer convective envelopes of G- (the Sun)
  and Ftype stars, briefly of M dwarfs, and in full convective cores
  within more massive A- and B-type stars. Our previous work suggests
  that M dwarfs could display a broad range of dynamo behavior, from
  cyclic reversals to more chaotic variations, and further to both weak
  and strong dynamo states. We will focus on the latter, exploring how
  superequipartition magnetic fields could be achieved by dynamo action
  in M dwarfs, as are likely needed to energize super-flares and huge
  active regions, and what limits the peak field strengths. M-type
  stars are distinctive in becoming fully convective with decreasing
  mass at about M3.5 in spectral type (or about 0.35 solar masses). At
  this transition, a steep rise in the fraction of magnetically active
  stars is observed that is accompanied by an increasing rotational
  velocity. Clearly how mass-loss and spin-down can lead to this is of
  interest in itself. However, here we propose to study the manner in
  which dynamos operating in fully convective M dwarf interiors beyond
  the transition may be able to achieve very strong magnetic fields,
  and how field strengths and apparent magnetic activity increases
  with rotation rate as suggested by observations. We believe that
  global connectivity of flows and fields across the core center will
  admit new classes of strong behavior, as revealed by our B star core
  dynamos, not realized when a convective envelope is bounded below by a
  tachocline. These ideas need to be tested in a self-consistent manner
  with global ASH simulations to gain theoretical insights into what is
  the origin of the fierce magnetic activity in some of M dwarfs that
  may be potential hosts to Earth-like planets. Such 3-D MHD simulations,
  though challenging, are now feasible and would complement the intensive
  observational searches under way.

Title: Prospects and Challenges for Helioseismology
Authors: Toomre, J.; Thompson, M. J.
Bibcode: 2015SSRv..196....1T
Altcode: 2015SSRv..tmp...22T
  Helioseismology has advanced considerably our knowledge of the interior
  of the Sun over the past three decades. Our understanding of the Sun's
  internal structure, its dynamics, rotation, convection and magnetism,
  have all been advanced. Yet there are challenges, areas where the
  results from helioseismology are tantalizing but inconclusive, and
  aspects where the interpretation of the data has still to be put on
  a firm footing. In this paper we shall focus on a number of those
  challenges and give our assessment of where progress needs to be made
  in the next decade.

Title: Large-Eddy Simulations of Magnetohydrodynamic Turbulence in
    Heliophysics and Astrophysics
Authors: Miesch, Mark; Matthaeus, William; Brandenburg, Axel;
   Petrosyan, Arakel; Pouquet, Annick; Cambon, Claude; Jenko, Frank;
   Uzdensky, Dmitri; Stone, James; Tobias, Steve; Toomre, Juri; Velli,
   Marco
Bibcode: 2015SSRv..194...97M
Altcode: 2015arXiv150501808M; 2015SSRv..tmp...83M
  We live in an age in which high-performance computing is transforming
  the way we do science. Previously intractable problems are now becoming
  accessible by means of increasingly realistic numerical simulations. One
  of the most enduring and most challenging of these problems is
  turbulence. Yet, despite these advances, the extreme parameter regimes
  encountered in space physics and astrophysics (as in atmospheric and
  oceanic physics) still preclude direct numerical simulation. Numerical
  models must take a Large Eddy Simulation (LES) approach, explicitly
  computing only a fraction of the active dynamical scales. The success
  of such an approach hinges on how well the model can represent the
  subgrid-scales (SGS) that are not explicitly resolved. In addition
  to the parameter regime, heliophysical and astrophysical applications
  must also face an equally daunting challenge: magnetism. The presence
  of magnetic fields in a turbulent, electrically conducting fluid flow
  can dramatically alter the coupling between large and small scales,
  with potentially profound implications for LES/SGS modeling. In this
  review article, we summarize the state of the art in LES modeling of
  turbulent magnetohydrodynamic (MHD) flows. After discussing the nature
  of MHD turbulence and the small-scale processes that give rise to energy
  dissipation, plasma heating, and magnetic reconnection, we consider how
  these processes may best be captured within an LES/SGS framework. We
  then consider several specific applications in heliophysics and
  astrophysics, assessing triumphs, challenges, and future directions.

Title: Grand Minima and Equatorward Propagation in a Cycling Stellar
    Convective Dynamo
Authors: Augustson, Kyle; Brun, Allan Sacha; Miesch, Mark; Toomre, Juri
Bibcode: 2015ApJ...809..149A
Altcode: 2014arXiv1410.6547A
  The 3D MHD Anelastic Spherical Harmonic code, using slope-limited
  diffusion, is employed to capture convective and dynamo processes
  achieved in a global-scale stellar convection simulation for a
  model solar-mass star rotating at three times the solar rate. The
  dynamo-generated magnetic fields possesses many timescales, with
  a prominent polarity cycle occurring roughly every 6.2 years. The
  magnetic field forms large-scale toroidal wreaths, whose formation is
  tied to the low Rossby number of the convection in this simulation. The
  polarity reversals are linked to the weakened differential rotation and
  a resistive collapse of the large-scale magnetic field. An equatorial
  migration of the magnetic field is seen, which is due to the strong
  modulation of the differential rotation rather than a dynamo wave. A
  poleward migration of magnetic flux from the equator eventually leads to
  the reversal of the polarity of the high-latitude magnetic field. This
  simulation also enters an interval with reduced magnetic energy at
  low latitudes lasting roughly 16 years (about 2.5 polarity cycles),
  during which the polarity cycles are disrupted and after which the
  dynamo recovers its regular polarity cycles. An analysis of this grand
  minimum reveals that it likely arises through the interplay of symmetric
  and antisymmetric dynamo families. This intermittent dynamo state
  potentially results from the simulation’s relatively low magnetic
  Prandtl number. A mean-field-based analysis of this dynamo simulation
  demonstrates that it is of the α-Ω type. The timescales that appear
  to be relevant to the magnetic polarity reversal are also identified.

Title: Super-equipartition Convective Dynamo Action in the Cores of
    B-Type Stars
Authors: Augustson, Kyle C.; Brown, Benjamin P.; Brun, Allan Sacha;
   Toomre, Juri
Bibcode: 2015IAUGA..2258137A
Altcode:
  Observations have revealed the presence and topology of magnetic fields
  on the surfaces of some main sequence massive stars. These stars
  possess a convective core that supports strong dynamo action. This
  core is linked to the dynamics of the rest of the star through
  overshooting convection and magnetic fields and may influence
  the surface magnetism. Such effects are captured through 3-D MHD
  simulations of a 10 M<SUB>⊙</SUB> B-type star, using the anelastic
  spherical harmonic (ASH) code. These simulations capture the inner 65%
  of the star by radius, encompassing the convective core and an extensive
  portion of the radiative exterior. Vigorous dynamo action is achieved
  in the convective core with self-consistent super-equipartition (SE)
  states sustained over a range of rotation rates. Indeed, the ratio
  of magnetic to convective kinetic energy shows a distinct scaling
  with Elsasser and Coriolis number. The impact of this dynamo action
  upon the differential rotation of the core is assessed by contrasting
  hydrodynamic and magnetohydrodynamic simulations. The processes that
  permit the maintenance of such SE states are examined. We further
  study how the magnetic field generated during main-sequence dynamo
  action may carry over into later evolutionary stages.

Title: Super-equipartition Convective Dynamo Action in the Cores of
    B-Type Stars
Authors: Augustson, Kyle C.; Brown, Benjamin P.; Brun, Allan Sacha;
   Toomre, Juri
Bibcode: 2015IAUGA..2257925A
Altcode:
  Observations have revealed the presence and topology of magnetic fields
  on the surfaces of some main sequence massive stars. These stars
  possess a convective core that supports strong dynamo action. This
  core is linked to the dynamics of the rest of the star through
  overshooting convection and magnetic fields and may influence
  the surface magnetism. Such effects are captured through 3-D MHD
  simulations of a 10 M<SUB>⊙</SUB> B-type star, using the anelastic
  spherical harmonic (ASH) code. These simulations capture the inner 65%
  of the star by radius, encompassing the convective core and an extensive
  portion of the radiative exterior. Vigorous dynamo action is achieved
  in the convective core with self-consistent super-equipartition (SE)
  states sustained over a range of rotation rates. Indeed, the ratio
  of magnetic to convective kinetic energy shows a distinct scaling
  with Elsasser and Coriolis number. The impact of this dynamo action
  upon the differential rotation of the core is assessed by contrasting
  hydrodynamic and magnetohydrodynamic simulations. The processes that
  permit the maintenance of such SE states are examined. We further
  study how the magnetic field generated during main-sequence dynamo
  action may carry over into later evolutionary stages.

Title: Grand Minima and Equatorward Propagation in a Cycling Stellar
    Convective Dynamo
Authors: Augustson, Kyle C.; Brun, Allan Sacha; Miesch, Mark;
   Toomre, Juri
Bibcode: 2015IAUGA..2257912A
Altcode:
  The 3-D magnetohydrodynamic (MHD) Anelastic Spherical Harmonic (ASH)
  code, using slope-limited diffusion, is employed to capture convective
  and dynamo processes achieved in a global-scale stellar convection
  simulation for a model solar-mass star rotating at three times the solar
  rate. The dynamo generated magnetic fields possesses many time scales,
  with a prominent polarity cycle occurring roughly every 6.2 years. The
  magnetic field forms large-scale toroidal wreaths, whose formation is
  tied to the low Rossby number of the convection in this simulation. The
  polarity reversals are linked to the weakened differential rotation and
  a resistive collapse of the large-scale magnetic field. An equatorial
  migration of the magnetic field is seen, which is due to the strong
  modulation of the differential rotation rather than a dynamo wave. A
  poleward migration of magnetic flux from the equator eventually leads to
  the reversal of the polarity of the high-latitude magnetic field. This
  simulation also enters an interval with reduced magnetic energy at
  low latitudes lasting roughly 16 years (about 2.5 polarity cycles),
  during which the polarity cycles are disrupted and after which the
  dynamo recovers its regular polarity cycles. An analysis of this
  grand minimum reveals that it likely arises through the interplay of
  symmetric and antisymmetric dynamo families. This intermittent dynamo
  state potentially results from the simulations relatively low magnetic
  Prandtl number. A mean-field-based analysis of this dynamo simulation
  demonstrates that it is of the α-Ω type. The time scales that appear
  to be relevant to the magnetic polarity reversal are also identified.

Title: Grand Minima and Equatorward Propagation in a Cycling Stellar
    Convective Dynamo
Authors: Augustson, Kyle C.; Brun, Allan Sacha; Miesch, Mark;
   Toomre, Juri
Bibcode: 2015IAUGA..2258283A
Altcode:
  The 3-D magnetohydrodynamic (MHD) Anelastic Spherical Harmonic (ASH)
  code, using slope-limited diffusion, is employed to capture convective
  and dynamo processes achieved in a global-scale stellar convection
  simulation for a model solar-mass star rotating at three times the solar
  rate. The dynamo generated magnetic fields possesses many time scales,
  with a prominent polarity cycle occurring roughly every 6.2 years. The
  magnetic field forms large-scale toroidal wreaths, whose formation is
  tied to the low Rossby number of the convection in this simulation. The
  polarity reversals are linked to the weakened differential rotation and
  a resistive collapse of the large-scale magnetic field. An equatorial
  migration of the magnetic field is seen, which is due to the strong
  modulation of the differential rotation rather than a dynamo wave. A
  poleward migration of magnetic flux from the equator eventually leads to
  the reversal of the polarity of the high-latitude magnetic field. This
  simulation also enters an interval with reduced magnetic energy at
  low latitudes lasting roughly 16 years (about 2.5 polarity cycles),
  during which the polarity cycles are disrupted and after which the
  dynamo recovers its regular polarity cycles. An analysis of this
  grand minimum reveals that it likely arises through the interplay of
  symmetric and antisymmetric dynamo families. This intermittent dynamo
  state potentially results from the simulations relatively low magnetic
  Prandtl number. A mean-field-based analysis of this dynamo simulation
  demonstrates that it is of the α-Ω type. The time scales that appear
  to be relevant to the magnetic polarity reversal are also identified.

Title: Helioseismic Imaging of Fast Convective Flows throughout the
    Near-surface Shear Layer
Authors: Greer, Benjamin J.; Hindman, Bradley W.; Featherstone,
   Nicholas A.; Toomre, Juri
Bibcode: 2015ApJ...803L..17G
Altcode: 2015arXiv150400699G
  Using a new implementation of ring-diagram helioseismology,
  we ascertain the strength and spatial scale of convective flows
  throughout the near-surface shear layer. Our ring-diagram technique
  employs highly overlapped analysis regions and an efficient method
  of three-dimensional inversion to measure convective motions with a
  resolution that ranges from 3 Mm at the surface to 80 Mm at the base
  of the layer. We find the rms horizontal flow speed to peak at 427
  m s<SUP>-1</SUP> at the photosphere and fall to a minimum of 124 m
  s<SUP>-1</SUP> between 20 and 30 Mm. From the velocity amplitude and
  the dominant horizontal scales seen at each depth, we infer the level
  of rotational influence on convection to be low near the surface,
  but transition to a significant level at the base of the near-surface
  shear layer with a Rossby number varying between 2.2 to as low as 0.1.

Title: Convective Dynamo Simulation with a Grand Minimum
Authors: Augustson, Kyle C.; Brun, A. S.; Miesch, Mark; Toomre, Juri
Bibcode: 2015csss...18..451A
Altcode: 2015arXiv150304225A
  The global-scale dynamo action achieved in a simulation of a Sun-like
  star rotating at thrice the solar rate is assessed. The 3-D MHD
  Anelastic Spherical Harmonic (ASH) code, augmented with a viscosity
  minimization scheme, is employed to capture convection and dynamo
  processes in this G-type star. The simulation is carried out in a
  spherical shell that encompasses 3.8 density scale heights of the solar
  convection zone. It is found that dynamo action with a high degree of
  time variation occurs, with many periodic polarity reversals occurring
  roughly every 6.2 years. The magnetic energy also rises and falls with
  a regular period. The magnetic energy cycles arise from a Lorentz-force
  feedback on the differential rotation, whereas the processes leading
  to polarity reversals are more complex, appearing to arise from the
  interaction of convection with the mean toroidal fields. Moreover,
  an equatorial migration of toroidal field is found, which is linked
  to the changing differential rotation, and potentially to a nonlinear
  dynamo wave. This simulation also enters a grand minimum lasting roughly
  20 years, after which the dynamo recovers its regular polarity cycles.

Title: Measuring the Solar Meridional Circulation Using Local
    Helioseismology
Authors: Greer, B.; Hindman, B.; Toomre, J.
Bibcode: 2014AGUFMSH41B4143G
Altcode:
  The solar meridional circulation plays an important role in the
  transport of angular momentum and magnetic field throughout the
  convection zone and is a key component in setting the time-scale
  for the solar cycle in flux-transport dynamo models. The meridional
  flow is detectable with a variety of methods, including ring-diagram
  helioseismology. Many of these methods are plagued with systematic
  errors that have only recently been analyzed in detail. For
  ring-diagram analysis, the systematic errors introduce a signal that
  is easily confused with that of the meridional flow and is often of
  significant amplitude. Accurately determining the character of the solar
  meridional circulation requires careful attention to these errors. I use
  observations from the Helioseismic and Magnetic Imager (HMI) onboard the
  Solar Dynamics Observatory (SDO) to measure both the meridional flow and
  the associated systematics. I will present recent measurements of the
  solar meridional circulation with all known systematics accounted for.

Title: Multi-Ridge Fitting for Ring-Diagram Helioseismology
Authors: Greer, Benjamin J.; Hindman, Bradley W.; Toomre, Juri
Bibcode: 2014SoPh..289.2823G
Altcode: 2014arXiv1402.5166G; 2014SoPh..tmp...46G
  Inferences of subsurface flow velocities using local domain ring-diagram
  helioseismology depend on measuring the frequency shifts of oscillation
  modes seen in acoustic power spectra. Current methods for making
  these measurements use maximum-likelihood fitting techniques to
  match a model of modal power to the spectra. The model typically
  describes a single oscillation mode, and each mode in a given power
  spectrum is fit independently. We present a new method that produces
  measurements with higher reliability and accuracy by fitting multiple
  modes simultaneously. We demonstrate that this method permits measuring
  sub-surface flows deeper into the Sun while providing higher uniformity
  in data coverage and velocity response closer to the limb of the
  solar disk. While the previous fitting method performs better for some
  measurements of low phase-speed modes, we find this new method to be
  particularly useful for high phase-speed modes and small spatial areas.

Title: Towards a Unified Simulation of Convective Dynamo Action and
    Flux Emergence in the Sun
Authors: Nelson, Nicholas J.; Brown, Benjamin; Miesch, Mark S.;
   Toomre, Juri
Bibcode: 2014AAS...22421104N
Altcode:
  Our global 3D simulations of convection and dynamo action in a
  Sun-like star reveal that persistent wreaths of strong magnetism
  can be built within the bulk of the convention zone. Our recent
  simulations have achieved sufficiently high levels of turbulence to
  permit portions of these wreaths to become magnetically buoyant and
  rise through the simulated convective layer through a combination of
  magnetic buoyancy and advection by convective giant cells. Here we
  examine the characteristics of buoyant magnetic structures that are
  self-consistently created by dynamo action and turbulent convective
  motions. These buoyant loops originate within sections of the magnetic
  wreaths in which turbulent flows amplify the fields to much higher
  values than is possible through laminar processes. Examining many such
  loops over a simulated magnetic activity cycle, we measure statistical
  trends in the polarity, twist, and tilt of these loops that mimic
  Hale’s Law, Joy’s Law, and the hemispheric helicity rule observed in
  sunspots. We further show that these magnetic structures are primarily
  generated by non-axisymmetric turbulent amplification on timescales
  of about 15 days and not by the Ω-effect which primarily generates
  the large-scale wreaths.

Title: Buoyant Magnetic Loops Generated by Global Convective Dynamo
    Action
Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Sacha Brun, A.;
   Miesch, Mark S.; Toomre, Juri
Bibcode: 2014SoPh..289..441N
Altcode: 2012arXiv1212.5612N
  Our global 3D simulations of convection and dynamo action in a
  Sun-like star reveal that persistent wreaths of strong magnetism
  can be built within the bulk of the convention zone. Here we
  examine the characteristics of buoyant magnetic structures that are
  self-consistently created by dynamo action and turbulent convective
  motions in a simulation with solar stratification but rotating at three
  times the current solar rate. These buoyant loops originate within
  sections of the magnetic wreaths in which turbulent flows amplify
  the fields to much higher values than is possible through laminar
  processes. These amplified portions can rise through the convective
  layer by a combination of magnetic buoyancy and advection by convective
  giant cells, forming buoyant loops. We measure statistical trends
  in the polarity, twist, and tilt of these loops. Loops are shown to
  preferentially arise in longitudinal patches somewhat reminiscent of
  active longitudes in the Sun, although broader in extent. We show
  that the strength of the axisymmetric toroidal field is not a good
  predictor of the production rate for buoyant loops or the amount of
  magnetic flux in the loops that are produced.

Title: Center-to-Limb Velocity Systematic in Ring-Diagram Analysis
Authors: Greer, B.; Hindman, B.; Toomre, J.
Bibcode: 2013ASPC..478..199G
Altcode:
  We use HMI ring-diagram pipeline data to measure a center-to-limb
  systematic effect seen in velocities. To separate this signal from
  persistent flow patterns of physical origin, we perform a least-squares
  fit to the data for each wave mode. We fit a model that includes both
  the radially symmetric systematic as well as global zonal and meridional
  flow components. The resulting measurements of the systematic error
  reveal a smooth trend as a function of both mode frequency and phase
  speed. The systematic error at 45° from disk center ranges from 20
  m/s radially inward to 50 m/s radially outward. The implications for
  determining global scale meridional flow is discussed.

Title: Dynamo Action and Magnetic Cycles in F-type Stars
Authors: Augustson, Kyle C.; Brun, Allan Sacha; Toomre, Juri
Bibcode: 2013ApJ...777..153A
Altcode:
  Magnetic activity and differential rotation are commonly observed
  features on main-sequence F-type stars. We seek to make contact with
  such observations and to provide a self-consistent picture of how
  differential rotation and magnetic fields arise in the interiors
  of these stars. The three-dimensional magnetohydrodynamic anelastic
  spherical harmonic code is employed to simulate global-scale convection
  and dynamo processes in a 1.2 M <SUB>⊙</SUB> F-type star at two
  rotation rates. The simulations are carried out in spherical shells
  that encompass most of the convection zone and a portion of the stably
  stratified radiative zone below it, allowing us to explore the effects
  a stable zone has upon the morphology of the global-scale magnetic
  fields. We find that dynamo action with a high degree of time variation
  occurs in the star rotating more rapidly at 20 Ω<SUB>⊙</SUB>, with
  the polarity of the mean field reversing on a timescale of about 1600
  days. Between reversals, the magnetic energy rises and falls with a
  fairly regular period, with three magnetic energy cycles required to
  complete a reversal. The magnetic energy cycles and polarity reversals
  arise due to a linking of the polar-slip instability in the stable
  region and dynamo action present in the convection zone. For the more
  slowly rotating case (10 Ω<SUB>⊙</SUB>), persistent wreaths of
  magnetism are established and maintained by dynamo action. Compared
  to their hydrodynamic progenitors, the dynamo states here involve a
  marked reduction in the exhibited latitudinal differential rotation,
  which also vary during the course of a cycle.

Title: Cycling Dynamo in a Young Sun: Grand Minima and Equatorward
    Propagation
Authors: Augustson, Kyle; Brun, Allan Sacha; Miesch, Mark Steven;
   Toomre, Juri
Bibcode: 2013arXiv1310.8417A
Altcode:
  We assess the global-scale dynamo action achieved in a simulation of
  a sun-like star rotating at three times the solar rate. The 3-D MHD
  Anelastic Spherical Harmonic code, using slope-limited diffusion,
  is employed to capture convection and dynamo processes in such a
  young sun. The simulation is carried out in a spherical shell that
  encompasses 3.8 density scale heights of the solar convection zone. We
  find that dynamo action with a high degree of time variation occurs,
  with many periodic polarity reversals every 6.2 years. The magnetic
  energy also rises and falls with a regular period, with two magnetic
  energy cycles required to complete a polarity cycle. These magnetic
  energy cycles arise from a Lorentz-force feedback on the differential
  rotation, whereas the polarity reversals are present due to the
  spatial separation of the equatorial and polar dynamos. Moreover,
  an equatorial migration of toroidal field is found, which is linked
  to the changing differential rotation and to a near-surface shear
  layer. This simulation also enters a grand minimum lasting roughly 20
  years, after which the dynamo recovers its regular polarity cycles.

Title: Magnetic Wreaths and Cycles in Convective Dynamos
Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Brun, Allan Sacha;
   Miesch, Mark S.; Toomre, Juri
Bibcode: 2013ApJ...762...73N
Altcode: 2012arXiv1211.3129N
  Solar-type stars exhibit a rich variety of magnetic activity. Seeking
  to explore the convective origins of this activity, we have carried out
  a series of global three-dimensional magnetohydrodynamic simulations
  with the anelastic spherical harmonic code. Here we report on the
  dynamo mechanisms achieved as the effects of artificial diffusion are
  systematically decreased. The simulations are carried out at a nominal
  rotation rate of three times the solar value (3 Ω<SUB>⊙</SUB>), but
  similar dynamics may also apply to the Sun. Our previous simulations
  demonstrated that convective dynamos can build persistent toroidal flux
  structures (magnetic wreaths) in the midst of a turbulent convection
  zone and that high rotation rates promote the cyclic reversal of
  these wreaths. Here we demonstrate that magnetic cycles can also be
  achieved by reducing the diffusion, thus increasing the Reynolds and
  magnetic Reynolds numbers. In these more turbulent models, diffusive
  processes no longer play a significant role in the key dynamical
  balances that establish and maintain the differential rotation and
  magnetic wreaths. Magnetic reversals are attributed to an imbalance
  in the poloidal magnetic induction by convective motions that is
  stabilized at higher diffusion levels. Additionally, the enhanced
  levels of turbulence lead to greater intermittency in the toroidal
  magnetic wreaths, promoting the generation of buoyant magnetic loops
  that rise from the deep interior to the upper regions of our simulated
  domain. The implications of such turbulence-induced magnetic buoyancy
  for solar and stellar flux emergence are also discussed.

Title: New Era in 3-D Modeling of Convection and Magnetic Dynamos
    in Stellar Envelopes and Cores
Authors: Toomre, J.; Augustson, K. C.; Brown, B. P.; Browning, M. K.;
   Brun, A. S.; Featherstone, N. A.; Miesch, M. S.
Bibcode: 2012ASPC..462..331T
Altcode:
  The recent advances in asteroseismology and spectropolarimetry are
  beginning to provide estimates of differential rotation and magnetic
  structures for a range of F and G-type stars possessing convective
  envelopes, and in A-type stars with convective cores. It is essential
  to complement such observational work with theoretical studies based
  on 3-D simulations of highly turbulent convection coupled to rotation,
  shear and magnetic fields in full spherical geometries. We have so
  employed the anelastic spherical harmonic (ASH) code, which deals
  with compressible magnetohydrodynamics (MHD) in spherical shells, to
  examine the manner in which the global-scale convection can establish
  differential rotation and meridional circulations under current
  solar rotation rates, and these make good contact with helioseismic
  findings. For younger G stars rotating 3 to 5 times faster than
  the current Sun, the convection establishes ever stronger angular
  velocity contrasts between their fast equators and slow poles, and
  these are accompanied by prominent latitudinal temperature contrasts as
  well. Turning to MHD simulation of magnetic dynamo action within these
  younger G stars, the resulting magnetism involves wreaths of strong
  toroidal magnetic fields (up to 50 to 100 kG strengths) in the bulk
  of the convection zone, typically of opposite polarity in the northern
  and southern hemispheres. These fields can persist for long intervals
  despite being pummeled by the fast convective downflows, but they can
  also exhibit field reversals and cycles. Turning to shallower convective
  envelopes in the more luminous F-type stars that range in mass from 1.2
  to 1.4 solar masses and for various rotation rates, we find that the
  convection can again establish solar-like differential rotation profiles
  with a fast equator and slow poles, but the opposite is achieved at
  the slower rotation rates. The F stars are also capable of building
  strong magnetic fields, often as wreaths, through dynamo action. We
  also consider dynamo action within the cores of rotating A-type stars,
  finding that striking super-equipartition magnetic fields can be built
  there. These families of 3-D simulations are showing that a new era of
  detailed stellar modeling is becoming feasible through rapid advances
  in supercomputing, and these have the potential to help interpret and
  possibly even guide some of the observational efforts now under way.

Title: Convection and Differential Rotation in F-type Stars
Authors: Augustson, Kyle C.; Brown, Benjamin P.; Brun, Allan Sacha;
   Miesch, Mark S.; Toomre, Juri
Bibcode: 2012ApJ...756..169A
Altcode:
  Differential rotation is a common feature of main-sequence spectral
  F-type stars. In seeking to make contact with observations and to
  provide a self-consistent picture of how differential rotation is
  achieved in the interiors of these stars, we use the three-dimensional
  anelastic spherical harmonic (ASH) code to simulate global-scale
  turbulent flows in 1.2 and 1.3 M <SUB>⊙</SUB> F-type stars
  at varying rotation rates. The simulations are carried out in
  spherical shells that encompass most of the convection zone and a
  portion of the stably stratified radiative zone below it, allowing
  us to explore the effects of overshooting convection. We examine
  the scaling of the mean flows and thermal state with rotation rate
  and mass and link these scalings to fundamental parameters of the
  simulations. Indeed, we find that the differential rotation becomes
  much stronger with more rapid rotation and larger mass, scaling as
  ΔΩvpropM <SUP>3.9</SUP>Ω<SUP>0.6</SUP> <SUB>0</SUB>. Accompanying the
  growing differential rotation is a significant latitudinal temperature
  contrast, with amplitudes of 1000 K or higher in the most rapidly
  rotating cases. This contrast in turn scales with mass and rotation
  rate as ΔTvpropM <SUP>6.4</SUP>Ω<SUP>1.6</SUP> <SUB>0</SUB>. On
  the other hand, the meridional circulations become much weaker with
  more rapid rotation and with higher mass, with their kinetic energy
  decreasing as KE<SUB>MC</SUB>vpropM <SUP>-1.2</SUP>Ω<SUP>-0.8</SUP>
  <SUB>0</SUB>. Additionally, three of our simulations exhibit
  a global-scale shear instability within their stable regions that
  persists for the duration of the simulations. The flow structures
  associated with the instabilities have a direct coupling to and impact
  on the flows within the convection zone.

Title: Effects of Granulation upon Larger-Scale Convection
Authors: Hurlburt, N. E.; DeRosa, M. L.; Augustson, K. C.; Toomre, J.
Bibcode: 2012ASPC..454...13H
Altcode: 2012arXiv1201.4809H
  We examine the role of small-scale granulation in helping to drive
  supergranulation and even larger scales of convection. The granulation
  is modeled as localized cooling events introduced at the upper boundary
  of a 3-D simulation of compressible convection in a rotating spherical
  shell segment. With a sufficient number of stochastic cooling events
  compared to uniform cooling, we find that supergranular scales are
  realized, along with a differential rotation that becomes increasingly
  solar-like.

Title: Modeling the Dynamical Coupling of Solar Convection with the
    Radiative Interior
Authors: Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri
Bibcode: 2011ApJ...742...79B
Altcode:
  The global dynamics of a rotating star like the Sun involves the
  coupling of a highly turbulent convective envelope overlying a
  seemingly benign radiative interior. We use the anelastic spherical
  harmonic code to develop a new class of three-dimensional models
  that nonlinearly couple the convective envelope to a deep stable
  radiative interior. The numerical simulation assumes a realistic solar
  stratification from r = 0.07 up to 0.97R (with R the solar radius),
  thus encompassing part of the nuclear core up through most of the
  convection zone. We find that a tachocline naturally establishes itself
  between the differentially rotating convective envelope and the solid
  body rotation of the interior, with a slow spreading that is here
  diffusively controlled. The rapid angular momentum redistribution in
  the convective envelope leads to a fast equator and slow poles, with a
  conical differential rotation achieved at mid-latitudes, much as has
  been deduced by helioseismology. The convective motions are able to
  overshoot downward about 0.04R into the radiative interior. However,
  the convective meridional circulation there is confined to a smaller
  penetration depth and is directed mostly equatorward at the base
  of the convection zone. Thermal wind balance is established in the
  lower convection zone and tachocline but departures are evident in
  the upper convection zone. Internal gravity waves are excited by the
  convective overshooting, yielding a complex wave field throughout the
  radiative interior.

Title: Global-scale Magnetism (and Cycles) in Dynamo Simulations of
    Stellar Convection Zones
Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Miesch, M. S.;
   Toomre, J.
Bibcode: 2011ASPC..448..277B
Altcode: 2011arXiv1101.0171B; 2011csss...16..277B
  Young solar-type stars rotate rapidly and are very magnetically
  active. The magnetic fields at their surfaces likely originate in their
  convective envelopes where convection and rotation can drive strong
  dynamo action. Here we explore simulations of global-scale stellar
  convection in rapidly rotating suns using the 3-D MHD anelastic
  spherical harmonic (ASH) code. The magnetic fields built in these
  dynamos are organized on global-scales into wreath-like structures
  that span the convection zone. We explore one case rotates five times
  faster than the Sun in detail. This dynamo simulation, called case
  D5, has repeated quasi-cyclic reversals of global-scale polarity. We
  compare this case D5 to the broader family of simulations we have been
  able to explore and discuss how future simulations and observations
  can advance our understanding of stellar dynamos and magnetism.

Title: The 3D Nature of Convective Dynamos
Authors: Miesch, M.; Brown, B.; Nelson, N.; Browning, M.; Brun, A. S.;
   Toomre, J.
Bibcode: 2011AGUFMSH23D..01M
Altcode:
  Solar observations throughout the extended minimum between cyles 23 and
  24 have highlighted the intrinsically three-dimensional (3D) nature of
  the solar magnetic field. These include prominent multipolar components
  and low-latitude coronal holes observed with STEREO, asymmetric
  surface flux distributions in photospheric magnetograms, ond global,
  multi-scale magnetic linkages revealed by SDO. Axisymmetric mean-field
  dynamo models cannot capture this complexity, which ultimately arises
  from turbulent convection. The solar dynamo is a convective dynamo;
  convection is clearly responsible for the diversity of solar magnetic
  activity we observe, generating and organizing magnetic fields both
  directly by turbulent induction and indirectly via mean flows and MHD
  instabilities. Simulations of convective dynamos reveal the 3D nature
  of how large-scale magnetic fields are generated and provide insight
  into the intricate topology of the solar magnetic field, apparent
  even during solar minimum. I will describe recent work on the role of
  helicity and shear in magnetic self-organization and promising first
  steps toward linking convective dynamos with flux emergence.

Title: Exploring the Deep Convection and Magnetism of A-type stars
Authors: Featherstone, Nicholas; Browning, Matthew; Brun, Allan Sacha;
   Toomre, Juri
Bibcode: 2011APS..DPPN10003F
Altcode:
  A-type stars have both a near-surface layer of fast convection that
  can excite acoustic modes and a deep zone of core convection whose
  properties may be probed with asteroseismology. Many A-type stars also
  exhibit large magnetic spots that are often attributed to surviving
  primordial fields of global scale in the intervening radiative zone. We
  have explored the potential for core convection in rotating A-type
  stars to build strong magnetic fields through dynamo action. Using the
  ASH code, we model the inner 30% by radius of a two solar mass A-type
  star, rotating at four times the solar rate and capturing the convective
  core and a portion of the overlying radiative envelope. Convection in
  these stars drives a strong retrograde differential rotation and yields
  a core that is prolate in shape. When dynamo action is admitted, the
  convection generates strong magnetic fields largely in equipartition
  with the dynamics. Remarkably, introducing a modest but large-scale
  external field threading the radiative envelope (which may be of
  primordial origin) can substantially alter the turbulent dynamics
  of the convective interior. The resulting convection establishes a
  complex assembly of helical rolls that link distant portions of the
  core and yield magnetic fields of super-equipartition strength.

Title: Buoyant Magnetic Loops in a Global Dynamo Simulation of a
    Young Sun
Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Brun, Allan Sacha;
   Miesch, Mark S.; Toomre, Juri
Bibcode: 2011ApJ...739L..38N
Altcode: 2011arXiv1108.4697N
  The current dynamo paradigm for the Sun and Sun-like stars places the
  generation site for strong toroidal magnetic structures deep in the
  solar interior. Sunspots and starspots on Sun-like stars are believed
  to arise when sections of these magnetic structures become buoyantly
  unstable and rise from the deep interior to the photosphere. Here, we
  present the first three-dimensional global magnetohydrodynamic (MHD)
  simulation in which turbulent convection, stratification, and rotation
  combine to yield a dynamo that self-consistently generates buoyant
  magnetic loops. We simulate stellar convection and dynamo action in
  a spherical shell with solar stratification, but rotating three times
  faster than the current solar rate. Strong wreaths of toroidal magnetic
  field are realized by dynamo action in the convection zone. By turning
  to a dynamic Smagorinsky model for subgrid-scale turbulence, we here
  attain considerably reduced diffusion in our simulation. This permits
  the regions of strongest magnetic field in these wreaths to rise toward
  the top of the convection zone via a combination of magnetic buoyancy
  instabilities and advection by convective giant cells. Such a global
  simulation yielding buoyant loops represents a significant step forward
  in combining numerical models of dynamo action and flux emergence.

Title: Convection and dynamo action in B stars
Authors: Augustson, Kyle C.; Brun, Allan S.; Toomre, Juri
Bibcode: 2011IAUS..271..361A
Altcode: 2010arXiv1011.1016A
  Main-sequence massive stars possess convective cores that likely
  harbor strong dynamo action. To assess the role of core convection
  in building magnetic fields within these stars, we employ the 3-D
  anelastic spherical harmonic (ASH) code to model turbulent dynamics
  within a 10 M<SUB>solar</SUB> main-sequence (MS) B-type star rotating
  at 4 Ω<SUB>solar</SUB>. We find that strong (900 kG) magnetic fields
  arise within the turbulence of the core and penetrate into the stably
  stratified radiative zone. These fields exhibit complex, time-dependent
  behavior including reversals in magnetic polarity and shifts between
  which hemisphere dominates the total magnetic energy.

Title: Onward from solar convection to dynamos in cores of massive
    stars
Authors: Toomre, Juri
Bibcode: 2011IAUS..271..347T
Altcode:
  We reflect upon a few of the research challenges in stellar convection
  and dynamo theory that are likely to be addressed in the next five
  or so years. These deal firstly with the Sun and continuing study of
  the two boundary layers at the top and bottom of its convection zone,
  namely the tachocline and the near-surface shear layer, both of which
  are likely to have significant roles in how the solar dynamo may be
  operating. Another direction concerns studying core convection and
  dynamo action within the central regions of more massive A, B and O-type
  stars, for the magnetism may have a key role in controlling the winds
  from these stars, thus influencing their ultimate fate. Such studies
  of the interior dynamics of massive stars are becoming tractable with
  recent advances in codes and supercomputers, and should also be pursued
  with some vigor.

Title: Global-scale wreath-building dynamos in stellar convection
    zones
Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha;
   Miesch, Mark S.; Toomre, Juri
Bibcode: 2011IAUS..271...78B
Altcode: 2010arXiv1011.0445B
  When stars like our Sun are young they rotate rapidly and are very
  magnetically active. We explore dynamo action in rapidly rotating suns
  with the 3-D MHD anelastic spherical harmonic (ASH) code. The magnetic
  fields built in these dynamos are organized on global-scales into
  wreath-like structures that span the convection zone. Wreath-building
  dynamos can undergo quasi-cyclic reversals of polarity and such behavior
  is common in the parameter space we have been able to explore. These
  dynamos do not appear to require tachoclines to achieve their spatial
  or temporal organization. Wreath-building dynamos are present to some
  degree at all rotation rates, but are most evident in the more rapidly
  rotating simulations.

Title: Global magnetic cycles in rapidly rotating younger suns
Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Browning, Matthew
   K.; Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri
Bibcode: 2011IAUS..273..272N
Altcode: 2010arXiv1010.6073N
  Observations of sun-like stars rotating faster than our current
  sun tend to exhibit increased magnetic activity as well as magnetic
  cycles spanning multiple years. Using global simulations in spherical
  shells to study the coupling of large-scale convection, rotation,
  and magnetism in a younger sun, we have probed effects of rotation
  on stellar dynamos and the nature of magnetic cycles. Major 3-D MHD
  simulations carried out at three times the current solar rotation
  rate reveal hydromagnetic dynamo action that yields wreaths of strong
  toroidal magnetic field at low latitudes, often with opposite polarity
  in the two hemispheres. Our recent simulations have explored behavior in
  systems with considerably lower diffusivities, achieved with sub-grid
  scale models including a dynamic Smagorinsky treatment of unresolved
  turbulence. The lower diffusion promotes the generation of magnetic
  wreaths that undergo prominent temporal variations in field strength,
  exhibiting global magnetic cycles that involve polarity reversals. In
  our least diffusive simulation, we find that magnetic buoyancy coupled
  with advection by convective giant cells can lead to the rise of
  coherent loops of magnetic field toward the top of the simulated domain.

Title: Magnetic Cycles and Meridional Circulation in Global Models
    of Solar Convection
Authors: Miesch, Mark S.; Brown, Benjamin P.; Browning, Matthew K.;
   Brun, Allan Sacha; Toomre, Juri
Bibcode: 2011IAUS..271..261M
Altcode: 2010arXiv1009.6184M
  We review recent insights into the dynamics of the solar convection
  zone obtained from global numerical simulations, focusing on two recent
  developments in particular. The first is quasi-cyclic magnetic activity
  in a long-duration dynamo simulation. Although mean fields comprise
  only a few percent of the total magnetic energy they exhibit remarkable
  order, with multiple polarity reversals and systematic variability
  on time scales of 6-15 years. The second development concerns the
  maintenance of the meridional circulation. Recent high-resolution
  simulations have captured the subtle nonlinear dynamical balances with
  more fidelity than previous, more laminar models, yielding more coherent
  circulation patterns. These patterns are dominated by a single cell in
  each hemisphere, with poleward and equatorward flow in the upper and
  lower convection zone respectively. We briefly address the implications
  of and future of these modeling efforts.

Title: Exploring the deep convection and magnetism of A-type stars
Authors: Featherstone, Nicholas A.; Browning, Matthew K.; Brun,
   Allan Sacha; Toomre, Juri
Bibcode: 2011IAUS..273..111F
Altcode:
  A-type stars have both a near-surface layer of fast convection that
  can excite acoustic modes and a deep zone of core convection whose
  properties may be probed with asteroseismology. Many A-type stars also
  exhibit large magnetic spots that are often attributed to surviving
  primordial fields of global scale in the intervening radiative zone. We
  have explored the potential for core convection in rotating A-type
  stars to build strong magnetic fields through dynamo action. These
  3-D simulations using the ASH code provide guidance on the nature
  of differential rotation and magnetic fields that may be present in
  the deep interiors of these stars, thus informing the asteroseismic
  deductions now becoming feasible. Our models encompass the inner 30%
  by radius of a two solar mass A-type star, rotating at four times
  the solar rate and capturing the convective core and a portion of the
  overlying radiative envelope. Convection in these stars drives a strong
  retrograde differential rotation and yields a core that is prolate in
  shape. When dynamo action is admitted, the convection generates strong
  magnetic fields largely in equipartition with the dynamics. Remarkably,
  introducing a modest but large-scale external field threading the
  radiative envelope (which may be of primordial origin) can substantially
  alter the turbulent dynamics of the convective interior. The resulting
  convection involves a complex assembly of helical rolls that link
  distant portions of the core and stretch and advect magnetic field,
  ultimately yielding magnetic fields of super-equipartition strength.

Title: Probing Subsurface Flows Around Sunspots with 3-Dimensional
    Ring Inversions
Authors: Featherstone, Nicholas Andrew; Hindman, Bradley W.; Thompson,
   Michael J.; Toomre, Juri
Bibcode: 2011shin.confE...7F
Altcode:
  We examine convective flows around sunspots as inferred through
  ring-analysis helioseismology of MDI Dopplergrams. These flow
  measurements were obtained using a novel 3-D inversion procedure
  termed Adaptively Resolved Ring-Diagram Inversions, or ARRDI, which
  uses sensitivity kernels based on the Born approximation. The ARRDI
  algorithm is multi-scale in nature, folding together information from
  tiles located at different positions on the solar surface and from
  tiles of different sizes, thus enabling fine control of the horizontal
  resolution and the probing depth. When we apply ARRDI to sunspots,
  we measure outflows persisting to depths of at least 7 Mm. In many
  instances, the surface outflow diminishes within the upper 3 Mm
  of the convection zone. Beyond 3 Mm, such outflows strengthen and
  attain peak amplitudes of 200 m/s at depths of 5-7 Mm. We discuss the
  implications of such a two-component outflow for understanding the
  magneto-hydrodynamic behavior and evolution of sunspots.

Title: Magnetic Cycles in a Convective Dynamo Simulation of a Young
    Solar-type Star
Authors: Brown, Benjamin P.; Miesch, Mark S.; Browning, Matthew K.;
   Brun, Allan Sacha; Toomre, Juri
Bibcode: 2011ApJ...731...69B
Altcode: 2011arXiv1102.1993B
  Young solar-type stars rotate rapidly and many are magnetically
  active. Some appear to undergo magnetic cycles similar to the 22 yr
  solar activity cycle. We conduct simulations of dynamo action in rapidly
  rotating suns with the three-dimensional magnetohydrodynamic anelastic
  spherical harmonic (ASH) code to explore dynamo action achieved in
  the convective envelope of a solar-type star rotating at five times
  the current solar rotation rate. We find that dynamo action builds
  substantial organized global-scale magnetic fields in the midst of the
  convection zone. Striking magnetic wreaths span the convection zone
  and coexist with the turbulent convection. A surprising feature of this
  wreath-building dynamo is its rich time dependence. The dynamo exhibits
  cyclic activity and undergoes quasi-periodic polarity reversals where
  both the global-scale poloidal and toroidal fields change in sense on
  a roughly 1500 day timescale. These magnetic activity patterns emerge
  spontaneously from the turbulent flow and are more organized temporally
  and spatially than those realized in our previous simulations of the
  solar dynamo. We assess in detail the competing processes of magnetic
  field creation and destruction within our simulations that contribute to
  the global-scale reversals. We find that the mean toroidal fields are
  built primarily through an Ω-effect, while the mean poloidal fields
  are built by turbulent correlations which are not well represented by
  a simple α-effect. During a reversal the magnetic wreaths propagate
  toward the polar regions, and this appears to arise from a poleward
  propagating dynamo wave. As the magnetic fields wax and wane in
  strength and flip in polarity, the primary response in the convective
  flows involves the axisymmetric differential rotation which varies on
  similar timescales. Bands of relatively fast and slow fluid propagate
  toward the poles on timescales of roughly 500 days and are associated
  with the magnetic structures that propagate in the same fashion. In
  the Sun, similar patterns are observed in the poleward branch of the
  torsional oscillations, and these may represent poleward propagating
  magnetic fields deep below the solar surface.

Title: Magnetic Cycles in a Wreath-Building Dynamo Simulation of a
    Young Solar-type Star
Authors: Brown, Benjamin; Miesch, M. S.; Browning, M. K.; Brun, A. S.;
   Nelson, N. J.; Toomre, J.
Bibcode: 2011AAS...21724222B
Altcode: 2011BAAS...4324222B
  Stars like the Sun build global-scale magnetic fields though dynamo
  processes in their convection zones. There, global-scale plasma motions
  couple with rotation and likely drive cycles of magnetic activity,
  though the exact processes at work in solar and stellar dynamos remain
  elusive. Observations of younger suns indicate that they rotate quite
  rapidly, have strong magnetic fields at their surfaces, and show
  signs of cyclic activity. Here we explore recent 3-D MHD simulations
  of younger, more rapidly rotating solar-type stars conducted with
  the anelastic spherical harmonic (ASH) code. These simulations of
  global-scale convection and dynamo action produce strikingly organized
  magnetic structures in the bulk of their convection zones. Wreaths of
  magnetic field fill the convection zone and can undergo regular cycles
  of polarity reversal. Indeed, we find that cyclic behavior is a common
  feature throughout the parameter space we have explored. Though these
  magnetic wreaths can coexist with tachoclines of penetration and shear,
  they do not rely on that internal boundary layer for their formation or
  persistence. Tachoclines may play a less critical role in the stellar
  dynamos of younger Suns than has been supposed in solar dynamo theory.

Title: Modeling the Near-Surface Shear Layer: Diffusion Schemes
    Studied With CSS
Authors: Augustson, Kyle; Rast, Mark; Trampedach, Regner; Toomre, Juri
Bibcode: 2011JPhCS.271a2070A
Altcode: 2010arXiv1012.4781A
  As we approach solar convection simulations that seek to model the
  interaction of small-scale granulation and supergranulation and even
  larger scales of convection within the near-surface shear layer (NSSL),
  the treatment of the boundary conditions and minimization of sub-grid
  scale diffusive processes become increasingly crucial. We here assess
  changes in the dynamics and the energy flux balance of the flows
  established in rotating spherical shell segments that capture much
  of the NSSL with the Curved Spherical Segment (CSS) code using two
  different diffusion schemes. The CSS code is a new massively parallel
  modeling tool capable of simulating 3-D compressible MHD convection with
  a realistic solar stratification in rotating spherical shell segments.

Title: Magnetic Cycles and Buoyant Magnetic Structures in a Rapidly
    Rotating Sun
Authors: Nelson, Nicholas J.; Brown, B. P.; Brun, S.; Miesch, M. S.;
   Toomre, J.
Bibcode: 2011AAS...21715512N
Altcode: 2011BAAS...4315512N
  Observations of sun-like stars rotating faster than our current sun
  show that they exhibit solar-like magnetic cycles and features, such
  as star spots. Using global 3-D simulations to study the coupling
  of large-scale convection, rotation, and magnetism in a younger sun,
  we have probed the effects of more rapid rotation on stellar dynamos
  and the nature of magnetic cycles. Our anelastic spherical harmonics
  (ASH) code allows study of the convective envelope, occupying
  the outer 30% by radius of a sun-like star. Major MHD simulations
  carried out at three times the current solar rotation rate reveal
  magnetic dynamo action that can produce wreaths of strong toroidal
  magnetic field at low latitudes, often with opposite polarity in the
  two hemispheres. The presence of the wreaths is quite surprising, for
  they arise as quite persistent global structures amidst the vigorous
  and turbulent convection. We have recently explored behavior in
  systems with considerably lower diffusivities, achieved with a dynamic
  Smagorinsky treatment of unresolved turbulence. The lower levels of
  diffusion create magnetic wreaths that undergo prominent variations in
  field strength, even exhibiting global magnetic cycles that involve
  polarity reversals. Additionally, during the cycle maximum, when
  magnetic energies and mean magnetic fields peak, the wreaths possess
  buoyant magnetic structures that rise coherently through much of the
  convective envelope via a combination of advection by convective upflows
  and magnetic buoyancy. We explore aspects of these rising magnetic
  structures and the evolving global dynamo action which produces them.

Title: Assessing the Deep Interior Dynamics and Magnetism of A-type
    Stars
Authors: Featherstone, Nicholas A.; Browning, Matthew K.; Brun,
   Allan Sacha; Toomre, Juri
Bibcode: 2011JPhCS.271a2068F
Altcode:
  A-type stars have both a shallow near-surface zone of fast convection
  that can excite acoustic modes and a deep zone of core convection
  whose properties may be studied through asteroseismology. Many A stars
  also exhibit large magnetic spots as they rotate. We have explored the
  properties of core convection in rotating A-type stars and their ability
  to build strong magnetic fields. These 3-D simulations using the ASH
  code may serve to inform asteroseismic deductions of interior rotation
  and magnetism that are now becoming feasible. Our models encompass the
  inner 30% by radius of a 2 solar mass A-type star, capturing both the
  convective core and some of the overlying radiative envelope. Convection
  can drive a column of strong retrograde differential rotation and
  yield a core prolate in shape. When dynamo action is admitted, the
  convection is able to generate strong magnetic fields largely in
  equipartition with the dynamics. Introducing a modest external field
  (which may be of primordial origin) into the radiative envelope can
  substantially alter the turbulent dynamics of the convective core,
  yielding magnetic fields of remarkable super-equipartition strength. The
  turbulent convection involves a complex assembly of helical rolls that
  link distant portions of the core and stretch and advect magnetic field
  into broad swathes of strong toroidal field. These simulations reveal
  that supercomputing is providing a perspective of the deep dynamics
  that may become testable with asteroseismology for these stars.

Title: Rotation-rate variations at the tachocline: An update
Authors: Howe, R.; Komm, R.; Hill, F.; Christensen-Dalsgaard, J.;
   Larson, T. P.; Schou, J.; Thompson, M. J.; Toomre, J.
Bibcode: 2011JPhCS.271a2075H
Altcode:
  After 15 years of GONG and MDI observations of the solar interior
  rotation, we revisit the issue of variations in the rotation rate near
  the base of the convection zone. The 1.3-year period seen in the first
  few years of the observations disappeared after 2000 and has still
  not returned. On the other hand, the agreement between GONG and MDI
  observations suggests that variations seen in this region have some
  solar origin, whether a true rotation-rate change or possibly mere
  stochastic variation; we present a numerical experiment supporting
  this contention.

Title: The Influence of Tracking Rate on Helioseismic Flow Inferences
Authors: Routh, Swati; Haber, Deborah A.; Hindman, Bradley W.; Bogart,
   Richard S.; Toomre, Juri
Bibcode: 2011JPhCS.271a2014R
Altcode:
  Traditionally, most local helioseismic studies of subsurface flows
  have removed the large signal due to the Sun's rotation by tracking
  the analysis region across the solar surface. In order to work in a
  uniformly rotating reference frame, the ring-analysis pipeline of the
  recently launched Helioseismic and Magnetic Imager (HMI) will track
  all analysis regions at the solid-body Carrington rate. To test this
  tracking scheme, we compare flow determinations resulting from two
  different tracking schemes. In one scheme we use the HMI pipeline
  implementation which tracks at the Carrington rotation rate. In
  the other, the tiles are tracked at the local differential surface
  rotation rate as measured by Snodgrass (1984). We observe systematic
  differences between the flows obtained by the two schemes even after
  transforming them to a common frame (Snodgrass frame), with the zonal
  flows measured in the Carrington frame being faster by 5-20 m/s.

Title: Developing Physics-Based Procedures for Local Helioseismic
    Probing of Sunspots and Magnetic Regions
Authors: Birch, Aaron; Braun, D. C.; Crouch, A.; Rempel, M.; Fan,
   Y.; Centeno, R.; Toomre, J.; Haber, D.; Hindman, B.; Featherstone,
   N.; Duvall, T., Jr.; Jackiewicz, J.; Thompson, M.; Stein, R.; Gizon,
   L.; Cameron, R.; Saidi, Y.; Hanasoge, S.; Burston, R.; Schunker, H.;
   Moradi, H.
Bibcode: 2010AAS...21630805B
Altcode:
  We have initiated a project to test and improve the local helioseismic
  techniques of time-distance and ring-diagram analysis. Our goals are
  to develop and implement physics-based methods that will (1) enable the
  reliable determinations of subsurface flow, magnetic field, and thermal
  structure in regions of strong magnetic fields and (2) be quantitatively
  tested with realistic solar magnetoconvection simulations in the
  presence of sunspot-like magnetic fields. We are proceeding through a
  combination of improvements in local helioseismic measurements, forward
  modeling of the helioseismic wavefield, kernel computations, inversions,
  and validation through numerical simulations. As improvements over
  existing techniques are made they will be applied to the SDO/HMI
  observations. This work is funded through the the NASA Heliophysics
  Science Division through the Solar Dynamics Observatory (SDO) Science
  Center program.

Title: Core Convection and Dynamos in Spectral Type O and B Stars
Authors: Augustson, Kyle; Brun, A. S.; Toomre, J.
Bibcode: 2010AAS...21642301A
Altcode: 2010BAAS...41..835A
  Recent observations have revealed that about one-third of O and B type
  stars have strong magnetic fields at their surfaces. It is currently
  unclear where these fields originate. In order to address this question,
  we examine the effects of core convection and magnetic dynamo processes
  within massive O and B stars with simulations in rotating spherical
  shells using the 3-D Spherical Harmonic (ASH) magnetohydrodynamic code.

Title: Modeling the Near-Surface Shear Layer Through Coupled
    Simulations of Surface and Deep Convection
Authors: Augustson, Kyle; Hurlburt, N.; DeRosa, M.; Toomre, J.
Bibcode: 2010AAS...21640008A
Altcode: 2010BAAS...41..855A
  We examine the role of small-scale granulation in helping to drive
  supergranulation and even larger scales of convection. The granulation
  is modeled as localized plumes with statistics taken from surface
  convection simulations introduced at the upper boundary of a 3-D
  simulation of compressible convection in a rotating spherical shell
  segment. With a sufficient number of stochastic plume events compared
  to a uniform cooling, we find that supergranular scales are realized,
  along with a differential rotation that becomes increasingly solar-like.

Title: Persistent Magnetic Wreaths in a Rapidly Rotating Sun
Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha;
   Miesch, Mark S.; Toomre, Juri
Bibcode: 2010ApJ...711..424B
Altcode: 2010arXiv1011.2831B
  When our Sun was young it rotated much more rapidly than
  now. Observations of young, rapidly rotating stars indicate that many
  possess substantial magnetic activity and strong axisymmetric magnetic
  fields. We conduct simulations of dynamo action in rapidly rotating
  suns with the three-dimensional magnetohydrodynamic anelastic spherical
  harmonic (ASH) code to explore the complex coupling between rotation,
  convection, and magnetism. Here, we study dynamo action realized in the
  bulk of the convection zone for a system rotating at 3 times the current
  solar rotation rate. We find that substantial organized global-scale
  magnetic fields are achieved by dynamo action in this system. Striking
  wreaths of magnetism are built in the midst of the convection zone,
  coexisting with the turbulent convection. This is a surprise, for
  it has been widely believed that such magnetic structures should be
  disrupted by magnetic buoyancy or turbulent pumping. Thus, many solar
  dynamo theories have suggested that a tachocline of penetration and
  shear at the base of the convection zone is a crucial ingredient for
  organized dynamo action, whereas these simulations do not include
  such tachoclines. We examine how these persistent magnetic wreaths
  are maintained by dynamo processes and explore whether a classical
  mean-field α-effect explains the regeneration of poloidal field. We
  find that the global-scale toroidal magnetic fields are maintained by an
  Ω-effect arising from the differential rotation, while the global-scale
  poloidal fields arise from turbulent correlations between the convective
  flows and magnetic fields. These correlations are not well represented
  by an α-effect that is based on the kinetic and magnetic helicities.

Title: Solar Convective Dynamo Action With A Tachocline
Authors: Featherstone, Nicholas; Brun, A. S.; Miesch, M. S.; Brown,
   B. P.; Toomre, J.
Bibcode: 2010AAS...21532202F
Altcode: 2010BAAS...42..323F
  We present continuing simulations of solar-like convection penetrating
  into the tachocline at the base of the convection zone and examine
  the resulting dynamo action. Prior simulations using the 3-D anelastic
  spherical harmonic (ASH) code of convection in a full spherical shell
  admitting penetration into a tachocline have yielded differential
  rotation profiles whose latitudinal contrast is considerably smaller
  than in simulations without penetration. We believe that the relatively
  soft stabilizing entropy gradients in the overshooting regions may
  have resulted in unusually strong circulations that worked against the
  Reynolds stresses, thus diminishing the differential rotation. Here we
  turn to ASH simulations with more realistic stiffer entropy gradients
  and reduced diffusivities in the radiative zone. We report on the
  hydrodynamic balances achieved within the region of penetration that
  allows the convection zone to return to differential rotation profiles
  in closer accord with helioseismic deductions, including possessing
  a tachocline of shear. We then examine the possibilities for dynamo
  action in this system and find that weak wreathes of toroidal field,
  similar to those found in simulations of faster rotating suns, are
  realized in the convection zone. Convective pumping of these fields
  into the tachocline leads to the generation of strong axisymmetric
  toroidal fields there, with oppositely signed polarities about the
  equator. We examine the temporal variation of these magnetic fields
  as well as their effects on the angular momentum transport within the
  bulk of the convection zone.

Title: Wreath-Building Dynamos in Rapidly Rotating Suns
Authors: Brown, Benjamin; Browning, M. K.; Brun, A. S.; Miesch, M. S.;
   Toomre, J.
Bibcode: 2010AAS...21542415B
Altcode: 2010BAAS...42..332B
  When stars like our Sun are young, they rotate quite
  rapidly. Observations of these young suns indicate that they generally
  possess strong magnetic activity. Here we explore 3-D MHD simulations
  of dynamo action in rapidly rotating suns. Our simulations with
  the anelastic spherical harmonic (ASH) code extend from 0.72 to
  0.97 solar radii and thus span the bulk of the stellar convection
  zone. We find that these stars achieve strong dynamo action, and
  naturally build remarkable global-scale magnetic structures in their
  convection zones. These wreaths of magnetism fill the convection zone
  and retain coherence over long epochs despite being embedded in the
  turbulent convection. This is in striking contrast to many theories
  of the global solar dynamo, which is thought to require a tachocline
  of shear and penetration at the base of the convection zone to achieve
  such structures. Wreath-building dynamos can undergo repeated cycles of
  magnetic polarity reversal, with the global-scale magnetic structures
  changing their sense on thousand day timescales.

Title: Three-Dimensional Simulations of Solar and Stellar Dynamos:
    The Influence of a Tachocline
Authors: Miesch, M. S.; Browning, M. K.; Brun, A. S.; Toomre, J.;
   Brown, B. P.
Bibcode: 2009ASPC..416..443M
Altcode: 2008arXiv0811.3032M
  We review recent advances in modeling global-scale convection and
  dynamo processes with the Anelastic Spherical Harmonic (ASH) code. In
  particular, we have recently achieved the first global-scale solar
  convection simulations that exhibit turbulent pumping of magnetic
  flux into a simulated tachocline and the subsequent organization and
  amplification of toroidal field structures by rotational shear. The
  presence of a tachocline not only promotes the generation of mean
  toroidal flux, but it also enhances and stabilizes the mean poloidal
  field throughout the convection zone, promoting dipolar structure with
  less frequent polarity reversals. The magnetic field generated by a
  convective dynamo with a tachocline and overshoot region is also more
  helical overall, with a sign reversal in the northern and southern
  hemispheres. Toroidal tachocline fields exhibit little indication of
  magnetic-buoyancy instabilities, but may be undergoing magneto-shear
  instabilities.

Title: Dynamo Action and Wreaths of Magnetism in a Younger Sun
Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Miesch, M. S.;
   Toomre, J.
Bibcode: 2009ASPC..416..369B
Altcode:
  When our Sun was younger it rotated much more rapidly. Observations of
  many young stars indicate that magnetic activity and perhaps dynamo
  action are stronger in the rapidly rotating suns. Here we use the
  anelastic spherical harmonic (ASH) code to explore 3-D MHD simulations
  of the dynamo action that might occur in such younger suns. As a great
  surprise, we find that coherent global-scale structures of toroidal
  magnetic field are formed in the bulk of the convection zone. These
  wreaths of magnetism persist for long periods of time amidst the still
  turbulent convection. In contrast to previous solar dynamo simulations,
  the wreaths of magnetism formed in these more rapidly rotating suns
  do not require a tachocline of penetration and shear at the base of
  the convection zone for their creation or survival.

Title: Effects of Fossil Magnetic Fields on Convective Core Dynamos
    in A-type Stars
Authors: Featherstone, Nicholas A.; Browning, Matthew K.; Brun,
   Allan Sacha; Toomre, Juri
Bibcode: 2009ApJ...705.1000F
Altcode:
  The vigorous magnetic dynamo action achieved within the convective cores
  of A-type stars may be influenced by fossil magnetic fields within their
  radiative envelopes. We study such effects through three-dimensional
  simulations that model the inner 30% by radius of a 2 M <SUB>sun</SUB>
  A-type star, capturing the convective core and a portion of the
  overlying radiative envelope within our computational domain. We
  employ the three-dimensional anelastic spherical harmonic code to
  model turbulent dynamics within a deep rotating spherical shell. The
  interaction between a fossil field and the core dynamo is examined by
  introducing a large-scale magnetic field into the radiative envelope
  of a mature A star dynamo simulation. We find that the inclusion of
  a twisted toroidal fossil field can lead to a remarkable transition
  in the core dynamo behavior. Namely, a super-equipartition state can
  be realized in which the magnetic energy built by dynamo action is
  10-fold greater than the kinetic energy of the convection itself. Such
  strong-field states may suggest that the resulting Lorentz forces should
  seek to quench the flows, yet we have achieved super-equipartition
  dynamo action that persists for multiple diffusion times. This is
  achieved by the relative co-alignment of the flows and magnetic fields
  in much of the domain, along with some lateral displacements of the
  fastest flows from the strongest fields. Convection in the presence of
  such strong magnetic fields typically manifests as 4-6 cylindrical rolls
  aligned with the rotation axis, each possessing central axial flows that
  imbue the rolls with a helical nature. The roll system also possesses
  core-crossing flows that couple distant regions of the core. We find
  that the magnetic fields exhibit a comparable global topology with
  broad, continuous swathes of magnetic field linking opposite sides of
  the convective core. We have explored several poloidal and toroidal
  fossil field geometries, finding that a poloidal component is essential
  for a transition to super-equipartition to occur.

Title: Subsurface Circulations Established by Active Regions
Authors: Hindman, Bradley Wade; Haber, Deborah; Toomre, Juri
Bibcode: 2009shin.confE..17H
Altcode:
  Using the local helioseismic technique of ring analysis we deduce
  subsurface flows within and surrounding magnetic active regions. We
  apply this technique to data from MDI and analyze the resulting flow
  fields for durations of several months from each of three consecutive
  years. We compute the mean motion of magnetic plage, mean inflow
  rates into magnetic complexes and mean circulation speeds around
  active regions. We find that the plage within active regions rotates
  more rapidly than quiet sun by roughly 20 m/s, yet advects poleward
  at the same rate as quiet sun. We also find that almost all active
  regions possess a mean inflow (20-30 m/s) and a cyclonic circulation
  ( 5 m/s) at their peripheries; whereas their cores, where the sunspots
  are located, are zones of strong anticyclonic outflow ( 50 m/s).

Title: Subsurface Circulations within Active Regions
Authors: Hindman, Bradley W.; Haber, Deborah A.; Toomre, Juri
Bibcode: 2009ApJ...698.1749H
Altcode: 2009arXiv0904.1575H
  Using high-resolution ring analysis, we deduce subsurface flows within
  magnetic active regions and within the quiet Sun. With this procedure,
  we are capable of measuring flows with a horizontal spatial resolution
  of 2° in heliographic angle (or roughly 20 Mm). From the resulting flow
  fields we deduce mean inflow rates into active regions, mean circulation
  speeds around active regions, and probability density functions (PDFs)
  of properties of the flow field. These analyses indicate that active
  regions have a zonal velocity that exceeds that of the quiet Sun at
  the same latitude by 20 m s<SUP>-1</SUP>, yet active regions advect
  poleward at the same rate as the quiet Sun. We also find that almost
  all active regions possess a mean inflow (20-30 m s<SUP>-1</SUP>) and
  a cyclonic circulation (≈5 m s<SUP>-1</SUP>) at their peripheries,
  whereas their cores, where the sunspots are located, are zones of
  strong anticyclonic outflow (≈50 m s<SUP>-1</SUP>). From the PDFs,
  we find that active regions modify the structure of convection with
  a scale greater than that of supergranulation. Instead of possessing
  an asymmetry between inflows and outflows (with a larger percentage
  of the surface occupied by outflows), as is seen in the quiet Sun,
  active regions possess symmetric distributions.

Title: Wreathes of Magnetism in Rapidly Rotating Suns
Authors: Brown, Benjamin P.; Browning, Matthew K.; Miesch, Mark S.;
   Brun, Allan Sacha; Toomre, Juri
Bibcode: 2009arXiv0906.2407B
Altcode:
  When our Sun was young it rotated much more rapidly than
  now. Observations of young, rapidly rotating stars indicate that
  many possess substantial magnetic activity and strong axisymmetric
  magnetic fields. We conduct simulations of dynamo action in rapidly
  rotating suns with the 3-D MHD anelastic spherical harmonic (ASH)
  code to explore the complex coupling between rotation, convection
  and magnetism. Here we study dynamo action realized in the bulk of
  the convection zone for two systems, rotating at three and five times
  the current solar rate. We find that substantial organized global-scale
  magnetic fields are achieved by dynamo action in these systems. Striking
  wreathes of magnetism are built in the midst of the convection zone,
  coexisting with the turbulent convection. This is a great surprise,
  for many solar dynamo theories have suggested that a tachocline of
  penetration and shear at the base of the convection zone is a crucial
  ingredient for organized dynamo action, whereas these simulations do
  not include such tachoclines. Some dynamos achieved in these rapidly
  rotating states build persistent global-scale fields which maintain
  amplitude and polarity for thousands of days. In the case at five
  times the solar rate, the dynamo can undergo cycles of activity,
  with fields varying in strength and even changing polarity. As the
  magnetic fields wax and wane in strength, the primary response in
  the convective flows involves the axisymmetric differential rotation,
  which begins to vary on similar time scales. Bands of relatively fast
  and slow fluid propagate toward the poles on time scales of roughly 500
  days. In the Sun, similar patterns are observed in the poleward branch
  of the torsional oscillations, and these may represent a response to
  poleward propagating magnetic field deep below the solar surface.

Title: Mean-Field Generation in Turbulent Convective Dynamos: The
    Role of a Tachocline
Authors: Miesch, Mark S.; Browning, M. K.; Brun, A. S.; Brown, B. P.;
   Toomre, J.
Bibcode: 2009SPD....40.0406M
Altcode:
  Turbulent dynamos tend to generate turbulent magnetic fields. The
  Sun exhibits such disordered fields but it also exhibits large-scale
  magnetic activity patterns of striking order, including cyclically
  varying sunspot distributions and a reversing dipole moment. The
  challenge of global solar dynamo theory is to account for such
  order. Rotational shear almost certainly plays an essential role,
  placing the solar tachocline at center stage. Here we present global
  simulations of convective dynamos with and without a tachocline,
  focusing on how the presence of a tachocline alters mean field
  generation. The presence of a tachocline not only promotes the
  generation of mean toroidal flux, but it also enhances and stabilizes
  the mean poloidal field throughout the convection zone, promoting
  dipolar structure with less frequent polarity reversals. Magnetic fields
  generated in the presence of a tachocline are more helical overall,
  with opposite senses among hemispheres and among mean and fluctuating
  components. Toroidal tachocline fields exhibit little indication of
  magnetic buoyancy instabilities but may be undergoing magneto-shear
  instabilities.

Title: Stochastic Effects of Granulation and Supergranulation Upon
    Deep Convection
Authors: Augustson, Kyle; De Rosa, M. L.; Hurlburt, N. E.; Toomre, J.
Bibcode: 2009SPD....40.0805A
Altcode:
  Vigorous fluid motions associated with the observed patterns of
  supergranulation, mesogranulation, and granulation play a large
  role in the turbulent transport of heat to the solar surface. The
  downflows associated with these convective motions plunge from the
  surface into the near-surface layers of the Sun bringing cooler,
  low entropy material with them. These flow structures may provide
  some stochastic effects upon the dynamics of the giant cells of deep
  convection that extend into the near-surface regions. To investigate
  such dynamics, we have carried out several 3-D numerical simulations of
  fully compressible fluids within curved, spherical segments that, at
  this stage, approximate conditions near the top of the rotating solar
  convection zone. The upper boundary of the segment is stochastically
  driven with cool plumes that approximate the spatial and temporal
  scales of supergranular cell downflows, in essence creating a network
  of supergranular cells. The segment spans 30° in latitude and 30°
  in longitude, and has a radial extent of 15% of the solar radius. We
  explore the formation and evolution of the boundary layer resulting
  from such stochastic driving, and discuss these dynamics in the context
  of the near-surface shear layer of the solar convection zone.

Title: Marching Toward More Realistic Penetration of Convection into
    a Tachocline
Authors: Featherstone, Nicholas; Brun, A. S.; Miesch, M. S.; Toomre, J.
Bibcode: 2009SPD....40.0803F
Altcode:
  The solar convection zone has provided many challenges for the
  theoretical modeling of dynamics within our nearest star. The
  tachocline, a region of strong shear near the base of the convection
  zone, has received much attention due to its likely role in the
  generation of the global-scale magnetic fields. The establishment and
  maintenance of the solar tachocline has been variously attributed to
  angular momentum transport via gravity waves, magnetic torques and
  anisotropic mixing processes. Self consistently capturing the turbulent
  dynamics of the convection zone and underlying radiative zone through
  3-D numerical modeling is difficult due to the wide range of scales
  involved. Prior simulations using the 3-D anelastic spherical harmonic
  (ASH) code of convection in a full spherical shell admitting penetration
  into a stable region below have yielded differential rotation profiles
  whose latitudinal contrast is considerably smaller than in simulations
  without penetration. We believe that the relatively soft stabilizing
  entropy gradients in the overshooting regions may have resulted
  in unusually strong circulations that worked against the Reynolds
  stresses, thus diminishing the differential rotation. Here we turn
  to ASH simulations with more realistic stiffer entropy gradients and
  reduced diffusivities in the radiative zone. We report on the balances
  achieved within the region of penetration that allows the convection
  zone to return to differential rotation profiles in closer accord with
  helioseismic deductions, including possessing a tachocline of shear.

Title: Global Magnetic Reversal in a Rapidly Rotating Sun
Authors: Nelson, Nicholas J.; Brown, B. P.; Toomre, J.
Bibcode: 2009SPD....40.0804N
Altcode:
  Global MHD simulations of the solar convection zone and a tachocline
  of shear at its base have demonstrated that strong bands of toroidal
  magnetic field can be built in the tachocline through stretching and
  organizing of small-scale fields that have been pumped downward into
  it. Recent 3-D simulations of more rapidly rotating suns have revealed
  that global-scale wreathes of toroidal magnetic field can even be
  achieved in the bulk of the convection zone itself, remarkably without
  a tachocline of shear present at its base. Continuing this work, we
  simulate a sun without a tachocline, rotating at three times the solar
  rate, and at a higher turbulence level than previous simulations. We
  find toroidal magnetic wreathes which have large temporal variations
  in field strength as they interact with turbulent convection and global
  differential rotation, yet rebuild themselves, persisting in the bulk of
  the convection zone for thousands of days. These magnetic structures can
  even undergo a reversal of global magnetic polarity, and may persist in
  this state for some time. We describe here the nature of such a reversal
  and the relative timing of changes in the poloidal and toroidal fields.

Title: Turbulence, Magnetism, and Shear in Stellar Interiors
Authors: Miesch, Mark S.; Toomre, Juri
Bibcode: 2009AnRFM..41..317M
Altcode:
  Stars can be fascinating settings in which to study intricate couplings
  among convection, rotation, magnetism, and shear, usually under
  distinctly nonlinear conditions that yield vigorous turbulence. The
  emerging flux and the rotation rates of stars can vary widely,
  yet there are common elements that must contribute to building and
  maintaining the vibrantly evolving magnetic activity they exhibit. Some
  of these elements, such as the rotational shear and meridional flows
  established by the coupling of convection with rotation, can now be
  studied in detail within our nearest star using helioseismology. Major
  three-dimensional numerical simulations help refine our intuitions
  about such interior dynamics, aided by rapid advances in supercomputing
  that are improving the fidelity of the modeling. These developments,
  combined with intense thrusts at new high resolution and continuous
  observations of solar magnetism and solar oscillations, herald a
  promising era for exploring such astrophysical fluid dynamics.

Title: Rapidly Rotating Suns and Active Nests of Convection
Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha;
   Miesch, Mark S.; Toomre, Juri
Bibcode: 2008ApJ...689.1354B
Altcode: 2008arXiv0808.1716B
  In the solar convection zone, rotation couples with intensely turbulent
  convection to drive a strong differential rotation and achieve complex
  magnetic dynamo action. Our Sun must have rotated more rapidly in
  its past, as is suggested by observations of many rapidly rotating
  young solar-type stars. Here we explore the effects of more rapid
  rotation on the global-scale patterns of convection in such stars and
  the flows of differential rotation and meridional circulation, which
  are self-consistently established. The convection in these systems is
  richly time-dependent, and in our most rapidly rotating suns a striking
  pattern of localized convection emerges. Convection near the equator in
  these systems is dominated by one or two nests in longitude of locally
  enhanced convection, with quiescent streaming flow in between them at
  the highest rotation rates. These active nests of convection maintain a
  strong differential rotation despite their small size. The structure of
  differential rotation is similar in all of our more rapidly rotating
  suns, with fast equators and slower poles. We find that the total
  shear in differential rotation Δ Ω grows with more rapid rotation,
  while the relative shear Δ Ω/Ω<SUB>0</SUB> decreases. In contrast,
  at more rapid rotation, the meridional circulations decrease in energy
  and peak velocities and break into multiple cells of circulation in
  both radius and latitude.

Title: Structure and Evolution of Giant Cells in Global Models of
    Solar Convection
Authors: Miesch, Mark S.; Brun, Allan Sacha; DeRosa, Marc L.;
   Toomre, Juri
Bibcode: 2008ApJ...673..557M
Altcode: 2007arXiv0707.1460M
  The global scales of solar convection are studied through
  three-dimensional simulations of compressible convection carried out
  in spherical shells of rotating fluid that extend from the base of
  the convection zone to within 15 Mm of the photosphere. Such modeling
  at the highest spatial resolution to date allows study of distinctly
  turbulent convection, revealing that coherent downflow structures
  associated with giant cells continue to play a significant role in
  maintaining the differential rotation that is achieved. These giant
  cells at lower latitudes exhibit prograde propagation relative to
  the mean zonal flow, or differential rotation, that they establish,
  and retrograde propagation of more isotropic structures with vortical
  character at mid and high latitudes. The interstices of the downflow
  networks often possess strong and compact cyclonic flows. The
  evolving giant-cell downflow systems can be partly masked by the
  intense smaller scales of convection driven closer to the surface,
  yet they are likely to be detectable with the helioseismic probing that
  is now becoming available. Indeed, the meandering streams and varying
  cellular subsurface flows revealed by helioseismology must be sampling
  contributions from the giant cells, yet it is difficult to separate
  out these signals from those attributed to the faster horizontal flows
  of supergranulation. To aid in such detection, we use our simulations
  to describe how the properties of giant cells may be expected to vary
  with depth and how their patterns evolve in time.

Title: Rapid rotation, active nests of convection and global-scale
    flows in solar-like stars
Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Miesch, M. S.;
   Toomre, J.
Bibcode: 2007AN....328.1002B
Altcode: 2008arXiv0801.1672B
  In the solar convection zone, rotation couples with intensely turbulent
  convection to build global-scale flows of differential rotation and
  meridional circulation. Our sun must have rotated more rapidly in its
  past, as is suggested by observations of many rapidly rotating young
  solar-type stars. Here we explore the effects of more rapid rotation
  on the patterns of convection in such stars and the global-scale
  flows which are self-consistently established. The convection in
  these systems is richly time dependent and in our most rapidly
  rotating suns a striking pattern of spatially localized convection
  emerges. Convection near the equator in these systems is dominated by
  one or two patches of locally enhanced convection, with nearly quiescent
  streaming flow in between at the highest rotation rates. These active
  nests of convection maintain a strong differential rotation despite
  their small size. The structure of differential rotation is similar
  in all of our more rapidly rotating suns, with fast equators and
  slower poles. We find that the total shear in differential rotation,
  as measured by latitudinal angular velocity contrast, \Delta \Omega,
  increases with more rapid rotation while the relative shear, \Delta
  \Omega/ \Omega, decreases. In contrast, at more rapid rotation the
  meridional circulations decrease in both energy and peak velocities and
  break into multiple cells of circulation in both radius and latitude.

Title: Dynamo action in simulations of penetrative solar convection
    with an imposed tachocline
Authors: Browning, M. K.; Brun, A. S.; Miesch, M. S.; Toomre, J.
Bibcode: 2007AN....328.1100B
Altcode:
  We summarize new and continuing three-dimensional spherical shell
  simulations of dynamo action by convection allowed to penetrate
  downward into a tachocline of rotational shear. The inclusion
  of an imposed tachocline allows us to examine several processes
  believed to be essential in the operation of the global solar dynamo,
  including differential rotation, magnetic pumping, and the stretching
  and organization of fields within the tachocline. In the stably
  stratified core, our simulations reveal that strong axisymmetric
  magnetic fields (of ∼ 3000 G strength) can be built, and that those
  fields generally exhibit a striking antisymmetric parity, with fields
  in the northern hemisphere largely of opposite polarity to those in
  the southern hemisphere. In the convection zone above, fluctuating
  fields dominate over weaker mean fields. New calculations indicate
  that the tendency toward toroidal fields of antisymmetric parity
  is relatively insensitive to initial magnetic field configurations;
  they also reveal that on decade-long timescales, the magnetic fields
  can briefly enter (and subsequently emerge from) states of symmetric
  parity. We have not yet observed any overall reversals of the field
  polarity, nor systematic latitudinal propagation.

Title: Dynamo action in the presence of an imposed magnetic field
Authors: Featherstone, N. A.; Browning, M. K.; Brun, A. S.; Toomre, J.
Bibcode: 2007AN....328.1126F
Altcode:
  Dynamo action within the cores of Ap stars may offer intriguing
  possibilities for understanding the persistent magnetic fields observed
  on the surfaces of these stars. Deep within the cores of Ap stars,
  the coupling of convection with rotation likely yields magnetic dynamo
  action, generating strong magnetic fields. However, the surface fields
  of the magnetic Ap stars are generally thought to be of primordial
  origin. Recent numerical models suggest that a primordial field in
  the radiative envelope may possess a highly twisted toroidal shape. We
  have used detailed 3-D simulations to study the interaction of such a
  twisted magnetic field in the radiative envelope with the core-dynamo
  operating in the interior of a 2 solar mass A-type star. The resulting
  dynamo action is much more vigorous than in the absence of such a
  fossil field, yielding magnetic field strengths (of order 100 kG)
  much higher than their equipartition values relative to the convective
  velocities. We examine the generation of these fields, as well as the
  growth of large-scale magnetic structure that results from imposing
  a fossil magnetic field.

Title: Strong Dynamo Action in Rapidly Rotating Suns
Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha;
   Miesch, Mark S.; Nelson, Nicholas J.; Toomre, Juri
Bibcode: 2007AIPC..948..271B
Altcode: 2008arXiv0801.1684B
  Stellar dynamos are driven by complex couplings between rotation and
  turbulent convection, which drive global-scale flows and build and
  rebuild stellar magnetic fields. When stars like our sun are young,
  they rotate much more rapidly than the current solar rate. Observations
  generally indicate that more rapid rotation is correlated with stronger
  magnetic activity and perhaps more effective dynamo action. Here
  we examine the effects of more rapid rotation on dynamo action in a
  star like our sun. We find that vigorous dynamo action is realized,
  with magnetic field generated throughout the bulk of the convection
  zone. These simulations do not possess a penetrative tachocline of shear
  where global-scale fields are thought to be organized in our sun, but
  despite this we find strikingly ordered fields, much like sea-snakes
  of toroidal field, which are organized on global scales. We believe
  this to be a novel finding.

Title: Convective Core Dynamos of A-type Stars in the Presence of
    Fossil Magnetic Fields
Authors: Featherstone, N. A.; Browning, M. K.; Brun, A. S.; Toomre, J.
Bibcode: 2007AIPC..948..279F
Altcode:
  The persistent magnetic fields of Ap stars are generally thought to
  be of primordial origin, but dynamo generation of magnetic fields may
  offer alternative possibilities. Deep within the interiors of such
  stars, vigorous core convection likely couples with rotation to yield
  magnetic dynamo action, generating strong magnetic fields. Recent
  numerical models suggest that a primordial field remaining from the
  star's formation may possess a highly twisted toroidal shape in the
  radiative interior. We have used detailed 3-D simulations to study the
  interaction of such a magnetic field with a dynamo generated within the
  core of a 2 solar mass A-type star. Dynamo action realized under these
  circumstances is much more vigorous than in the absence of a fossil
  field in the radiative envelope, yielding magnetic field strengths (of
  order 100 kG) much higher than their equipartition values relative to
  the convective velocities. We examine the generation of these fields,
  as well as their effect on the complex dynamics of the convective core.

Title: Global Models of Solar Convection
Authors: Miesch, Mark S.; Browning, Matthew K.; Brun, Allan Sacha;
   Toomre, Juri
Bibcode: 2007AIPC..948..149M
Altcode:
  Convection is fundamental and enigmatic enough to rank high on any
  pundit's list of unsolved problems in stellar physics. It is responsible
  in large part for why stars shine since most stellar interiors are
  at least partially convective. Furthermore, convection plays an
  essential role in how stars build magnetic fields. Magnetism in turn
  accounts for most short-term solar and stellar variability. Despite
  its ubiquity, stellar convection is challenging to model theoretically
  or numerically. In this paper we provide an overview of some recent
  insights into solar and stellar convection obtained from high-resolution
  numerical simulations. Thanks to continuing advances in high performance
  computing technology, such simulations continue to achieve unprecedented
  parameter regimes revealing turbulent dynamics inaccessible to previous
  models. Here we focus in particular on the subtle and profound influence
  of the complex boundary layers which exist near the top and bottom of
  the solar convection zone.

Title: Challenges of magnetism in the turbulent Sun
Authors: Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri
Bibcode: 2007IAUS..239..488B
Altcode:
  No abstract at ADS

Title: Simulations of solar magnetic dynamo action in the convection
    zone and tachocline
Authors: Browning, Matthew K.; Miesch, Mark S.; Brun, Allan Sacha;
   Toomre, Juri
Bibcode: 2007IAUS..239..510B
Altcode:
  No abstract at ADS

Title: Magnetic Dynamo Action In The Convective Cores Of A-type
    Stars In The Presence Of Fossil Fields
Authors: Featherstone, Nicholas; Browning, M. K.; Brun, A. S.;
   Toomre, J.
Bibcode: 2007AAS...210.1702F
Altcode: 2007BAAS...39Q.117F
  The intense surface magnetism of Ap stars has attracted much
  scrutiny. The observed persistent fields are generally thought to be
  of primordial origin, but dynamo generation of magnetic fields may
  offer alternative possibilities. Deep within the interiors of such
  stars, vigorous core convection likely couples with rotation to yield
  magnetic dynamo action, generating strong magnetic fields. Recent
  numerical models suggest that a primordial field remaining from the
  star’s formation may possess a highly twisted toroidal shape in the
  radiative interior. We have used detailed 3-D simulations to study the
  interaction of such a magnetic field with a dynamo generated within the
  core of a 2 solar mass A-type star. Dynamo action realized under these
  circumstances is much more vigorous than in the absence of a fossil
  field in the radiative envelope, yielding magnetic field strengths (of
  order 100 kG) much higher than their equipartition values relative to
  the convective velocities. We examine the generation of these fields,
  as well as their effect on the complex dynamics of the convective core.

Title: Structure and Evolution of Giant Cells in Global Models of
    Solar Convection
Authors: Miesch, Mark S.; Brun, A. S.; De Rosa, M. L.; Toomre, J.
Bibcode: 2007AAS...210.2217M
Altcode: 2007BAAS...39..127M
  We present the highest-resolution simulations of global-scale solar
  convection so far achieved, dealing with turbulent compressible
  flows interacting with rotation in a full spherical shell. The
  three-dimensional simulation domain extends from 0.71R-0.98R, close
  enough to the photosphere to overlap with solar subsurface weather
  (SSW) maps inferred from local helioseismology. The convective patterns
  achieved are complex and continually evolving on a time scale of several
  days. However, embedded within the intricate downflow network near
  the surface are coherent downflow lanes associated with giant cells
  which persist for weeks to months and which extend through much of the
  convection zone. These coherent downflow lanes are generally confined
  to low latitudes and are oriented in a north-south direction. The low
  dissipation in these simulations permits a more realistic balance of
  forces which yields differential rotation and meridional circulation
  profiles in good agreement with those inferred from helioseismology.

Title: Round table discussion of session G: MHD convection and dynamos
Authors: Toomre, Juri
Bibcode: 2007IAUS..239..494T
Altcode:
  No abstract at ADS

Title: Rapid Rotation And Nests Of Convection In Solar-like Stars
Authors: Brown, Benjamin; Browning, M. K.; Brun, A. S.; Miesch, M. S.;
   Toomre, J.
Bibcode: 2007AAS...210.1703B
Altcode: 2007BAAS...39..117B
  Earlier in its life our Sun must have rotated considerably more
  rapidly, given that its magnetized wind slowly carries away angular
  momentum. Indeed many G-type stars are found to rotate rapidly, and
  their deep convective envelopes and the dynamos operating there must
  sense the effects of rotation. Here we use 3-D simulations to study
  the differential rotation and patterns of convection established in
  these more rapidly rotating stars. Our simulations with the anelastic
  spherical harmonic (ASH) code capture the deep solar convection
  zone with a solar-like radial stratification and within a spherical
  geometry, which admits global-scale flows. We explore a range of
  rotation rates from 1 to 10 times the solar rotation rate. Convection
  in the equatorial regions of these rapidly rotating stars shows strong
  longitudinal modulation. At the fastest rotation rates, convection is
  restricted to active nests spanning compact regions in longitude, with
  quiescent streaming flow filling the regions in between. These nests
  of convection persist for long periods and drive a strong differential
  rotation. Convection at high latitudes is more isotropic but couples
  to the equatorial regions through the meridional circulations present
  throughout the shell.

Title: Dynamo Action, Magnetic Activity, And Rotation In F Stars
Authors: Augustson, Kyle; Brown, B. P.; Brun, A. S.; Toomre, J.
Bibcode: 2007AAS...210.1701A
Altcode: 2007BAAS...39..117A
  The origin of stellar magnetic fields must rest with dynamo
  processes occurring deep within a star. Observations of F-type stars
  suggest unusual relations between their rotation rates and magnetic
  activity. Generally in cooler stars, magnetic activity increases with
  more rapid rotation, but, in F-type stars, there is observational
  evidence for a sharp transition from this behavior around spectral
  type F5. Stars hotter than F5 show an anti-correlation between
  magnetic activity and rotation: more rapidly rotating stars seem
  to possess weaker magnetic fields, possibly because they have less
  efficient dynamos. We have conducted 3-D simulations of compressible
  MHD convection with the anelastic spherical harmonic (ASH) code,
  in order to study F-type star convection zone dynamics in rotating
  spherical shells. Our initial radial stratification is based on stellar
  models of stars in the narrow mass range between 1.2 and 1.4 solar
  masses. We exhibit the resulting differential rotation profiles and
  rich convective behavior realized as the rotation rates of the stars
  are increased. We also discuss our preliminary foray into studying
  the magnetic dynamo achieved within several models, considering the
  effects of rotation rates.

Title: Helioseismic Searches for the Elusive Giant Cells of Convection
Authors: Featherstone, Nicholas; Hindman, B. W.; Haber, D. A.;
   Toomre, J.
Bibcode: 2007AAS...210.2216F
Altcode: 2007BAAS...39..127F
  The turbulent solar convection zone exhibits a range of scales of
  convection which are visible at the solar surface, ranging from
  granules ( 1 Mm) to supergranules ( 30 Mm). Numerical simulations of
  solar convection carried out in full-spherical shells consistently
  reveal even larger scales of convection, termed giant cells, which
  may span a few hundred Mm in the horizontal and extend throughout
  the depth of the convection zone. Recent correlation tracking of
  supergranular motions has revealed the tendency of supergranules to
  align themselves in the north-south direction. This alignment may be
  due to organization by larger-scale giant-cell motions and is generally
  weak, with the strongest alignment occurring at low latitudes. Using
  f-mode time-distance helioseismology, we have probed the flow signals
  associated with the presence of these giant cells and have found
  good agreement with the results from previous correlation tracking
  studies. Moreover, we find that the horizontal divergence of our
  measured flows exhibit particularly striking alignment at larger scales.

Title: Strong Global Dynamo Action in a Younger Sun
Authors: Brown, Benjamin; Brun, A. S.; Miesch, M. S.; Toomre, J.
Bibcode: 2007AAS...210.2414B
Altcode: 2007BAAS...39..130B
  Stellar dynamos are powered by the coupling of rotation, convection and
  the global scale flows which are established in these systems. Our Sun
  has lost angular momentum through its magnetized wind and once rotated
  more rapidly than it currently does. We explore the nature of dynamo
  action in a younger sun rotating five times its current rate. Our
  explorations employ 3-D simulations of compressible MHD convection
  within a spherical shell extending from 0.72 to 0.97 solar radii using
  the anelastic spherical harmonic (ASH) code on massively parallel
  supercomputers. The dynamo which naturally arises in this convective
  system is vigorous and builds organized magnetic structures which
  fill the bulk of the convection zone. This is in striking contrast
  to the global dynamo thought to operate in the current sun, which
  appears to require the pumping of magnetic field into a tachocline of
  shear at the base of the convection zone to generate similar magnetic
  structures. Particularly in the equatorial regions, we find strong
  toroidal fields ( 30 kG) coexisting with the turbulent convection. This
  dynamo system exhibits cyclic behavior, with the large-scale toroidal
  and poloidal fields switching their polarity.

Title: Temporal variations in solar rotation at the bottom of the
convection zone: The current status
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R.;
   Schou, J.; Thompson, M. J.; Toomre, J.
Bibcode: 2007AdSpR..40..915H
Altcode:
  We present the most recent results on the short-period variations
  in the solar rotation rate near the base of the convection zone. The
  1.3-year period which was reported in the early years of solar cycle 23
  appears not to persist after 2001, but there are hints of fluctuations
  at a different period during the declining phase of the cycle.

Title: Helioseismically Determined Near-Surface Flows Underlying a
    Quiescent Filament
Authors: Hindman, Bradley W.; Haber, Deborah A.; Toomre, Juri
Bibcode: 2006ApJ...653..725H
Altcode:
  The extended filaments seen in Hα images of the solar disk, and the
  corresponding prominences when viewed at the solar limb, are one of
  the great hallmarks of solar magnetism. Such arches of magnetic field
  and the coronal plasma structures they support are both beautiful and
  enigmatic. Many models of filament formation and maintenance invoke the
  existence of surface plasma flows, which are used to drive the magnetic
  reconnection needed to form twisted loops of flux held down by a coronal
  arcade. These flows are typically composed of a converging flow, which
  brings flux elements of opposite polarity together, combined with a
  tangential shear that stresses the coronal arcade. In this paper we
  present helioseismic measurements of near-surface flows underlying a
  single quiescent filament lying within a decayed active region. Newly
  devised high-resolution ring analyses (HRRA) with both 2° and 4°
  spatial resolution were applied to Doppler imaging data provided by the
  Michelson Doppler Imager (MDI) instrument on the SOHO spacecraft. A
  long-lived filament appearing in 2002 May and April was studied. We
  find that the filament channel is a region of vigorous subphotospheric
  convection. The largest observed scales of such convection span
  the region of weak magnetic field separating the active region's two
  polarities. Thus, the magnetic neutral line that forms the spine of the
  filament channel tends to lie along the centers of large convection
  cells. In temporal and spatial averages of the flow field, we do not
  find a systematic converging flow. However, we do detect a significant
  shearing flow parallel to the neutral line. This shear takes the form
  of two oppositely directed jets, one to either side of the neutral line
  and within 20 Mm of the line. The jets produce a net shear in the flow
  speed of 30 m s<SUP>-1</SUP> occurring over a distance of 20 Mm.

Title: Helioseismic probing of giant-cell convection
Authors: Featherstone, N. A.; Haber, D. A.; Hindman, B. W.; Toomre, J.
Bibcode: 2006ESASP.624E.133F
Altcode: 2006soho...18E.133F
  No abstract at ADS

Title: Subsurface convective flows within active regions
Authors: Hindman, B. W.; Haber, D. A.; Toomre, J.
Bibcode: 2006ESASP.624E..11H
Altcode: 2006soho...18E..11H
  No abstract at ADS

Title: Large-scale circulations using ring analysis
Authors: Haber, D.; Hindman, B.; Toomre, J.; Bogart, R. S.
Bibcode: 2006ESASP.624E..45H
Altcode: 2006soho...18E..45H
  No abstract at ADS

Title: Various dynamical puzzle pieces in the seismic Rubik's cube
Authors: Toomre, J.
Bibcode: 2006ESASP.624E...1T
Altcode: 2006soho...18E...1T
  No abstract at ADS

Title: Dynamo Action in the Solar Convection Zone and Tachocline:
    Pumping and Organization of Toroidal Fields
Authors: Browning, Matthew K.; Miesch, Mark S.; Brun, Allan Sacha;
   Toomre, Juri
Bibcode: 2006ApJ...648L.157B
Altcode: 2006astro.ph..9153B
  We present the first results from three-dimensional spherical shell
  simulations of magnetic dynamo action realized by turbulent convection
  penetrating downward into a tachocline of rotational shear. This permits
  us to assess several dynamical elements believed to be crucial to the
  operation of the solar global dynamo, variously involving differential
  rotation resulting from convection, magnetic pumping, and amplification
  of fields by stretching within the tachocline. The simulations reveal
  that strong axisymmetric toroidal magnetic fields (about 3000 G in
  strength) are realized within the lower stable layer, unlike in the
  convection zone where fluctuating fields are predominant. The toroidal
  fields in the stable layer possess a striking persistent antisymmetric
  parity, with fields in the northern hemisphere largely of opposite
  polarity to those in the southern hemisphere. The associated mean
  poloidal magnetic fields there have a clear dipolar geometry, but
  we have not yet observed any distinctive reversals or latitudinal
  propagation. The presence of these deep magnetic fields appears to
  stabilize the sense of mean fields produced by vigorous dynamo action
  in the bulk of the convection zone.

Title: Introductory - Overview: Close interplay between global
    helioseismology and dynamical models
Authors: Toomre, J.
Bibcode: 2006IAUJD..17E...1T
Altcode:
  The nearly continuous full-disk imaging of solar resonant oscillations
  with both the ground-based Global Oscillation Network Group (GONG)
  and the space-based Michelson Doppler Imager (MDI) on SOHO have
  yielded detailed inferences about differential rotation, meridional
  circulations, and large-scale streaming flows within the solar
  convection zone. Of particular interest has been the evolution of such
  dynamical structures, and their coupling to magnetism, variously in the
  tachocline of rotational shear at its base and in the near-surface shear
  layer. We review properties of such dynamics involving variations in
  rotation rates near the tachocline, of propagating banded features in
  the differential rotation in the upper reaches of the convection zone,
  and of evolving patterns in the circulations there. In addition, local
  helioseismic probing shows the presence of striking subsurface flows
  appearing variously as meandering jets and a wide range of structured
  and possibly cellular flows. These samplings of dynamics proceeding
  within the solar convection zone provides challenges and inspiration
  for three-dimensional simulations of turbulent convection, rotation
  and magnetism in spherical shells now enabled by massively-parallel
  supercomputers. We review the interplay between features emerging
  from such high-resolution simulations of the solar convection zone and
  the richness of dynamics being revealed by helioseismic probing. The
  simulations now make good contact with differential rotation profiles
  so deduced in the bulk of the convection zone. Yet all models possess
  complex downflow structures that extend over most of that zone. Such
  large-scale convection so evident in global simulations may now have
  been identified in the helioseismic data, with simulations guiding
  the manner in which the elusive giant cells may be detected amidst
  the intense flows of supergranulation.

Title: Solar-Cycle Variations of Internal Structure, Rotation and
    Circulations
Authors: Toomre, J.
Bibcode: 2006IAUJD...8E..67T
Altcode:
  Helioseismology is permitting detailed study of structure and dynamics
  in the solar interior as the magnetic cycle advances. Although
  many International helioseismic projects have contributed, the
  nearly continuous Doppler imaging provided for over ten years by the
  ground-based Global Oscillation Network Group (GONG) project and the
  Michelson Doppler Imager (MDI) on the SOHO spacecraft allow us to
  evaluate changes within the sun over a significant fraction of the
  22-year activity cycle. Nearly 10 million resonant acoustic modes of
  oscillation observable in the solar atmosphere provide probes of flows
  and structures over a wide range of depths within the solar convection
  zone and the tachocline of rotational shear at its base. The global
  magnetic dynamo responsible for the activity cycles is believed to
  operate in a distributed manner throughout these regions, but the
  principal stretching to achieve strong toroidal magnetic fields
  (responsible for the eventual emergence of sunspot pairs) proceeds
  in the tachocline. We review the evidence for variations in the
  differential rotation observed near the tachocline, of propagating
  bands of zonal flow speedup observed in the near-surface shear layer,
  and of changes in the meridional circulations as the cycle advances. We
  also discuss the evolving patterns of streaming flows known as solar
  subsurface weather (SSW) and of their interactions with magnetic active
  regions, often exhibiting prominent inflows at shallow depths and strong
  outflows deeper down within that near-surface shear layer. Such a range
  of clues being provided by helioseismology about the complex dynamics
  proceeding with the convection zone are serving to guide efforts to
  build self-consistent models of the solar global dynamo.

Title: Solar Filament Evolution in the Presence of Subsurface Flows
Authors: Haber, Deborah A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.
Bibcode: 2006SPD....37.3202H
Altcode: 2006BAAS...38..257H
  Many models of filament formation and evolution are driven by
  converging and shearing flows in the photosphere and upper convection
  zone, where the gas is dense enough to move the magnetic footpoints
  of a filament. With our recent development of High-Resolution Ring
  Analysis (HRRA) procedures, we are now able to measure flows below
  the surface with a horizontal resolution of 2 heliographic degrees
  (∼20 Mm). With this HRRA analysis of the flows underlying filaments
  and filament channels, we have found evidence of shearing flows along
  the neutral line in at least one instance and will be presenting the
  results from several more filaments. This research is funded in part
  by NASA grants NAG5-12491 and NNG05GM83G.

Title: Helioseismic Probing of Giant-Cell Convection
Authors: Featherstone, Nicholas; Haber, D. A.; Hindman, B. W.;
   Toomre, J.
Bibcode: 2006SPD....37.3201F
Altcode: 2006BAAS...38R.257F
  The turbulent solar convection zone exhibits a range of scales
  of convection which are visible at the solar surface, ranging from
  granules ( 1 Mm) to supergranules ( 30 Mm). Numerical simulations of
  solar convection carried out in full spherical shells consistently
  reveal even larger scales of convection, termed giant cells, which
  may span a few hundreds of Mm in the horizontal and extend over much
  of the convection zone. Recent correlation tracking of supergranular
  motions has revealed the tendency of supergranules to align themselves
  in the north-south direction. This alignment is possibly due to
  organization by larger-scale giant cell motions and is generally weak,
  with the strongest alignment occurring at the equator. Using f-mode
  time-distance and specialized averaging and tracking techniques, we
  probe for the possible flow signals associated with the presence of
  these giant cells near the solar equator.

Title: Localized Nests of Convection in Rapidly Rotating Suns
Authors: Brown, Benjamin; Browning, M.; Brun, A.; Toomre, J.
Bibcode: 2006SPD....37.3205B
Altcode: 2006BAAS...38..258B
  Many solar-like stars rotate more rapidly than the sun. Through
  their magnetized winds, these stars gradually lose angular momentum
  and spin down. By similar processes, our Sun must have rotated more
  rapidly in the past than it currently does. We explore the effects
  of more rapid rotation upon turbulent stellar convection, studying
  full spherical shells that admit global scale flows. We conduct 3-D
  simulations of compressible turbulent convection with the anelastic
  spherical harmonic (ASH) code on massively parallel supercomputers. For
  simplicity, we adopt the radial stratification of the present-day sun
  and examine global scale convection in a zone extending from 0.72 to
  0.97 solar radii, and consider a range of rotation rates from 1 to 5
  times the solar rotation rate. With increasing rotation we observe
  that convection at low latitudes becomes spatially modulated in
  strength, yielding localized nests of strong convection. These nests
  are persistent over very long periods and propagate in longitude at
  slower rates than individual convective structures within them. It
  is striking that a strong differential rotation is achieved by these
  modulated states. The convection at high latitudes is more isotropic
  but influenced by the meridional circulations present throughout the
  shell. Weak modulation can be recognized even at the solar rotation
  rate, with some implications for active magnetic longitudes in the Sun.

Title: Solar Differential Rotation Influenced by Latitudinal Entropy
    Variations in the Tachocline
Authors: Miesch, Mark S.; Brun, Allan Sacha; Toomre, Juri
Bibcode: 2006ApJ...641..618M
Altcode:
  Three-dimensional simulations of solar convection in spherical shells
  are used to evaluate the differential rotation that results as thermal
  boundary conditions are varied. In some simulations a latitudinal
  entropy variation is imposed at the lower boundary in order to take
  into account the coupling between the convective envelope and the
  radiative interior through thermal wind balance in the tachocline. The
  issue is whether the baroclinic forcing arising from tachocline-induced
  entropy variations can break the tendency for numerical simulations of
  convection to yield cylindrical rotation profiles, unlike the conical
  profiles deduced from helioseismology. As the amplitude of the imposed
  variation is increased, cylindrical rotation profiles do give way to
  more conical profiles that exhibit nearly radial angular velocity
  contours at midlatitudes. Conical rotation profiles are maintained
  primarily by the resolved convective heat flux, which transmits entropy
  variations from the lower boundary into the convective envelope, giving
  rise to baroclinic forcing. The relative amplitude of the imposed
  entropy variations is of order 10<SUP>-5</SUP>, corresponding to a
  latitudinal temperature variation of about 10 K. The role of thermal
  wind balance and tachocline-induced entropy variations in maintaining
  the solar differential rotation is discussed.

Title: Simulations of Core Convection in Rotating A-Type Stars:
    Magnetic Dynamo Action
Authors: Brun, Allan Sacha; Browning, Matthew K.; Toomre, Juri
Bibcode: 2005ApJ...629..461B
Altcode: 2006astro.ph.10072B
  Core convection and dynamo activity deep within rotating A-type
  stars of 2 M<SUB>solar</SUB> are studied with three-dimensional
  nonlinear simulations. Our modeling considers the inner 30% by
  radius of such stars, thus capturing within a spherical domain the
  convective core and a modest portion of the surrounding radiative
  envelope. The magnetohydrodynamic (MHD) equations are solved using the
  anelastic spherical harmonic (ASH) code to examine turbulent flows and
  magnetic fields, both of which exhibit intricate time dependence. By
  introducing small seed magnetic fields into our progenitor hydrodynamic
  models rotating at 1 and 4 times the solar rate, we assess here how
  the vigorous convection can amplify those fields and sustain them
  against ohmic decay. Dynamo action is indeed realized, ultimately
  yielding magnetic fields that possess energy densities comparable to
  that of the flows. Such magnetism reduces the differential rotation
  obtained in the progenitors, partly by Maxwell stresses that transport
  angular momentum poleward and oppose the Reynolds stresses in the
  latitudinal balance. In contrast, in the radial direction we find
  that the Maxwell and Reynolds stresses may act together to transport
  angular momentum. The central columns of slow rotation established in
  the progenitors are weakened, with the differential rotation waxing and
  waning in strength as the simulations evolve. We assess the morphology
  of the flows and magnetic fields, their complex temporal variations,
  and the manner in which dynamo action is sustained. Differential
  rotation and helical convection are both found to play roles in
  giving rise to the magnetic fields. The magnetism is dominated by
  strong fluctuating fields throughout the core, with the axisymmetric
  (mean) fields there relatively weak. The fluctuating magnetic fields
  decrease rapidly with radius in the region of overshooting, and the
  mean toroidal fields less so due to stretching by rotational shear.

Title: Helioseismic Ring Analyses of Artificial Data Computed for
    Two-dimensional Shearing Flows
Authors: Hindman, Bradley W.; Gough, Douglas; Thompson, Michael J.;
   Toomre, Juri
Bibcode: 2005ApJ...621..512H
Altcode:
  The local helioseismological technique of ring analysis has been
  crucial in the discovery of complex large-scale flows in the Sun's
  near-surface shear layer. However, current implementations of
  ring-analysis procedures assume that the flow field is horizontally
  homogeneous over the analysis region. This assumption is certainly
  incorrect, and in the present paper we assess the significance of this
  approximation by analyzing artificial data sets computed from models of
  horizontal shear flows. We consider the simple case of purely horizontal
  and unidirectional flow that varies solely in the horizontal direction
  orthogonal to the flow in a piecewise-constant manner. An ensemble
  of plane waves is incident on the flow, and the scattered wave field
  produced by the prescribed two-dimensional flow is computed to generate
  an artificial helioseismic power spectrum. The artificial spectrum
  is processed in a manner similar to standard ring analysis, and the
  flow field that is thereby inferred is compared with the known imposed
  flow. We find that the inferred flow velocity is essentially an average
  of the true flow velocity over the region of the analysis, weighted by
  the square of the spatial apodization function used in processing the
  oscillation signal. Furthermore, the shape of a p-mode line profile
  is determined by the distribution of speeds across the analysis region.

Title: Simulations of core convection and resulting dynamo action
    in rotating A-type stars
Authors: Browning, Matthew K.; Brun, Allan S.; Toomre, Juri
Bibcode: 2004IAUS..224..149B
Altcode: 2004astro.ph..9703B
  We present the results of 3-D nonlinear simulations of magnetic dynamo
  action by core convection within A-type stars of 2 M<SUB>⊙</SUB> with
  a range of rotation rates. We consider the inner 30% by radius of such
  stars, with the spherical domain thereby encompassing the convective
  core and a portion of the surrounding radiative envelope. The
  compressible Navier-Stokes equations, subject to the anelastic
  approximation, are solved to examine highly nonlinear flows that span
  multiple scale heights, exhibit intricate time dependence, and admit
  magnetic dynamo action. Small initial seed magnetic fields are found
  to be amplified greatly by the convective and zonal flows. The central
  columns of strikingly slow rotation found in some of our progenitor
  hydrodynamic simulations continue to be realized in some simulations
  to a lesser degree, with such differential rotation arising from the
  redistribution of angular momentum by the nonlinear convection and
  magnetic fields. We assess the properties of the magnetic fields thus
  generated, the extent of the convective penetration, the magnitude of
  the differential rotation, and the excitation of gravity waves within
  the radiative envelope.

Title: Evolution of Solar Supergranulation
Authors: De Rosa, Marc L.; Toomre, Juri
Bibcode: 2004ApJ...616.1242D
Altcode:
  The structure and evolution of solar supergranulation is studied using
  horizontal velocity fields, deduced from applying local correlation
  tracking (LCT) techniques to full-disk, line-of-sight Doppler velocity
  data observed by the Michelson Doppler Imager on board the Solar
  and Heliospheric Observatory spacecraft. Two 45° square regions
  of photospheric plasma, one of the quiet Sun and one with increased
  magnetic activity, are tracked for as long as they remain visible on
  the disk of the Sun (about 6 days), enabling a determination of the
  complete life histories of over 3000 supergranules in each region. With
  this method, the horizontal outflows associated with the pattern of
  supergranulation are revealed with clarity, even for locations near
  disk center where little of the horizontal velocity field is projected
  into the line of sight. The LCT flow mappings are of sufficient temporal
  extent that they can be used to study the complex evolution of a broad
  spectrum of supergranules, revealing that merging and fragmentation
  events figure prominently in the life histories of more than half of the
  supergranules in each data set. Such dynamics lead to many short-lived
  supergranules (about 75% of the total population) having lifetimes of
  less than 24 hr, coexisting among numerous long-lived supergranules,
  many of which exist for several days. Average supergranular lifetimes
  lie in the 16-23 hr range, although about 7% of all are recognizable
  for time periods of 48 hr or more. The average supergranular cell
  diameter lies in the 12-20 Mm range, with smaller cells more prevalent
  in areas of greater magnetism. There exists a tendency for larger cells
  to preferentially have longer lifetimes when embedded in a region of
  increased magnetic flux.

Title: Core Convection and Dynamo Action in Rotating A-type Stars
Authors: Browning, M. K.; Brun, A. S.; Toomre, J.
Bibcode: 2004AAS...205.3403B
Altcode: 2004BAAS...36.1402B
  We have carried out 3-D simulations of core convection and dynamo
  activity within A-type stars of two solar masses at a range of rotation
  rates. Our models consider the inner 30% by radius of such stars, thus
  capturing the entire convective core and a portion of the surrounding
  radiative envelope within the spherical computational domain. Using
  the anelastic spherical harmonic (ASH) code on massively parallel
  supercomputers, we solve the compressible MHD equations to examine
  highly nonlinear and evolving flows and magnetic fields. Vigorous
  dynamo action is realized, with initial seed magnetic fields amplified
  by many orders of magnitude and sustained against ohmic decay. The
  resulting complex magnetism possesses energy densities comparable to
  that in the flows, is structured on many scales, and serves to modify
  the convective and zonal flows that gave rise to it. The differential
  rotation established in progenitor hydrodynamic simulations is weakened,
  and waxes and wanes in strength as the simulations evolve. We discuss
  the morphology and evolution of the flows and magnetic fields,
  the penetrative properties of the convection, and the nature of the
  dynamo process.

Title: Simulations of Core Convection and Dynamo Activity in Rotating
    A-Type Stars
Authors: Browning, M. K.; Brun, A. S.; Toomre, J.
Bibcode: 2004ESASP.559..349B
Altcode: 2004soho...14..349B
  No abstract at ADS

Title: Subphotospheric Flows Near Active Region NOAA 10486
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
   Thompson, M. J.
Bibcode: 2004ESASP.559..148H
Altcode: 2004soho...14..148H
  No abstract at ADS

Title: Cause of Shrinking Sun Effect in Local Correlation Tracking
    and Impacts on the Mapping of Ssw Flows
Authors: Lisle, J.; Toomre, J.
Bibcode: 2004ESASP.559..556L
Altcode: 2004soho...14..556L
  No abstract at ADS

Title: Differential Rotation when the Sun Spun Faster
Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Toomre, J.
Bibcode: 2004ESASP.559..341B
Altcode: 2004soho...14..341B
  No abstract at ADS

Title: Comparison of Solar Subsurface Flows Assessed by Ring and
    Time-Distance Analyses
Authors: Hindman, Bradley W.; Gizon, Laurent; Duvall, Thomas L., Jr.;
   Haber, Deborah A.; Toomre, Juri
Bibcode: 2004ApJ...613.1253H
Altcode:
  The solar near-surface shear layer exhibits a rich medley of flows
  that are now being measured by a variety of local helioseismic
  techniques. We present comparisons of the horizontal flows obtained
  with two of these techniques, ring and time-distance analyses, applied
  to Michelson Doppler Imager (MDI) Dynamics Program data from the years
  1998 and 1999. The ring analyses use the frequencies of both f and
  p modes in inversions to obtain flows within the near-surface shear
  layer as a function of depth. The f-mode time-distance analyses make
  velocity inferences just beneath the photosphere. After degrading
  the spatial resolution of the time-distance analyses to match the
  coarser resolution of the ring analyses, we find that the flows deduced
  with the two methods are remarkably similar, with common inflow and
  outflow sites as well as agreement in flow direction. The flows from
  ring and time-distance analyses are highly correlated with each other
  (correlation coefficients ~0.8) direct correspondence of features
  in the flows is largely realized in both the quiet-Sun and magnetic
  active regions.

Title: Time-Distance Helioseismology: a Fourier Transform Method
    and Measurement of Reynolds Stresses
Authors: Featherstone, N. A.; Hindman, B. W.; Haber, D. A.; Toomre, J.
Bibcode: 2004ESASP.559..428F
Altcode: 2004soho...14..428F
  No abstract at ADS

Title: Comparison of Local Helioseismic Techniques Applied to MDI
    Doppler Data
Authors: Hindman, B. W.; Featherstone, N. A.; Haber, D. A.; Musman,
   S.; Toomre, J.
Bibcode: 2004ESASP.559..460H
Altcode: 2004soho...14..460H
  No abstract at ADS

Title: Global-Scale Turbulent Convection and Magnetic Dynamo Action
    in the Solar Envelope
Authors: Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri
Bibcode: 2004ApJ...614.1073B
Altcode: 2006astro.ph.10073B
  The operation of the solar global dynamo appears to involve many
  dynamical elements, including the generation of fields by the intense
  turbulence of the deep convection zone, the transport of these fields
  into the tachocline region near the base of the convection zone,
  the storage and amplification of toroidal fields in the tachocline by
  differential rotation, and the destabilization and emergence of such
  fields due to magnetic buoyancy. Self-consistent magnetohydrodynamic
  (MHD) simulations that realistically incorporate all of these processes
  are not yet computationally feasible, although some elements can now
  be studied with reasonable fidelity. Here we consider the manner in
  which turbulent compressible convection within the bulk of the solar
  convection zone can generate large-scale magnetic fields through dynamo
  action. We accomplish this through a series of three-dimensional
  numerical simulations of MHD convection within rotating spherical
  shells using our anelastic spherical harmonic (ASH) code on massively
  parallel supercomputers. Since differential rotation is a key ingredient
  in all dynamo models, we also examine here the nature of the rotation
  profiles that can be sustained within the deep convection zone as strong
  magnetic fields are built and maintained. We find that the convection
  is able to maintain a solar-like angular velocity profile despite the
  influence of Maxwell stresses, which tend to oppose Reynolds stresses
  and thus reduce the latitudinal angular velocity contrast throughout
  the convection zone. The dynamo-generated magnetic fields exhibit a
  complex structure and evolution, with radial fields concentrated in
  downflow lanes and toroidal fields organized into twisted ribbons
  that are extended in longitude and achieve field strengths of up to
  5000 G. The flows and fields exhibit substantial kinetic and magnetic
  helicity although systematic hemispherical patterns are only apparent in
  the former. Fluctuating fields dominate the magnetic energy and account
  for most of the back-reaction on the flow via Lorentz forces. Mean
  fields are relatively weak and do not exhibit systematic latitudinal
  propagation or periodic polarity reversals as in the Sun. This may
  be attributed to the absence of a tachocline, i.e., a penetrative
  boundary layer between the convection zone and the deeper radiative
  interior possessing strong rotational shear. The influence of such a
  layer will await subsequent studies.

Title: Variations of Solar Subsurface Weather in the Vicinity of
    Active Regions
Authors: Brown, B. P.; Haber, D. A.; Hindman, B. W.; Toomre, J.
Bibcode: 2004ESASP.559..345B
Altcode: 2004soho...14..345B
  No abstract at ADS

Title: Solar Differential Revealed by Helioseismology and Simulations
    of Deep Shells of Turbulent Convection
Authors: Toomre, J.; Brun, A. S.
Bibcode: 2004IAUS..215..326T
Altcode:
  No abstract at ADS

Title: The Spectrum of the Solar Supergranulation: Multiple Nonwave
    Components
Authors: Rast, Mark P.; Lisle, Jason P.; Toomre, Juri
Bibcode: 2004ApJ...608.1156R
Altcode:
  It has recently been suggested that the solar supergranulation undergoes
  oscillations, with a spectrum of superposed traveling waves of unknown
  origin showing excess prograde power to yield superrotation. We show
  here that the observed supergranular spectrum does not necessarily
  imply a wave origin but is instead consistent with two components of
  nonoscillatory bulk motions having differing rotation rates and somewhat
  asymmetrically distributed in space. The two components are identified
  with solar mesogranulation and supergranulation, and the spatial
  asymmetry is shown to be caused by a weak north-south alignment of the
  supergranular flows. The source of both the supergranular alignment and
  its enhanced rotation is likely underlying giant cell motions. Because
  no single rotation rate characterizes all components of a solar image,
  the spectral properties, including the Fourier dispersion relation, are
  extremely sensitive to the rate at which the solar disk is tracked when
  making up the time series. A spuriously wavelike spectrum is obtained
  when the image tracking rate falls between the actual mesogranular
  and supergranular rotation rates.

Title: Looking Deep Within an A-type Star: Core Convection Under
    the Influence of Rotation
Authors: Brun, A. S.; Browning, M.; Toomre, J.
Bibcode: 2004IAUS..215..388B
Altcode: 2003astro.ph..2598B
  The advent of massively parallel supercomputing has begun to permit
  explicit 3--D simulations of turbulent convection occurring within the
  cores of early-type main sequence stars. Such studies should complement
  the stellar structure and evolution efforts that have so far largely
  employed 1--D nonlocal mixing length descriptions for the transport,
  mixing and overshooting achieved by core convection. We have turned
  to A-type stars as representative of many of the dynamical challenges
  raised by core convection within rotating stars. The differential
  rotation and meridional circulations achieved deep within the star by
  the convection, the likelihood of sustained magnetic dynamo action
  there, and the bringing of fresh fuel into the core by overshooting
  motions, thereby influencing main sequence lifetimes, all constitute
  interesting dynamical questions that require detailed modelling
  of global-scale convection. Using our anelastic spherical harmonic
  (ASH) code tested on the solar differential rotation problem, we have
  conducted a series of 3--D spherical domain simulations that deal with
  a simplified description of the central regions of rotating A-type
  stars, i.e a convectively unstable core is surrounded by a stable
  radiative envelope. A sequence of 3--D simulations are used to assess
  the properties of the convection (its global patterns, differential
  rotation, meridional circulations, extent and latitudinal variation of
  the overshooting) as transitions are made between laminar and turbulent
  states by changing the effective diffusivities, rotation rates, and
  subadiabaticity of the radiative exterior. We report on the properties
  deduced from these models for both the extent of penetration and the
  profile of rotation sustained by the convection.

Title: Simulations of Core Convection Dynamos in Rotating A-type Stars
Authors: Browning, M.; Brun, A. S.; Toomre, J.
Bibcode: 2004IAUS..215..376B
Altcode:
  No abstract at ADS

Title: Persistent North-South Alignment of the Solar Supergranulation
Authors: Lisle, Jason P.; Rast, Mark P.; Toomre, Juri
Bibcode: 2004ApJ...608.1167L
Altcode:
  We have found evidence of an alignment of the solar supergranulation
  in the direction parallel to the Sun's rotation axis. Signatures
  of the alignment are apparent in both time-averaged images and in
  three-dimensional power spectra. The north-south organization is
  persistent in time, extending over many supergranular lifetimes. It
  occurs over a wide latitudinal extent, to +/-60°, and shows variation
  on a 10°-30° scale. These properties, as well as the rotation rate
  of the pattern, suggest a underlying larger scale dynamical cause. We
  examine a mechanism by which giant cell motions may contribute to
  such alignment.

Title: Subphotospheric Flows Around Active Region NOAA 10486
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
   Thompson, M. J.; LoHCo Team
Bibcode: 2004AAS...204.0211H
Altcode: 2004BAAS...36Q.669H
  We have used MDI Dynamics Program Doppler data taken between October
  18th and November 15th 2003 to study the interaction of solar subsurface
  flows with NOAA 10486, one of the most dynamic active regions of the
  past solar cycle. Using the local helioseismic techniques of ring and
  time-distance analyses, we assess the horizontal flows that surrounded
  and permeated this region and how they varied with depth in the upper
  14 Mm of the convection zone. We examine and identify structures in the
  flow field that may have been associated with the energetic flares that
  occurred during the period of observation. This research is in part
  supported by NASA through grants NAG5-11920, NAG5-10917, and NAG5-12491.

Title: Simulations of Core Convection and Dynamo Activity in A-type
    Stars at a Range of Rotation Rates
Authors: Browning, M. K.; Brun, A. S.; Toomre, J.
Bibcode: 2004AAS...204.0707B
Altcode: 2004BAAS...36..786B
  We present the results of nonlinear 3--D simulations of magnetic dynamo
  action by core convection within A-type stars of 2 solar masses, at a
  range of rotation rates. We consider the inner 30% by radius of such
  stars, with the spherical domain thereby encompassing the convective
  core and a portion of the surrounding radiative envelope. We solve the
  compressible Navier-Stokes equations in the anelastic approximation to
  examine highly nonlinear flows that span multiple scale heights, exhibit
  intricate time dependence, and admit magnetic dynamo action. Small
  initial seed magnetic fields are found to be amplified greatly by the
  convective and zonal flows. The central columns of strikingly slow
  rotation found in some of our progenitor hydrodynamic simulations
  continue to be realized in some simulations to a lesser degree,
  with such differential rotation arising from the redistribution of
  angular momentum by the nonlinear convection and magnetic fields. We
  assess the properties of the magnetic fields thus generated and the
  magnitude of the differential rotation sustained as the rotation rate
  in our simulations is varied.

Title: Organized Subsurface Flows near Active Regions
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Thompson, M. J.
Bibcode: 2004SoPh..220..371H
Altcode:
  Local helioseismic techniques, such as ring analysis and time-distance
  helioseismology, have already shown that large-scale flows near the
  surface converge towards major active regions. Ring analysis has further
  demonstrated that at greater depths some active regions exhibit strong
  outflows. A critique leveled at the ring-analysis results is that the
  Regularized Least Squares (RLS) inversion kernels on which they are
  based have negative sidelobes near the surface. Such sidelobes could
  result in a surface inflow being misidentified as a diverging outflow
  at depth. In this paper we show that the Optimally Located Averages
  (OLA) inversion technique, which produces kernels without significant
  sidelobes, generates flows markedly similar to the RLS results. Active
  regions are universally zones of convergence near the surface, while
  large complexes evince strong outflows deeper down.

Title: Simulations of Core Convection in Rotating A-Type Stars:
    Differential Rotation and Overshooting
Authors: Browning, Matthew K.; Brun, Allan Sacha; Toomre, Juri
Bibcode: 2004ApJ...601..512B
Altcode: 2003astro.ph.10003B
  We present the results of three-dimensional simulations of core
  convection within A-type stars of 2 M<SUB>solar</SUB>, at a range of
  rotation rates. We consider the inner 30% by radius of such stars,
  thereby encompassing the convective core and some of the surrounding
  radiative envelope. We utilize our anelastic spherical harmonic
  code, which solves the compressible Navier-Stokes equations in the
  anelastic approximation, to examine highly nonlinear flows that can
  span multiple scale heights. The cores of these stars are found to
  rotate differentially, with central cylindrical regions of strikingly
  slow rotation achieved in our simulations of stars whose convective
  Rossby number (R<SUB>oc</SUB>) is less than unity. Such differential
  rotation results from the redistribution of angular momentum by the
  nonlinear convection that strongly senses the overall rotation of
  the star. Penetrative convective motions extend into the overlying
  radiative zone, yielding a prolate shape (aligned with the rotation
  axis) to the central region in which nearly adiabatic stratification
  is achieved. This is further surrounded by a region of overshooting
  motions, the extent of which is greater at the equator than at the
  poles, yielding an overall spherical shape to the domain experiencing
  at least some convective mixing. We assess the overshooting achieved
  as the stability of the radiative exterior is varied and the weak
  circulations that result in that exterior. The convective plumes
  serve to excite gravity waves in the radiative envelope, ranging from
  localized ripples of many scales to some remarkable global resonances.

Title: Simulations of core convection in rotating A-type stars:
    Magnetic dynamo action
Authors: Browning, M. K.; Brun, A. S.; Toomre, J.
Bibcode: 2003AAS...203.8502B
Altcode: 2003BAAS...35.1342B
  We present the results of 3--D simulations of core convection dynamos
  within A-type stars of 2 solar masses, at a range of rotation rates. The
  inner 30% by radius of such stars are considered in our calculations,
  with the spherical domain thereby encompassing the convective core and
  some of the surrounding radiative envelope. We utilize our anelastic
  spherical harmonic (ASH) code to examine highly nonlinear flows that can
  admit magnetic dynamo action. Small initial seed magnetic fields are
  found to be amplified greatly by the convective and zonal flows. The
  resulting global fields possess structure on many scales, are strong
  enough to influence the convective flows themselves, and persist for
  as long as we have continued our calculations. The central columns of
  strikingly slow rotation found in some of our progenitor hydrodynamic
  simulations continue to be realized here to a lesser degree, with
  such differential rotation arising from the redistribution of angular
  momentum by the nonlinear convection and magnetic fields. We assess the
  properties of the magnetic fields, the extent of convective penetration,
  and the excitation of gravity waves within the radiative envelope.

Title: The LoHCo Project. 1 -- Comparison of Ring-Diagram Local
    Helioseismology on GONG++, MDI and Mt. Wilson Data Sets
Authors: Bogart, R. S.; Schou, J.; Basu, S.; Bolding, J.; Hill, F.;
   Howe, R.; Komm, R. W.; Leibacher, J. W.; Toner, C. G.; Corbard, T.;
   Haber, D. A.; Hindman, B. W.; Toomre, J.; Rhodes, E. J.; Rose, P. J.;
   LoHCo Project Team
Bibcode: 2003SPD....34.0804B
Altcode: 2003BAAS...35..822B
  Full deployment of the GONG+ enhanced observing network in October
  2001 and implementation of ring-diagram helioseismology in the
  GONG++ analysis pipeline this year has enabled us to make a detailed
  intercomparison of results obtained through multiple paths, from
  observation through each of the analysis steps. Such comparisons
  can provide a certain degree of validation of the implementations
  of the analysis procedures, hints of systematic errors, and better
  characterization of the observations, possibly leading to improved
  calibrations. The Local Helioseismology Comparison (LoHCo) Project
  has been established to provide standards for intercomparison of
  results obtained with different local helioseismic analysis techniques
  applied to the available observational data sources. We present here
  a detailed comparison of ring-diagram determinations of localized
  sub-surface flows and frequency shifts obtained from both MDI and
  GONG in common observing intervals during Carrington Rotation 1988
  (2002/3/30 -- 2002/4/26), using both the MDI and the GONG analysis
  pipelines. We also present preliminary results of similar analyses of
  data obtained by the Mt. Wilson MOF during the same times. <P />This
  work is partially supported by grants from NASA and NSF.

Title: Comparison of Solar Subsurface Weather Obtained with
    Time-Distance Tomography and Ring Analysis
Authors: Hindman, B. W.; Zhao, J.; Haber, D. A.; Kosovichev, A. G.;
   Toomre, J.
Bibcode: 2003SPD....34.0806H
Altcode: 2003BAAS...35R.822H
  The near-surface shear layer exhibits a rich medley of flows that
  vary in size from granular and supergranular flows to flows of global
  scale. The largest of these flows have been dubbed Solar Surface Weather
  (SSW), and have been detected with both time-distance tomography and
  ring analysis. We present comparisons of synoptic maps of SSW flows
  obtained with both techniques from SOI-MDI Dynamics Program data. Both
  techniques provide measurements of the flows as a function of depth
  through inversion. The time-distance method utilizes only p-mode
  oscillations, while the ring analysis uses f modes as well. We find that
  the flows obtained with the two helioseismic techniques are remarkably
  similar, with common inflow and outflow sites as well as agreement in
  the general flow direction. At a depth of roughly 1.5 Mm the Spearman
  rank correlation coefficient between maps is on the order of 0.80. As
  the depth increases the correlation become weaker. The reduction in the
  correlation coefficient with depth is due to the increasing difference
  between the vertical resolution kernel of the two seismic techniques.

Title: Overview - where do we stand with helioseismology?
Authors: Toomre, Juri
Bibcode: 2003ESASP.517....3T
Altcode: 2003soho...12....3T
  The advent of GONG+ and the selection of the Helioseismic and Magnetic
  Imager (HMI) for the Solar Dynamics Observatory (SDO) together promise
  a high-resoluton future for helioseismology in probing the internal
  dynamics and structure of the sun. We address some of the dynamical
  issues in the upper reaches of the solar convection zone that inspire
  these observational efforts which seek to understand the complex
  couplings between the highly turbulent convection and the intense
  magnetism exhibited by the sun. We examine findings to date about
  the evolving flows, called Solar Subsurface Weather (SSW), and their
  interaction with magnetism deduced from various local helioseismic
  approaches. We discuss the substantial efforts that appear to be
  required to make these procedures capable of subsurface flows with
  GONG+ and HMI over a wide range of depths for much of the visible solar
  disk. We shall also review some recent evidence for variability with
  advancing solar cycle both within the body of the convection zone and
  within its upper shear layer.

Title: Comparison of near-surface flows assessed by ring-diagram
    and f-mode time-distance analyses
Authors: Hindman, Bradley; Gizon, Laurent; Haber, Deborah; Duval,
   Thomas, Jr.; Toomre, Juri
Bibcode: 2003ESASP.517..299H
Altcode: 2003soho...12..299H
  The near-surface shear layer exhibits a rich medley of flows that are
  now being measured by time-distance and ring analysis techniques. We
  present comparisons of the flows obtained with the two techniques
  using SOI-MDI Dynamics Program data from the years 1998 and 1999. The
  time-distance analyses utilize f-mode data without depth inversion. The
  flows deduced with the two methods are remarkably similar, with common
  inflow and outflow sites as well as agreement in the general flow
  directions. The direct correspondence of features in the flows is
  realized in both quiet and active regions.

Title: Transient oscillations near the solar tachocline
Authors: Toomre, Juri; Christensen-Dalsgaard, Jorgen; Hill, Frank;
   Howe, Rachel; Komm, Rudolf W.; Schou, Jesper; Thompson, Michael J.
Bibcode: 2003ESASP.517..409T
Altcode: 2003soho...12..409T
  We report on further developments in the 1.3-yr quasi-periodic
  oscillations reported by Howe et al. (2000). These are small (6 to 8
  nHz peak-to-peak) oscillations in the inferred rotation rate near the
  bottom of the convection zone and in the outer part of the radiative
  interior. The oscillations are strongest and most coherent at about a
  fractional radius of 0.72 in the equatorial region. Further monitoring
  of the oscillations near the equator shows that they continued for a
  period after the end of the data analyzed by Howe et al., but appear to
  have now diminished in amplitude. This is reminiscent of the transient
  behavior of similar (1.3 to 1.4 yr) periodicities in solar-wind and
  geomagnetic datasets previously reported. We speculate that the near
  tachocline oscillation is associated with the rising phase of the
  solar cycle. We discuss tests performed to eliminate various possible
  explanations of the oscillations due to systematic errors in the data
  and in their analyses.

Title: Interaction of solar subsurface flows with major active regions
Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri
Bibcode: 2003ESASP.517..103H
Altcode: 2003soho...12..103H
  Solar Subsurface Weather (SSW), which consists of complex and meandering
  large-scale horizontal flows below the solar surface, has been studied
  in detail with ring analyses of SOI-MDI data from SOHO. SSW flows are of
  particular significance since they appear to interact and influence the
  magnetic fields visible at the surface, with active regions appearing as
  zones of convergent flow and possible downflows. Such subsurface flows
  over a range of depths can mechanically twist and displace field lines,
  possibly leading to unstable magnetic configurations that may flare or
  erupt as coronal mass ejections. It is highly likely that such flows
  and magnetic fields are broadly linked in their evolution. We have
  studied in detail horizontal flow fields in the vicinity of several
  major active regions observed during 2001 and 2002, finding that at
  shallow depths there is general flow convergence toward these regions
  and noticeable flow deflections in the large-scale zonal and meridional
  circulations. We have detected strengthening of jet-like features in
  the converging flows occurring over the course of several days. These
  features are accompanied by prominent diverging outflows at greater
  depths. It appears that the large-scale flow fields surrounding active
  complexes have a distinct cellular structure that may contribute to both
  the overall cohesion of active regions as well as to the movement of
  magnetic flux within those regions that can lead to flares and other
  eruptive phenomena.

Title: Solar Differential Rotation and Magnetism: a 3--D MHD View
Authors: Brun, Allan Sacha; Toomre, Juri
Bibcode: 2003IAUJD..12E...7B
Altcode:
  We discuss recent progresses made in modelling the complex
  magnetohydrodynamics of the Sun using our anelastic spherical harmonics
  (ASH) code on massively parallel computers. We have conducted 3--D
  MHD simulations of compressible convection in spherical shells to
  study the coupling between convection rotation and magnetic field
  in seeking to understand how the solar differential rotation is
  established and maintained. The resulting convection within domains
  that capture a good fraction of the bulk of the solar convection zone
  is highly time dependent and intricate and is dominated by intermittent
  upflows and networks of strong downflows (i.e. plumes). These plumes
  play a significant role in yielding Reynolds stresses that serve to
  redistribute angular momentum leading to angular velocity profiles
  that make good contact with helioseismic deductions. Such complex
  convective flows are efficient in amplifying the magnetic energy near
  equipartition. The resulting magnetic fields are found to concentrate
  around the downflowing networks and to have significant north-south
  asymmetry and helicity. But these strong fields yield Maxwell stresses
  that seek to speed up the poles and destroy the agreement with
  helioseismic observations. So for a given angular velocity profile
  the level of magnetism that the Sun can sustain is likely to be limited

Title: Bridges between helioseismology and models of convection
    zone dynamics
Authors: Toomre, Juri
Bibcode: 2003safd.book..299T
Altcode:
  The sun is a magnetic star whose variable activity has a profound
  effect on our technological society. The high speed solar wind and
  its energetic particles, mass ejections and flares that affect the
  solar-terrestrial interaction all stem from the variability of the
  underlying solar magnetic fields. We are in an era of fundamental
  discovery about the overall dynamics of the solar interior and its
  ability to generate magnetic fields through dynamo action. This has
  come about partly through guidance and challenges to theory from
  helioseismology as we now observationally probe the interior of this
  star. It also rests on our increasing ability to conduct simulations
  of the crucial solar turbulent processes using the latest generation
  of supercomputers.

Title: Solar Turbulence and Magnetism Studied Within a Rotating
    Convective Spherical Shell
Authors: Brun, A. S.; Toomre, J.
Bibcode: 2003ASPC..293..134B
Altcode: 2003astro.ph..2593B; 2003tdse.conf..134B
  We discuss recent advances made in modelling the complex
  magnetohydrodynamics of the Sun using our anelastic spherical harmonics
  (ASH) code. We have conducted extensive 3--D simulations of compressible
  convection in rotating spherical shells with and without magnetic
  fields, to study the coupling between global-scale convection and
  rotation in seeking to understand how the solar differential rotation
  is established and maintained. Such simulations capable of studying
  fairly turbulent convection have been enabled by massively parallel
  supercomputers. The resulting convection within domains that capture
  a good fraction of the bulk of the convection zone is highly time
  dependent and intricate, and is dominated by intermittent upflows and
  networks of strong downflows. A high degree of coherent structures
  involving downflowing plumes can be embedded in otherwise chaotic flow
  fields. These vortical structures play a significant role in yielding
  Reynolds stresses that serve to redistribute angular momentum, leading
  to differential rotation profiles with pole-to-equator contrasts of
  about 30% in angular velocity, Omega, and some constancy along radial
  lines at mid latitudes, thereby making good contact with deductions
  from helioseismology. When a magnetic field is introduced, a dynamo
  regime can be found that does not destroy the strong differential
  rotation achieved in pure hydrodynamics cases. The magnetic fields
  are found to concentrate around the downflowing networks and to have
  significant north-south asymmetry and helicity.

Title: The Internal Rotation of the Sun
Authors: Thompson, Michael J.; Christensen-Dalsgaard, Jørgen; Miesch,
   Mark S.; Toomre, Juri
Bibcode: 2003ARA&A..41..599T
Altcode:
  Helioseismology has transformed our knowledge of the Sun's
  rotation. Earlier studies revealed the Sun's surface rotation,
  but now a detailed observational picture has been built up of the
  internal rotation of our nearest star. Unlike the predictions of
  stellar-evolution models, the radiative interior is found to rotate
  roughly uniformly. The rotation within the convection zone is also
  very different from prior expectations, which had been that the
  rotation rate would depend primarily on the distance from the rotation
  axis. Layers of rotational shear have been discovered at the base of
  the convection zone and in the subphotospheric layers. Studies of the
  time variation of rotation have uncovered zonal-flow bands, extending
  through a substantial fraction of the convection zone, which migrate
  over the course of the solar cycle, and there are hints of other
  temporal variations and of a jet-like structure. At the same time,
  building on earlier work with mean-field models, researchers have made
  great progress in supercomputer simulations of the intricate interplay
  between turbulent convection and rotation in the Sun's interior. Such
  studies are beginning to transform our understanding of how rotation
  organizes itself in a stellar interior.

Title: Solar Multiscale Convection and Rotation Gradients Studied
    in Shallow Spherical Shells
Authors: De Rosa, Marc L.; Gilman, Peter A.; Toomre, Juri
Bibcode: 2002ApJ...581.1356D
Altcode: 2002astro.ph..9054D
  The differential rotation of the Sun, as deduced from helioseismology,
  exhibits a prominent radial shear layer near the top of the convection
  zone wherein negative radial gradients of angular velocity are
  evident in the low- and midlatitude regions spanning the outer 5%
  of the solar radius. Supergranulation and related scales of turbulent
  convection are likely to play a significant role in the maintenance
  of such radial gradients and may influence dynamics on a global scale
  in ways that are not yet understood. To investigate such dynamics, we
  have constructed a series of three-dimensional numerical simulations
  of turbulent compressible convection within spherical shells, dealing
  with shallow domains to make such modeling computationally tractable. In
  all but one case, the lower boundary is forced to rotate differentially
  in order to approximate the influence that the differential rotation
  established within the bulk of the convection zone might have upon a
  near-surface shearing layer. These simulations are the first models
  of solar convection in a spherical geometry that can explicitly
  resolve both the largest dynamical scales of the system (of order the
  solar radius) as well as smaller scale convective overturning motions
  comparable in size to solar supergranulation (20-40 Mm). We find that
  convection within these simulations spans a large range of horizontal
  scales, especially near the top of each domain, where convection
  on supergranular scales is apparent. The smaller cells are advected
  laterally by the larger scales of convection within the simulations,
  which take the form of a connected network of narrow downflow lanes that
  horizontally divide the domain into regions measuring approximately
  100-200 Mm across. We also find that the radial angular velocity
  gradient in these models is typically negative, especially in the low-
  and midlatitude regions. Analyses of the angular momentum transport
  indicate that such gradients are maintained by Reynolds stresses
  associated with the convection, transporting angular momentum inward
  to balance the outward transport achieved by viscous diffusion and
  large-scale flows in the meridional plane, a mechanism first proposed
  by Foukal &amp; Jokipii and tested by Gilman &amp; Foukal. We suggest
  that similar mechanisms associated with smaller scale convection in
  the Sun may contribute to the maintenance of the observed radial shear
  layer located immediately below the solar photosphere.

Title: Solar Subsurface Weather and Possible Giant Cell Signatures
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
   Hill, F.
Bibcode: 2002AAS...200.0414H
Altcode: 2002BAAS...34Q.645H
  Helioseismic observations taken with SOI-MDI aboard SOHO have led to
  a new era of discovery about complex and evolving dynamics within the
  upper solar convection zone. The data now span nearly six years. Using
  the technique of ring-diagram analysis applied to MDI Dynamics Program
  Doppler data over a large number of regions on the solar disk, we have
  generated synoptic maps of horizontal flows at a variety of depths
  below the photosphere. These maps have been assembled for all of the
  years for which the SOI-MDI Dynamics Program data are available, with
  the latest data coming from March 2002. Flows associated with Solar
  Subsurface Weather (SSW) are observed to vary from month to month and
  year to year, with the largest flows occurring in and around regions
  of intense magnetic activity. Longitudinal averages of the flows reveal
  that the fast banded zonal flows seen in previous years have now merged
  at the equator while the multiple cell structure found in the meridional
  circulation within the northern hemisphere over the last four years is
  still present at a reduced level in 2002. When the average flows are
  removed, it is possible to see areas of cyclonic flow in regions of
  quiet sun as well as divergent cells on the order of 30 to 40 degrees
  in diameter that might be signatures of giant convection cells. This
  research was supported by NAG5-7996.

Title: Turbulent Convection under the Influence of Rotation:
    Sustaining a Strong Differential Rotation
Authors: Brun, Allan Sacha; Toomre, Juri
Bibcode: 2002ApJ...570..865B
Altcode: 2002astro.ph..6196B
  The intense turbulence present in the solar convection zone is a major
  challenge to both theory and simulation as one tries to understand the
  origins of the striking differential rotation profile with radius and
  latitude that has been revealed by helioseismology. The differential
  rotation must be an essential element in the operation of the solar
  magnetic dynamo and its cycles of activity, yet there are many
  aspects of the interplay between convection, rotation, and magnetic
  fields that are still unclear. We have here carried out a series
  of three-dimensional numerical simulations of turbulent convection
  within deep spherical shells using our anelastic spherical harmonic
  (ASH) code on massively parallel supercomputers. These studies of the
  global dynamics of the solar convection zone concentrate on how the
  differential rotation and meridional circulation are established. We
  have addressed two issues raised by previous simulations with
  ASH. First, can solutions be obtained that possess the apparent
  solar property that the angular velocity Ω continues to decrease
  significantly with latitude as the pole is approached? Prior
  simulations had most of their rotational slowing with latitude
  confined to the interval from the equator to about 45°. Second, can a
  strong latitudinal angular velocity contrast ΔΩ be sustained as the
  convection becomes increasingly more complex and turbulent? There was
  a tendency for ΔΩ to diminish in some of the turbulent solutions
  that also required the emerging energy flux to be invariant with
  latitude. In responding to these questions, five cases of increasingly
  turbulent convection coupled with rotation have been studied along
  two paths in parameter space. We have achieved in one case the slow
  pole behavior comparable to that deduced from helioseismology and
  have retained in our more turbulent simulations a consistently strong
  ΔΩ. We have analyzed the transport of angular momentum in establishing
  such differential rotation and clarified the roles played by Reynolds
  stresses and the meridional circulation in this process. We have found
  that the Reynolds stresses are crucial in transporting angular momentum
  toward the equator. The effects of baroclinicity (thermal wind) have
  been found to have a modest role in the resulting mean zonal flows. The
  simulations have produced differential rotation profiles within the bulk
  of the convection zone that make reasonable contact with ones inferred
  from helioseismic inversions, namely, possessing a fast equator, an
  angular velocity difference of about 30% from equator to pole, and
  some constancy along radial lines at midlatitudes. Future studies must
  address the implications of the tachocline at the base of the convection
  zone, and the near-surface shear layer, on that differential rotation.

Title: Evolving Submerged Meridional Circulation Cells within the
    Upper Convection Zone Revealed by Ring-Diagram Analysis
Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri; Bogart,
   Richard S.; Larsen, Rasmus M.; Hill, Frank
Bibcode: 2002ApJ...570..855H
Altcode:
  Using the local helioseismic technique of ring-diagram analysis
  applied to Michelson Doppler Imager (MDI) Dynamics Program data from
  the Solar and Heliospheric Observatory, we have discovered that the
  meridional flow within the upper convection zone can develop additional
  circulation cells whose boundaries wander in latitude and depth as
  the solar cycle progresses. We report on the large-scale meridional
  and zonal flows that we observe from 1996 to 2001. In particular, we
  discuss the appearance and evolution of a submerged meridional cell
  during the years 1998-2001, which arose in the northern hemisphere
  and disrupted the orderly poleward flow and symmetry about the equator
  that is typically observed. The meridional flows in the southern and
  northern hemispheres exhibit striking asymmetry during the past four
  years of the advancing solar cycle. Such asymmetry and additional
  circulation cells should have profound impact on the transport of
  angular momentum and magnetic field within the surface layers. These
  flows may have a significant role in the establishment and maintenance
  of the near-surface rotational shear layer.

Title: Solar Subsurface Weather: Recent Measurements of Flows Using
    Ring-Diagram Analysis
Authors: Hindman, B. W.; Haber, D. A.; Toomre, J.; Bogart, R. S.
Bibcode: 2002AAS...200.7904H
Altcode: 2002BAAS...34..780H
  Continuous helioseismic observations from SOI-MDI on SOHO have led to
  a new era of discovery about complex and evolving dynamics within the
  solar convection zone. Local probing of the Sun's acoustic wave field,
  using ring-diagram analysis, has revealed the presence of large-scale
  horizontal flows within the near-surface layers of the Sun. These
  remarkable weather-like flow patterns, called Solar Subsurface Weather
  (SSW), possess intricate patterns that change from one day to the next,
  accompanied by more gradually evolving patterns such as banded zonal
  flows and meridional circulation cells. Synoptic maps of these flow
  structures reveal that solar magnetism strongly modulates flow speeds
  and directions with an effect that varies with depth. I will present
  out latest measurements of the flows associated with SSW and briefly
  discuss the implications of these measurements on the redistribution of
  angular momentum and magnetic fields. This research has been supported
  by NASA and NSF.

Title: Penetration and Overshooting in Turbulent Compressible
    Convection
Authors: Brummell, Nicholas H.; Clune, Thomas L.; Toomre, Juri
Bibcode: 2002ApJ...570..825B
Altcode:
  We present the results of a series of high-resolution, three-dimensional
  numerical experiments that investigate the nature of turbulent
  compressible convective motions extending from a convection zone into
  a stable layer below. In such convection, converging flows in the
  near-surface cellular convecting network create strong downflowing
  plumes that can traverse the multiple scale heights of the convection
  zone. Such structures can continue their downward motions beyond the
  convecting region, piercing the stable layer, where they are decelerated
  by buoyancy braking. If these motions mix entropy to an adiabatic
  state below the convection zone, the process is known as penetration;
  otherwise it is termed overshooting. We find that in three-dimensional
  turbulent compressible convection at the parameters studied, motions
  generally overshoot a significant fraction of the local pressure scale
  height but do not establish an adiabatic penetrative region, even at
  the highest Péclet numbers considered. This is mainly due to the low
  filling factor of the turbulent plumes. The scaling of the overshooting
  depth with the relative stability S of the two layers is affected by
  this lack of true penetration. Only an S<SUP>-1</SUP> dependence is
  exhibited, reflecting the existence of a thermal adjustment region
  without a nearly adiabatic penetration zone. Rotation about a vertical
  axis decreases the depth of overshooting, owing to horizontal mixing
  induced by the rotation. For rotation about an inclined axis, turbulent
  rotational alignment of the strong downflow structures decreases
  the overshooting further at mid-latitudes, but the laminar effects
  of cellular roll solutions take over at low latitudes. Turbulent
  penetrative convection is quite distinct from its laminar counterpart
  and from the equivalent motions in a domain confined by impenetrable
  horizontal boundaries. Although overshooting would not be so deep in
  the solar case, the lack of true penetration extending the adiabatic
  region may explain why helioseismic inferences show little evidence of
  the expected abrupt change between the convection zone and the radiative
  interior. These results may also provide insight into how overshooting
  motions can provide a coupling between the solar convection zone and
  the tachocline.

Title: Eddies and vortices in ocean basin dynamics
Authors: Siegel, A.; Weiss, Jeffrey B.; Toomre, Juri; McWilliams,
   James C.; Berloff, Pavel S.; Yavneh, Irad
Bibcode: 2001GeoRL..28.3183S
Altcode:
  A wind-driven, closed-basin quasi-geostrophic ocean model is computed
  at very high horizontal resolution to study the effect of increasing
  Reynolds number (Re) on eddy variability. Five numerical simulations
  are performed with identical configurations, varying only in horizontal
  resolution and viscosity coefficient (and therefore Re). Qualitative
  changes in the structure of eddy variability are evident in the dramatic
  increase of isolated vortex structures at the highest Re. While the
  time-mean kinetic energy is relatively independent of Re, the vortex
  emergence contributes to a continual increase with Re of eddy kinetic
  energy and meridional vorticity flux. The rate of increase slows
  somewhat at the highest Re, indicating the possibility of a regime
  where eddy variability becomes insensitive to further increases in Re.

Title: Evolving Large-Scale Flows With Advancing Solar Cycle Using
    Helioseismic Dense-Pack Ring-Diagram Analyses
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
   Hill, F.
Bibcode: 2001AGUSM..SP22A02H
Altcode:
  We have recently completed the first local helioseismic ring-diagram
  analysis of the entire SOI-MDI Dynamics Program data. These data sets
  include up to three months of continuous Doppler velocity data from
  each of the years 1996 through 2000. A single ring-diagram analysis
  over a 15<SUP>o</SUP> region of the sun, followed by an inversion
  of the frequency shifts thus obtained, yields measurements of the
  horizontal velocity field as a function of depth within the upper 14 Mm
  of the convection zone beneath that region. By performing the analysis
  over a Dense-Pack mosaic of 189 overlapping tiles and repeating the
  procedure for each day of data, we have mapped the velocity field as
  a function of time over a substantial fraction of the solar disk for
  a number of full Carrington rotations. Our studies of the dynamics
  of the upper convection zone have revealed the presence of striking
  north-south asymmetries in both the zonal and meridional flows as a
  function of depth. For example, a small second meridional flow cell
  appeared at depths below 10 Mm at latitudes north of 45<SUP>o</SUP>N
  in 1998, expanded upwards to 3 Mm in depth at all latitudes above
  22<SUP>o</SUP>N in 1999, and then receded again in 2000. Synoptic maps,
  formed from nearly 4500 ring-diagram analyses per Carrington rotation,
  show that active regions are sites of convergent flow and appear at
  the boundaries of the northern meridional cells in 1999. Even finer
  sampling grids show that there are steep gradients in the flows within
  active regions. Our work has also revealed a relationship between the
  fast zonal "torsional oscillation" bands that migrate towards the
  equator and the meridional flow as the solar cycle progresses. The
  dominantly poleward meridional flow reaches maxima in both hemispheres
  at the latitudes at which the zonal fast belts occur. As the zonal fast
  belts drift towards the equator, the latitudes of maximal meridional
  flow also drift equatorward.

Title: Variations in Rotation Rate Within the Solar Convection Zone
    From GONG and MDI 1995-2000
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
   Schou, J.; Thompson, M. J.; Toomre, J.
Bibcode: 2001AGUSM..SP31A15H
Altcode:
  Helioseismic measurements with the Michelson Doppler Imager (MDI)
  instrument aboard SOHO, and complementary measurements from the Global
  Oscillation Network Group (GONG) project, are revealing changes deep
  within the Sun as the solar cycle progresses. We will present the
  latest results based on recent data from both experiments, including
  flows in the upper part of the convection zone and variations in the
  rotation rate near its base.

Title: Transport and Storage of Magnetic Field by Overshooting
    Turbulent Compressible Convection
Authors: Tobias, Steven M.; Brummell, Nicholas H.; Clune, Thomas L.;
   Toomre, Juri
Bibcode: 2001ApJ...549.1183T
Altcode:
  We present the results of a series of numerical experiments that
  investigate the transport of magnetic fields by turbulent penetrative
  compressible convection. We find that magnetic flux is preferentially
  transported downward out of a turbulent convecting region and stored in
  a stably stratified region below. This pumping mechanism is believed
  to be a crucial component for the operation of a large-scale solar
  interface dynamo since it may be responsible for the transport
  of flux from the solar convection zone to the stable overshoot
  region. The high-resolution three-dimensional simulations show that
  efficient pumping occurs as a result of the action of strong coherent
  downflowing plumes. The properties of the transport are evaluated as a
  function of magnetic field strength, rotation rate, supercriticality,
  stiffness of the interface, and configuration. The turbulent pumping of
  magnetic flux is remarkably robust and more efficient than its laminar
  counterpart. The turbulent convection naturally amplifies magnetic
  energy from any existing mean field. The transport of flux from the
  convection zone removes the source for this local amplification there,
  and thus the peak magnetic energy also comes to reside in the stable
  region. This is important for an effective interface dynamo.

Title: Fractional Frequency Shifts of Local Helioseismic Modes With
    Magnetic Activity Using Ring-Diagram Analysis
Authors: Hindman, B.; Haber, D.; Toomre, J.; Bogart, R. S.
Bibcode: 2001IAUS..203..215H
Altcode:
  Using full-disk Doppler velocity data from SOI-MDI during the advancing
  solar cycle from 1996 through 1999, we have computed the local
  frequencies of high-degree p modes and f modes over a dense mosaic of
  localized regions of the sun using ring-diagram analysis. The motion of
  active regions as they rotate across the solar disk is well traced by
  changes in the frequencies. Active regions appear as locations of large
  positive frequency shifts. Depending on the radial order and wavenumber
  of the observed acoustic modes the frequency shifts can be as much as
  10 to 30 microHz. Shifts of this amplitude are 20 to 60 times larger
  than the shifts in global acoustic oscillations. The magnitude and
  frequency dependence of the large frequency shifts are consistent with
  those measured in global modes provided the local frequency shifts
  are averaged over the solar disk and are scaled to the appropriate
  wavenumber regimes. The frequency dependence of the shifts indicates
  that the physical phenomena inducing them is largely confined to the
  surface layers of the sun, although there is some indication that
  there may be a deeper structural component as well. These local area
  samplings may help to understand the restructuring of the near-surface
  layers of the convection zone by magnetic fields.

Title: Comparing local frequency shifts measured through ring-diagram
    analysis with global frequency shifts
Authors: Hindman, Bradley W.; Haber, Deborah A.; Toomre, Juri; Bogart,
   Richard S.
Bibcode: 2001ESASP.464..143H
Altcode: 2001soho...10..143H
  Using ring-diagram mode fitting of a subset of the MDI Dynamics Program
  data called the dense-pack data set (Haber et al. 2000), we measure
  the frequencies of high-degree p modes and f modes as a function of
  position on the solar disk and of time. Daily maps of the resulting
  frequencies reveal that high-degree mode frequencies are spatially and
  temporally variable and are composed of the sum of two components. One
  component is stationary and is produced primarily by imperfections in
  the MDI optics, while the other component is spatially intermittent,
  rotates with the solar surface, and is associated with the presence of
  active regions. The frequency shifts within active regions can exceed 60
  μHz for some wavelengths and mode orders. We remove the instrumentally
  dependent portion of the signal and average the resulting frequency
  shifts over the solar disk and over time producing a global average. The
  frequency and wavenumber dependence of these average frequency shifts
  indicates that the physical phenomena inducing the shifts is largely
  confined to the surface layers of the sun, although there is evidence
  that a small contribution from deeper layers exists. The average
  frequency shifts strongly resemble the solar cycle variations that
  are observed in the frequencies of global p-mode oscillations of low
  harmonic degree.

Title: Comparing mode frequencies from MDI and GONG
Authors: Howe, R.; Hill, F.; Basu, S.; Christensen-Dalsgaard, J.;
   Komm, R. W.; Munk Larsen, R.; Roth, M.; Schou, J.; Thompson, M. J.;
   Toomre, J.
Bibcode: 2001ESASP.464..137H
Altcode: 2001soho...10..137H
  We present results of analyses of MDI and GONG time series covering
  the same time intervals, and using both the MDI and GONG peakbagging
  algorithms. We discuss some of the likely causes of differences between
  the inferred frequencies and frequency splittings. In addition, we
  consider the effect of these differences on the results of inversions
  for the solar internal rotation and sound speed.

Title: Daily variations of large-scale subsurface flows and global
    synoptic flow maps from dense-pack ring-diagram analyses
Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri; Bogart,
   Richard S.; Hill, Frank
Bibcode: 2001ESASP.464..209H
Altcode: 2001soho...10..209H
  Ring-diagram analyses carried out daily on a mosaic of sites spanning
  much of the solar disk have allowed the mapping of large-scale flows in
  the upper portion of the solar convection zone. Inversion of frequency
  splittings from such local helioseismic analyses reveal large-scale
  flows, in addition to the mean zonal and meridional flows, that vary
  from day-to-day and with depth. We contrast such flow behavior in
  regions of active and quiet sun. We also provide synoptic maps based
  on dense-pack studies covering three full solar rotations in 1999.

Title: Solar cycle changes in convection zone dynamics from MDI and
    GONG 1995 - 2000
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
   Munk Larsen, R.; Schou, J.; Thompson, M. J.; Toomre, J.
Bibcode: 2001ESASP.464...19H
Altcode: 2001soho...10...19H
  The combined GONG and MDI medium-degree helioseismic data sets now cover
  just over 5 years and allow us to probe the changing dynamics of the
  convection zone in unprecedented detail. Here we present the latest
  results from both projects, showing the evolution of the migrating
  zonal flows close to the surface and also changes close to and below
  the base of the convection zone.

Title: Comparison of phase inversion and time-distance analysis of
    one-dimensional artificial seismic data
Authors: Gough, D. O.; Sekii, T.; Toomre, J.
Bibcode: 2001ESASP.464..207G
Altcode: 2001soho...10..207G
  We have studied the application of a phase inversion technique (Gough,
  Merryfield and Toomre 1991, 1993, 1998; Gough, Sekii and Toomre 1998,
  2000) to stochastically excited damped oscillations in an inhomogeneous
  one-dimensional loop, using artificial seismic data (Gough, Sekii and
  Toomre 2000). It has been found that within a parameter range that might
  be relevant to the solar case, strong damping can significantly degrade
  inversions for the wave propagation speed. Here we analyse the same
  artificial data by a time-distance technique, to compare how the two
  techniques differ in their response to the presence of strong damping.

Title: Development of multiple cells in meridional flows and evolution
    of mean zonal flows from ring-diagram analyses
Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri; Bogart,
   Richard S.; Hill, Frank
Bibcode: 2001ESASP.464..213H
Altcode: 2001soho...10..213H
  Meridional flows within the solar convection zone have been observed
  with both direct Doppler measurements and with local helioseismic
  techniques based on ring-diagram analyses and time-distance
  methods. Typically these mean flows are poleward with speeds of
  roughly 20 m s<SUP>-1</SUP>. Using ring-diagram analyses on a subset
  of the MDI Dynamics Program data, called the dense-pack data set, we
  find that a deviation from this general behavior occurs in 1999. A
  second meridional cell appears below the surface in the northern
  hemisphere. At the same time, the mean zonal flows do not reveal any
  evidence of this cell. The zonal bands or "torsional oscillations"
  continue their steady migration toward the equator.

Title: Numerical simulations of supergranular scales of convection
    in shallow spherical shells
Authors: De Rosa, Marc L.; Toomre, Juri
Bibcode: 2001ESASP.464..595D
Altcode: 2001soho...10..595D
  The differential rotation of the sun, as deduced from helioseismology,
  exhibits a prominent radial shear layer near the top of the convection
  zone. Supergranulation and related scales of turbulent convection
  are likely to play a significant role in the maintenance of strong
  radial gradients in angular velocity which vary with latitude near
  the surface. We present results from 3-D numerical simulations of such
  turbulent convection in shallow spherical shells, using the anelastic
  spherical harmonic (ASH) code running on massively parallel computers
  to study the effects of rotation and compressibility on the resulting
  highly nonlinear convection. Convection of supergranular nature is
  driven by imposing the solar heat flux at the bottom of a shallow
  spherical shell located near the top of the convection zone which is
  rotating at the mean solar rate. The angular momentum balance in the
  shell is studied for cases where a solar-like differential rotation
  profile is imposed at the lower boundary. Convection spanning a large
  range of horizontal scales is driven within the shell, especially near
  the top of the domain. The resulting radial angular velocity gradient
  is negative for all latitudes, suggesting that fluid parcels partially
  conserve their angular momentum while moving radially.

Title: Mean flows in rotating turbulent convective shells
Authors: Brun, Allan Sacha; Toomre, Juri
Bibcode: 2001ESASP.464..619B
Altcode: 2001soho...10..619B
  We conduct numerical simulations of turbulent compressible convection
  within rotating spherical shells to model solar differential rotation
  and meridional circulation. These 3-D simulations are carried out on
  massively parallel computers using the Anelastic Spherical Harmonic
  (ASH) code. The evolution of such convection is studied in four cases
  which sample several paths in achieving highly turbulent flows that are
  able to drive a strong differential rotation from equator to pole. The
  resulting angular velocity Ω profiles make reasonable contact with
  many aspects of the solar rotation profiles inferred from helioseismic
  inversions of both MDI and GONG data. The substantial contrast in Ω
  of order 30% achieved in our simulations of turbulent convection is
  considerably greater than realized in previous studies.

Title: Magnetic Pumping at the Base of the Solar Convection Zone
Authors: Tobias, S. M.; Brummell, N. H.; Toomre, J.
Bibcode: 2001IAUS..203..156T
Altcode:
  We present the results of a series of numerical experiments that
  investigate the pumping of magnetic fields by turbulent penetrative
  convection. This pumping mechanism, which is responsible for the
  transport of flux from the solar convection zone to the stable overshoot
  region, is believed to be a crucial component for the operation
  of a large-scale solar interface dynamo. The high-resolution three
  dimensional simulations show that efficient pumping occurs due to the
  action of strong coherent downwards plumes. The pumping depth is then
  calculated as a function of magnetic field strength, rotation rate,
  supercriticality and stiffness of the interface.

Title: Turbulent Convection and Subtleties of Differential Rotation
    Within the Sun
Authors: Toomre, J.; Brun, A. Sacha; De Rosa, M.; Elliott, J. R.;
   Miesch, M. S.
Bibcode: 2001IAUS..203..131T
Altcode:
  Differential rotation and cycles of magnetic activity are
  intimately linked dynamical processes within the deep shell of
  highly turbulent convection occupying the outer 200 Mm below the
  solar surface. Helioseismology has shown that the angular velocity
  Ω within the solar convection zone involves strong shear layers
  both near the surface and especially at its base near the interface
  with the radiative interior. The tachocline of radial shear there
  that varies with latitude is thought to be the site of the global
  magnetic dynamo. Most recent continuous helioseismic probing with
  MDI on SOHO and from GONG have revealed systematic temporal changes
  in Ω with the advancing solar cycle. These include propagating bands
  of zonal flow speedup extending from the surface to a depth of about
  70 Mm, distinctive out-of-phase vacillations in Ω above and below the
  tachocline with a period of about 1.3 years near the equator, a changing
  pattern of meridional circulation cells with broken symmetries in the
  two hemispheres, and complex speedups and slowdowns in the bulk of
  the convection zone. We review these helioseismic findings and their
  implications. We also describe current 3-D numerical simulations of
  anelastic rotating convection in full spherical shells used to study
  the differential rotation that can be established by such turbulence
  exhibiting coherent structures. These simulations enabled by massively
  parallel computers are making promising contact with aspects of the
  Ω profiles deduced from helioseismology, but challenges remain.

Title: Interior Solar-Cycle Changes Detected by Helioseismology
Authors: Howe, R.; Hill, F.; Komm, R. W.; Christensen-Dalsgaard, J.;
   Munk Larsen, R.; Schou, J.; Thompson, M. J.; Toomre, J.
Bibcode: 2001IAUS..203...40H
Altcode:
  Helioseismic measurements with the MDI instrument aboard SOHO,
  and complementary measurements from the GONG network, are revealing
  changes deep within the Sun as the solar cycle progresses. We will
  present results based on recent data from both experiments, including
  variations in the rotation rate deep inside the convection zone.

Title: Subsurface Flows with Advancing Solar Cycle Using Dense-Pack
    Ring-Diagram Analyses
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
   Hill, F.
Bibcode: 2001IAUS..203..211H
Altcode:
  Large-scale horizontal flows within the upper convection zone of
  the sun are analyzed using the helioseismic technique of ring-diagram
  analysis applied to data from SOI-MDI. We map the velocity field over a
  substantial fraction of the solar disk by carrying out local inversion
  analyses over a Dense-Pack mosaic of many overlapping sites. There
  are substantial changes in subsurface flows at any given site from
  one day to the next that appear to be of solar origin. Such mosaics
  are processed almost daily for at least two solar rotations during
  each of the MDI Dynamics Campaigns from 1996 through 1999. We find
  that longitudinally-averaged zonal velocity possess bands of fast and
  slow flow. As the solar cycle progresses, the latitudes at which the
  fast bands occur migrate towards the equator and vary in their flow
  amplitudes. These bands are not symmetric about the solar equator, and
  their asymmetry changes with time. The average meridional flow for the
  years 1996 to 1998 is primarily poleward, reaching maxima in the two
  hemispheres at the latitudes at which the zonal fast belts occur. The
  latitudes of maximal meridional flow drift equatorward in time much as
  the zonal fast belts. However, in 1999, the meridional circulation in
  the northern hemisphere develops a two-celled structure with latitude,
  whereas in the southern hemisphere it remains single celled.

Title: Solar Interior: Convection Zone
Authors: Toomre, J.
Bibcode: 2000eaa..bookE1995T
Altcode:
  The Sun, like all main sequence stars of moderate mass, possesses a
  deep convective envelope just below its surface in which turbulent
  fluid motions serve to carry outward the energy flux that results from
  nuclear burning within its core. Observations of the Sun reveal complex
  flows and magnetic structures that are evidence of highly turbulent
  convection just below the surface of this rotating s...

Title: New Approach to Study Extended Evolution of Supergranular
    Flows and Their Advection of Magnetic Elements
Authors: Lisle, Jason; De Rosa, Marc; Toomre, Juri
Bibcode: 2000SoPh..197...21L
Altcode:
  Using velocity and magnetogram data extracted from the full-disk field
  of view of MDI during the 1999 Dynamics Program, we have studied the
  dynamics of small-scale magnetic elements (3-7 Mm in size) over time
  periods as long as six days while they are readily visible on the
  solar disk. By exploiting concurrent time series of magnetograms and
  Doppler images, we have compared the motion of magnetic flux elements
  with the supergranular velocity field inferred from the correlation
  tracking of mesogranular motions. Using this new method (which combines
  the results from correlation tracking of mesogranules with detailed
  analysis of simultaneous magnetograms), it is now possible to correlate
  the motions of the velocity field and magnetic flux for long periods of
  time and at high temporal resolution. This technique can be utilized
  to examine the long-term evolution of supergranulation and associated
  magnetic fields, for it can be applied to data that span far longer
  time durations than has been possible previously. As tests of its
  efficacy, we are able to use this method to verify many results of
  earlier investigations. We confirm that magnetic elements travel at
  approximately 350 m s <SUP>−1</SUP> throughout the duration of their
  lifetime as they are transported by supergranular outflows. We also
  find that the positions of the magnetic flux elements coincide with
  the supergranular network boundaries and adjust as the supergranular
  network itself evolves over the six days of this data set. Thus
  we conclude that this new method permits us to study the extended
  evolution of the supergranular flow field and its advection of magnetic
  elements. Since small-scale magnetic elements are strongly advected
  by turbulent convection, their dynamics can give important insight
  into the properties of the subsurface convection.

Title: Phase inversion of one-dimensional artificial seismic data
Authors: Gough, D. O.; Sekii, T.; Toomre, J.
Bibcode: 2000SoPh..195....1G
Altcode:
  Oscillations of an inhomogeneous one-dimensional loop have been
  simulated for the purpose of examining the effect of excitation and
  damping on the sound-speed inversion based on phase analysis. It has
  been demonstrated that the procedure is robust against the realization
  noise arising from frequent, stochastic excitation of weakly damped
  waves, but that strong damping can spoil the inversion.

Title: Turbulent Convection, Rotation, and the Solar Dynamo
Authors: Tobias, Steve; Toomre, Juri; Weiss, Nigel
Bibcode: 2000astu.progE..30T
Altcode:
  No abstract at ADS

Title: Global Models of Turbulent Convection
Authors: Toomre, Juri
Bibcode: 2000astu.confE..35T
Altcode:
  No abstract at ADS

Title: Local Fractional Frequency Shifts of Helioseismic Modes
    Associated With Magnetic Activity Using Ring-Diagram Analyses
Authors: Hindman, B. W.; Haber, D. A.; Toomre, J.; Bogart, R. S.
Bibcode: 2000SPD....31.0109H
Altcode: 2000BAAS...32..802H
  Using full-disk velocity data from SOI-MDI during the advancing solar
  cycle from 1996 through 1999, we have computed the local frequencies of
  high-degree p modes and f modes over localized regions of the sun. The
  frequencies are obtained through ring-diagram mode fitting over
  Dense-Pack data sets consisting of mosaics of 189 overlapping tiles,
  each tracked separately at the surface rotation rate over 1664-minute
  time intervals during the MDI Dynamics Programs. Each tile is 16 degrees
  square, and the tile centers are separated by 7.5 degrees in latitude
  and longitude. For each observational day and for each tile, we have
  computed the frequency shift measured relative to the temporal and
  spatial average of the entire set of frequencies sampled over a full
  rotation. The magnetic field is computed for each of the 189 regions
  using the magnetograms supplied every 90 min by MDI. The motion of
  active regions as they rotate across the solar disk is vividly traced by
  changes in the frequencies. Active regions appear as locations of large
  positive frequency shifts. Depending on the radial order and wavenumber
  of the observed acoustic modes the frequency shifts can be as much as
  10 to 30 microHz. The magnitude and frequency dependence of the large
  frequency shifts are consistent with the far smaller changes measured
  in global oscillation frequencies over the solar cycle, provided the
  local frequency shifts are averaged over the solar disk and are scaled
  to the appropriate wavenumber regimes. The frequency dependence of
  the shifts indicates that the physical phenomena inducing the shifts
  is largely confined to the surface layers of the sun, although there
  is some indication that there may be a deeper structural component as
  well. This research was supported by NASA through grants NAG 5-8133
  and NAG 5-7996, and by NSF through grant ATM-9731676.

Title: Solar-Cycle Changes in Convection-Zone Dynamics from SOI and
    GONG Data
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
   Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J.
Bibcode: 2000SPD....31.0113H
Altcode: 2000BAAS...32..803H
  The combined GONG and MDI medium-degree helioseismic data sets now cover
  more than 4.5 years and allow us to probe the changing dynamics of the
  convection zone in unprecedented detail. Here we present the latest
  results from both projects, showing the evolution of the migrating zonal
  flows close to the surface and also changes close to and below the base
  of the convection zone. This work utilizes data obtained by the Global
  Oscillation Network Group (GONG) project, managed by the National Solar
  Observatory, a Division of the National Optical Astronomy Observatories,
  which is operated by AURA, Inc. under a cooperative agreement with the
  National Science Foundation. SOHO is a joint project of ESA and NASA.

Title: Evolving Dynamics of the Supergranular Flow Field
Authors: De Rosa, M. L.; Lisle, J. P.; Toomre, J.
Bibcode: 2000SPD....31.0106D
Altcode: 2000BAAS...32..802D
  We study several large (45-degree square) fields of supergranules
  for as long as they remain visible on the solar disk (about 6 days)
  to characterize the dynamics of the supergranular flow field and its
  interaction with surrounding photospheric magnetic field elements. These
  flow fields are determined by applying correlation tracking methods
  to time series of mesogranules seen in full-disk SOI-MDI velocity
  images. We have shown previously that mesogranules observed in this
  way are systematically advected by the larger scale supergranular
  flow field in which they are embedded. Applying correlation tracking
  methods to such time series yields the positions of the supergranular
  outflows quite well, even for locations close to disk center. These
  long-duration datasets contain several instances where individual
  supergranules are recognizable for time scales as long as 50 hours,
  though most cells persist for about 25 hours that is often quoted as a
  supergranular lifetime. Many supergranule merging and splitting events
  are observed, as well as other evolving flow patterns such as lanes
  of converging and diverging fluid. By comparing the flow fields with
  the corresponding images of magnetic fields, we confirm the result
  that small-scale photospheric magnetic field elements are quickly
  advected to the intercellular lanes to form a network between the
  supergranular outflows. In addition, we characterize the influence
  of larger-scale regions of magnetic flux, such as active regions,
  on the flow fields. Furthermore, we have measured even larger-scale
  flows by following the motions of the supergranules, but these flow
  fields contain a high noise component and are somewhat difficult to
  interpret. This research was supported by NASA through grants NAG
  5-8133 and NAG 5-7996, and by NSF through grant ATM-9731676.

Title: Helioseismic Dense-Pack Ring Diagram Analyses to Study
    Evolution of Subsurface Flows With Advancing Solar Cycle
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
   Larsen, R. M.; Hill, F.
Bibcode: 2000SPD....31.0103H
Altcode: 2000BAAS...32..801H
  We analyze data obtained from the Michelson Doppler Imager (MDI) on
  SOHO in 1996-1999 using the helioseismic ring-diagram technique to
  infer large-scale horizontal flows within the upper solar convection
  zone. Each separate ring analysis deduces the average flow components
  below a 16 degree square region on the solar surface. We map the
  velocity field over a substantial fraction of the solar disk by
  repeating the analysis over a Dense-Pack mosaic of 189 overlapping
  tiles, with each sampling interval spanning 1664 minutes. We process
  such a mosaic on a nearly daily schedule and have analyzed two
  Carrington rotations (48 days) in 1996 and one or two rotations each
  in 1997, 1998, and 1999. There are substantial changes in subsurface
  flows at any given site from one day to the next that appear to be of
  solar origin. The mean zonal and meridional flows display gradual and
  systematic changes. We find that the longitudinally-averaged zonal
  velocity, after removing a smooth differential rotation component,
  possesses bands of fast and slow flow, much like `torsional
  oscillations' first reported from surface Doppler measurements and
  recently from global helioseismic assessments. As the solar cycle
  progresses, the latitudes at which the fast bands occur migrate towards
  the equator. The amplitudes of these banded zonal flows increase with
  magnetic activity. Our local-area analyses reveal that these belts
  of fast and slow flow are not symmetric about the solar equator, and
  their asymmetry changes with time. The average meridional flow (of
  typical amplitudes 10-20 m/s) deduced from our samplings for 1996,
  1997 and 1998 is primarily poleward and reaches maxima in the two
  hemispheres at the latitudes at which the zonal fast belts occur. As
  these zonal fast belts drift towards the equator, the latitudes of
  maximal meridional flow also drift equatorward. We further find that
  in 1999 the meridional circulation in the northern hemisphere has
  developed a two-celled structure with latitude, whereas that in the
  southern hemisphere is still single celled. This research was supported
  by NASA through grants NAG 5-8133 and NAG 5-7996, and by NSF through
  grant ATM-9731676.

Title: Deeply Penetrating Banded Zonal Flows in the Solar Convection
    Zone
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
   Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J.
Bibcode: 2000ApJ...533L.163H
Altcode: 2000astro.ph..3121H
  Helioseismic observations have detected small temporal variations
  of the rotation rate below the solar surface that correspond to the
  so-called ``torsional oscillations'' known from Doppler measurements of
  the surface. These appear as bands of slower- and faster-than-average
  rotation moving equatorward. Here we establish, using complementary
  helioseismic observations over 4 yr from the GONG network and from
  the MDI instrument on board SOHO, that the banded flows are not
  merely a near-surface phenomenon: rather, they extend downward at
  least 60 Mm (some 8% of the total solar radius) and thus are evident
  over a significant fraction of the nearly 200 Mm depth of the solar
  convection zone.

Title: Turbulent Solar Convection and Its Coupling with Rotation:
    The Effect of Prandtl Number and Thermal Boundary Conditions on the
    Resulting Differential Rotation
Authors: Elliott, J. R.; Miesch, M. S.; Toomre, J.
Bibcode: 2000ApJ...533..546E
Altcode:
  The dynamics of the vigorous convection in the outer envelope of the Sun
  must determine the transport of energy, angular momentum, and magnetic
  fields and must therefore be responsible for the observed surface
  activity and the angular velocity profile inferred helioseismically
  from SOI-MDI p-mode frequency splittings. Many different theoretical
  treatments have been applied to the problem, ranging from simple
  physical models such as mixing-length theory to sophisticated numerical
  simulations. Although mixing-length models provide a good first
  approximation to the structure of the convection zone, recent progress
  has mainly come from numerical simulations. Computational constraints
  have until now limited simulations in full spheres to essentially
  laminar convection. The angular velocity profiles have shown constancy
  on cylinders, in striking contrast to the approximately constant angular
  velocity on radial lines inferred for the Sun. In an effort to further
  our understanding of the dynamics of the solar convection zone, we have
  developed a new computer code that, by exploiting massively parallel
  architectures, enables us to study fully turbulent spherical shell
  convection. Here we present five fully evolved solutions. Motivated
  by the fact that a constant entropy upper boundary condition produces
  a latitudinal modulation of the emergent energy flux (of about 10%,
  i.e., far larger than is observed for the Sun), three of these solutions
  have a constant energy flux upper boundary condition. This leads to a
  latitudinal modulation of the specific entropy that breaks the constancy
  of the angular velocity on cylinders, making it more nearly constant
  on radial lines at midlatitudes. The effect of lowering the Prandtl
  number is also considered-highly time-dependent, vortical convective
  motions are revealed, and the Reynolds stresses are altered, leading to
  a reduced differential rotation. The differential rotation in all of
  our simulations shows a balance between driving by Reynolds stresses
  and damping by viscosity. This contrasts with the situation in the
  Sun, where the effect of viscosity on the mean differential rotation
  is almost negligible.

Title: Near-Surface Flow Fields Deduced Using Correlation Tracking
    and Time-Distance Analyses
Authors: De Rosa, Marc; Duvall, T. L., Jr.; Toomre, Juri
Bibcode: 2000SoPh..192..351D
Altcode:
  Near-photospheric flow fields on the Sun are deduced using two
  independent methods applied to the same time series of velocity images
  observed by SOI-MDI on SOHO. Differences in travel times between f
  modes entering and leaving each pixel measured using time-distance
  helioseismology are used to determine sites of supergranular
  outflows. Alternatively, correlation tracking analysis of mesogranular
  scales of motion applied to the same time series is used to deduce
  the near-surface flow field. These two approaches provide the means to
  assess the patterns and evolution of horizontal flows on supergranular
  scales even near disk center, which is not feasible with direct
  line-of-sight Doppler measurements. We find that the locations of the
  supergranular outflows seen in flow fields generated from correlation
  tracking coincide well with the locations of the outflows determined
  from the time-distance analysis, with a mean correlation coefficient
  after smoothing of <SUB>s</SUB>=0.890. Near-surface velocity field
  measurements can be used to study the evolution of the supergranular
  network, as merging and splitting events are observed to occur in these
  images. The data consist of one 2048-min time series of high-resolution
  (0.6'' pixels) line-of-sight velocity images taken by MDI on 1997
  January 16 -18 at a cadence of one minute.

Title: Solar shear flows deduced from helioseismic dense-pack
    samplings of ring diagrams
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
   Thompson, M. J.; Hill, F.
Bibcode: 2000SoPh..192..335H
Altcode:
  We report on large-scale horizontal flows in the solar convection zone
  and their variability in time and space using a local-helioseismology
  technique known as ring-diagram analysis. By performing this analysis
  on a dense mosaic of individual regions on the solar disk, i.e.,
  a `Dense-Pack' sampling, and repeating the analysis periodically on
  several time scales, we are able to assess the variation of horizontal
  flows from day-to-day, week-to-week, and year-to-year. We find that
  although there are changes in the flows on all these time scales,
  there are also basic patterns that persist. On a daily time scale we
  observe that the flow is reduced in those areas which are occupied
  by large active regions. On somewhat longer time-scales we see bands
  of persistent fast and slow zonal flow that are identifiable as
  torsional oscillations. As we examine these bands during a series of
  years, we find that these bands migrate toward the equator as solar
  activity increases. Similarly, the latitudes at which the meridional
  flow reaches maximum follow these regions of fast zonal flow as they
  migrate equatorwards. These Dense-Pack samplings also reveal substantial
  differences in the zonal and meridional flow patterns in the northern
  and southern hemispheres.

Title: Time Variability of Rotation in Solar Convection Zone From
    soi-mdi
Authors: Toomre, J.; Christensen-Dalsgaard, J.; Howe, R.; Larsen,
   R. M.; Schou, J.; Thompson, M. J.
Bibcode: 2000SoPh..192..437T
Altcode:
  The variation of rotation in the convection zone over a period of two
  years from mid-1996 is studied using inversions of SOI-MDI data. We
  confirm the existence of near-surface banded zonal flows migrating
  towards the equator from higher latitudes, and reveal that these banded
  flows extend substantially beneath the surface, possibly to depths
  as great as 70 Mm (10% of the solar radius). Our results also reveal
  apparently significant temporal variations in the rotation rate at
  high latitudes and in the vicinity of the tachocline over the period
  of study.

Title: Dynamic Variations at the Base of the Solar Convection Zone
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
   Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J.
Bibcode: 2000Sci...287.2456H
Altcode:
  We have detected changes in the rotation of the sun near the base of
  its convective envelope, including a prominent variation with a period
  of 1.3 years at low latitudes. Such helioseismic probing of the deep
  solar interior has been enabled by nearly continuous observation of
  its oscillation modes with two complementary experiments. Inversion of
  the global-mode frequency splittings reveals that the largest temporal
  changes in the angular velocity Ω are of the order of 6 nanohertz
  and occur above and below the tachocline that separates the sun's
  differentially rotating convection zone (outer 30% by radius) from
  the nearly uniformly rotating deeper radiative interior beneath. Such
  changes are most pronounced near the equator and at high latitudes and
  are a substantial fraction of the average 30-nanohertz difference in Ω
  with radius across the tachocline at the equator. The results indicate
  variations of rotation close to the presumed site of the solar dynamo,
  which may generate the 22-year cycles of magnetic activity.

Title: Three-dimensional Spherical Simulations of Solar
    Convection. I. Differential Rotation and Pattern Evolution Achieved
    with Laminar and Turbulent States
Authors: Miesch, Mark S.; Elliott, Julian R.; Toomre, Juri; Clune,
   Tom L.; Glatzmaier, Gary A.; Gilman, Peter A.
Bibcode: 2000ApJ...532..593M
Altcode:
  Rotationally constrained convection possesses velocity correlations
  that transport momentum and drive mean flows such as differential
  rotation. The nature of this transport can be very complex in turbulent
  flow regimes, where large-scale, coherent vorticity structures and mean
  flows can be established by smaller scale turbulence through inverse
  cascades. The dynamics of the highly turbulent solar convection
  zone therefore may be quite different than in early global-scale
  numerical models, which were limited by computational resources to
  nearly laminar flows. Recent progress in high-performance computing
  technology and ongoing helioseismic investigations of the dynamics of
  the solar interior have motivated us to develop more sophisticated
  numerical models of global-scale solar convection. Here we report
  three-dimensional simulations of compressible, penetrative convection
  in rotating spherical shells in both laminar and turbulent parameter
  regimes. The convective structure in the laminar case is dominated
  by ``banana cells,'' but the turbulent case is much more complex,
  with an intricate, rapidly evolving downflow network in the upper
  convection zone and an intermittent, plume-dominated structure in
  the lower convection zone and overshoot region. Convective patterns
  generally propagate prograde at low latitudes and retrograde at high
  latitudes relative to the local rotation. The differential rotation
  profiles show some similarity with helioseismic determinations of
  the solar rotation but still exhibit significantly more cylindrical
  alignment. Strong, intermittent, vortical downflow lanes and plumes
  play an important dynamical role in turbulent flow regimes and are
  responsible for significant differences relative to laminar flows with
  regard to momentum and energy transport and to the structure of the
  overshoot region at the base of the convection zone.

Title: Local Fractional Frequency Shifts Used as Tracers of Magnetic
    Activity
Authors: Hindman, Bradley; Haber, Deborah; Toomre, Juri; Bogart, Rick
Bibcode: 2000SoPh..192..363H
Altcode:
  Using data from SOI-MDI (Haber et al., 2000), we compute the local
  frequencies of high-degree p modes and f modes. The frequencies are
  obtained through ring-diagram mode fitting. The Dense-Pack data set
  consists of a mosaic of 189 overlapping tiles, each tracked separately
  at the surface rotation rate over 1664-min time intervals during the
  Dynamics Programs. Each tile is 16° square and the tile centers are
  separated by 7.5° in latitude and longitude. For each sampling day and
  for each tile, we have computed the frequency shift measured relative to
  the temporal and spatial average of the entire set of frequencies. The
  motion of active regions as they rotate across the solar disk is vividly
  traced by these measurements. Active regions appear as locations of
  large positive frequency shifts. If the shifts are averaged over the
  solar disk and are scaled down to the appropriate wave number regime,
  the magnitude and frequency dependence of the shifts are consistent
  with the measured changes in global oscillation frequencies that occur
  over the solar cycle. As with the frequency shifts of low-degree global
  oscillations, the frequency dependence of the shifts indicates that
  the physical phenomena inducing the shifts is confined to the surface
  layers of the Sun.

Title: Helioseismic detection of temporal variations of solar rotation
    rate near the base of the convection zone
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
   Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J.
Bibcode: 1999AAS...19510702H
Altcode: 1999BAAS...31R1530H
  The differential rotation of the Sun and its ability to generate
  large-scale magnetic fields through cyclic dynamo action appear to be
  intimately linked. It is now commonly thought that the global dynamo
  behavior responsible for the emergence of active regions is derived
  from strong organized toroidal magnetic fields generated by rotational
  shear in a thin region (the tachocline) at the base of the convection
  zone. The magnetic field could well have a feedback effect on the fluid
  motions in the region. We are thus motivated to use helioseismology
  to look for changes in rotation profiles near the tachocline as the
  Sun's magnetic cycle progresses. This approach has become possible
  using frequency-splitting data for p- and f-mode oscillations derived
  over four years (from May 1995 to Sept 1999) of full-disk Doppler
  observations from the ground-based Global Oscillation Network Group
  (GONG) project and from the Michelson Doppler Imager (MDI) experiment
  aboard the SOHO spacecraft. Inversions using two different methods of
  the splittings from these two independent data sets reveal systematic
  variations of the rotation rate close to the base of the convection
  zone, with different behavior at low and high latitudes. Notable
  are variations of order 6 nHz in rotation rates near the equator,
  to be compared with the radial angular velocity contrast across the
  tachocline of about 30 nHz. These exhibit several nearly repetitive
  changes with a period of about 1.2-1.4 years and appear to be real
  changes in the deep convection zone and tachocline rotation rates that
  need to be followed as the solar cycle progresses. The GONG project is
  managed by the National Solar Observatory, a Division of the National
  Optical Astronomy Observatories, which is operated by AURA, Inc. under
  a cooperative agreement with the National Science Foundation. SOHO is
  a joint project of ESA and NASA.

Title: Evolution of Subsurface Zonal and Meridional Flows With
    Advancing Solar Cycle Using Helioseismic Dense-Pack Samplings of
    Ring Diagrams
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
   Larsen, R. M.; Hill, F.
Bibcode: 1999AAS...19510701H
Altcode: 1999BAAS...31Q1530H
  We report on the behavior of large-scale horizontal flows within the
  upper convection zone of the sun, using the helioseismic technique of
  ring-diagram analysis applied to data from the Michelson Doppler Imager
  (MDI) on the SOHO spacecraft. Horizontal flows yield displacements in
  the rings of power (at fixed frequency) associated with solar acoustic
  waves propagating in different directions below a localized area being
  studied. We pass these shifts through an inversion procedure and obtain
  measurements of the zonal and meridional flows as a function of depth to
  about 10 Mm below the surface. Each separate ring analysis deduces the
  average flow below a 16 degree square region on the solar surface. We
  map the velocity field over a substantial fraction of the solar disk by
  repeating the analysis over a densely packed mosaic of 189 overlapping
  tiles (called a Dense-Pack). We process such a mosaic on a nearly daily
  schedule and have fully analyzed two Carrington rotations (48 days) in
  1996 and one rotation each in 1997, 1998, and 1999 during MDI Dynamics
  Campaigns. We find that the longitudinally-averaged zonal velocity,
  after removing a smooth differential rotation component, possesses
  bands of fast and slow flow, much like `torsional oscillations'
  first reported from surface Doppler measurements and recently from
  global helioseismic assessments. As the solar cycle progresses,
  the latitudes at which the fast bands occur migrate towards the
  equator. The amplitudes of these banded zonal flows increase with
  magnetic activity. Our local-area analyses reveal that these belts of
  fast and slow flow are not symmetric about the solar equator, and their
  asymmetry changes with time. The average meridional flow is primarily
  poleward and reaches maxima in the two hemispheres at the latitudes
  at which the zonal fast belts occur. As these zonal fast belts drift
  towards the equator, the latitudes of maximal meridional flow also drift
  equatorward. This research was supported by NASA grants NAG 5--8133,
  NAG 5--7996 and NAG 5--3077 and by NSF grant ATM-9731676.

Title: Daily Variations and Average Structure of Solar Shear Flows
    Deduced from Helioseismic Dense-Pack Samplings of Ring Diagrams
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
   Schou, J.; Hill, F.
Bibcode: 1999AAS...194.5611H
Altcode: 1999BAAS...31..913H
  We report on the daily variations and average behavior of large-scale
  flows in the upper convection zone as determined by ring-diagram
  helioseismic analysis applied to SOI-MDI full-disk velocity data from
  the 1996 and 1998 Dynamics Campaigns. We have tracked many small regions
  of 15 degrees diameter whose centers are spaced 7.5 degrees apart in
  latitude and longitude, creating a mosaic of tiles that oversample
  the spatial domain. The tiles cover the solar disk out to a distance
  of 52.5 degrees from disk center. An individual dense-pack mosaic
  is prepared by tracking each of 189 regions for 1664 minutes (27.7
  hrs). Successive mosaics are prepared every 15 degrees in Carrington
  longitude, roughly once every 1633 minutes. Such mosaics now cover
  more than two full Carrington rotations in 1996 and one rotation in
  1998. This is the best spatial and temporal coverage of any ring-diagram
  study carried out to date. The longitudinally averaged meridional flow
  varies with latitude but remains relatively constant with depth below
  the upper shear layer at 2 Mm down to a depth of about 16 Mm. The
  averaged zonal flow increases with depth within this same layer and
  agrees well with the rotation rates found from global modes. However
  with the high-degree wave field data from this analysis we are better
  able to resolve that shear layer within the upper convection zone. We
  see bands of faster averaged zonal flow near 30 degrees latitude both
  in the northern and southern hemisphere that are present at all depths
  studied. We also present movies of the daily variations in the flows
  within this dense pack for given depths that show the evolution of
  the complex velocity field. This research was supported by NASA grants
  NAG5-3077 and NAG5-7996, and NSF grant AST-9417337.

Title: Comparison Between Near-Surface Flow Fields Deduced from
    Correlation Tracking and Time-Distance Helioseismology Methods
Authors: De Rosa, M. L.; Toomre, J.; Duvall, T. L., Jr.
Bibcode: 1999AAS...194.5608D
Altcode: 1999BAAS...31..913D
  Near-photospheric flow fields deduced using two independent methods
  applied to the same SOI-MDI time series of images from SOHO are
  compared. Differences in travel times between incoming and outgoing
  f modes measured using time-distance helioseismology are used to
  determine the sites of supergranule outflows. Alternatively, correlation
  tracking analysis is applied to granular and mesogranular structures
  seen in time series of Doppler and intensity images. We find that the
  locations of the supergranular outflows seen in flow fields generated
  from correlation tracking coincide well with the locations of the
  outflows determined from the time-distance analysis. The near-surface
  flow fields provide us with insight in understanding the dyanmics
  of the turbulent convection occurring below the photosphere. The data
  consist of four 512-minute time series of high-resolution (0.6'' pixels)
  Doppler images and continuum intensity images taken by MDI on 17--18
  January 1997 at a cadence of one minute.

Title: Time-Variability of the Inferred Rotation in the Upper
    Convection Zone
Authors: Toomre, J.; Christensen-Dalsgaard, J.; Howe, R.; Larsen,
   R. M.; Schou, J.; Thompson, M. J.
Bibcode: 1999soho....9E..87T
Altcode:
  We present results of inverting for the rotation of the upper convection
  zone, using frequency splittings derived from successive 72-day time
  series of SOI-MDI observations. Schou (1999; also Schou et al. 1998)
  has studied the evolution of the pattern of small-scale zonal flows
  in the near-surface layers using f-mode splittings and has found that
  this flow pattern migrates equatorward in a manner similar to that seen
  in the so-called torsional oscillation observed in surface Doppler
  measurements. In the present work we look at the time variability
  of the rotation at greater depth, in the upper convection zone, by
  inverting both f- and p-mode splittings. The evolution of the flow is
  less regular than is seen at the surface, but we do observe apparently
  significant variations in the inferred flow pattern, on latitudinal
  scales similar to those seen at the surface. In particular, in the
  subsurface shear layer we see intriguing variations, with the first
  year's data showing apparent emergence of zonal flows of some 10-15
  m/s amplitude at around 20 degrees latitude.

Title: Large-Eddy Simulations of Turbulent Solar Convection and its
    Coupling with Rotation
Authors: Elliott, J. R.; Miesch, M.; Toomre, J.
Bibcode: 1999soho....9E..54E
Altcode:
  Turbulent fluid motions in the sun's convection zone must play a
  large part in setting up the observed differential rotation. Studies
  of convection have either been based on the parametrizations of the
  effects of turbulent motions (for example the Reynolds stresses),
  or upon numerical simulations. Most of the recent progress has come
  from numerical simulations. In this poster we present results from
  anelastic convection simulations carried out in a spherical shell
  geometry, and calculated with a code specifically optimized for high
  performance on Massively Parallel machines. Whereas early simulations
  tended to show angular velocity approximately constant on cylinders
  aligned with the rotation axis (in disagreement with deductions from
  helioseismology), our latest simulations show a differential rotation
  in much closer agreement with helioseismic inversions. This results from
  several improvements over earlier models, including the use of a higher
  resolution coupled with longer integration times, and the implementation
  of the idea of large-eddy simulation. We hope to demonstrate convergence
  of our results as the resolution of the shell is increased.

Title: Comparison Between Near-Surface Flow Fields Deduced from
    Correlation Tracking and Time-Distance Helioseismology Methods
Authors: de Rosa, Marc; Toomre, Juri; Duvall, T. L., Jr.
Bibcode: 1999soho....9E..51D
Altcode:
  Near-photospheric flow fields deduced using two independent methods
  applied to the same SOI-MDI time series of images from SOHO are
  compared. Differences in travel times between incoming and outgoing f
  modes measured using time-distance helioseismology are used to determine
  the sites of supergranule outflows. Alternatively, correlation tracking
  analysis is applied to granular and mesogranular structures seen in time
  series of Doppler and intensity images. We find that the locations
  of the supergranular outflows seen in flow fields generated from
  correlation tracking coincide well with the locations of the outflows
  determined from the time-distance analysis. The near-surface flow fields
  provide us with insight in understanding the dynamics of the turbulent
  convection occurring below the photosphere. The data consist of four
  512-minute time series of high-resolution (0.6 arc-second pixels)
  Doppler images and continuum intensity images taken by MDI on 17-18
  January 1997 at a cadence of one minute.

Title: Long-Term Dynamics of Small-Scale Magnetic Flux Elements
    Embedded in the Near-Surface Velocity Field
Authors: Lisle, Jason; de Rosa, Marc; Toomre, Juri
Bibcode: 1999soho....9E..72L
Altcode:
  Using velocity and magnetogram data generated by SOI-MDI during the
  1999 Dynamics Program, we have studied the dynamics of small-scale
  magnetic elements over time periods of several days. By exploiting
  concurrent time series of MDI magnetograms and velocity images, we
  have correlated the motions of the magnetic flux elements with the
  supergranular velocity field inferred from tracking of mesogranular
  motions. We confirm that these magnetic elements travel at approximately
  200 m/s throughout the duration of their lifetime (10-20 hours) as they
  are transported by supergranular outflows. We also find that boundaries
  of supergranules traced by magnetic flux elements coincide with the
  boundaries determined from the tracking of mesogranules. In addition,
  we have studied the association between magnetic flux emergence and
  destruction events and the evolution of the supergranular network. The
  data consist of several tracked regions of corresponding magnetogram and
  photospheric velocity images extracted from full-disk SOI-MDI images
  taken during the 1999 Dynamics Program when the MDI instrument was at
  best focus. Time series were created by following these individual
  patches as they rotated across the solar disk. Individual magnetic
  elements were identified by thresholding the magnetograms, while the
  supergranular flow fields were determined by applying a correlation
  tracking algorithm to time series of mesogranules. The mesogranules
  were isolated by removing the signal due to solar rotation, p-mode
  oscillations, and supergranulation from the velocity data.

Title: Phase Inversion of One-Dimensional Artificial Seismic Data
Authors: Gough, D. O.; Sekii, T.; Toomre, J.
Bibcode: 1999soho....9E..30G
Altcode:
  It has been pointed out (Sekii 1997; Gough, Sekii &amp; Toomre 1998,
  1999) that the application of the phase inversion technique (Gough,
  Merryfield &amp; Toomre 1991, 1993, 1998) to the solar high-degree
  sectoral data, for detecting the background inhomogeneity in the
  solar equatorial region, may be facing difficulty arising from the
  presence of excitation and damping. We have studied the implication of
  the effects of these, using a simple model of stochastically excited
  damped oscillations of a one-dimensional loop. The results of phase
  inversions for various cases will be presented and various strategies
  to overcome the difficulty will be discussed.

Title: Simulation of Wave Fields to Assess the Sensitivity of
    Ring-Diagram Analyses to Shearing Flows
Authors: Hindman, B. W.; Gough, D. O.; Haber, D. A.; Thompson, M. J.;
   Toomre, J.
Bibcode: 1999soho....9E..64H
Altcode:
  Ring-diagram analyses of acoustic-wave distortion by flows map
  horizontal motions within the solar convection beneath the localized
  regions where the observations are taken. To leading order, the
  flow field responsible for the advection of waves is taken to be
  horizontally uniform across the region. Current ring-diagram analyses
  are only carried out to this order, although in reality the flow
  is likely to vary across the local patch of the Sun. It is crucial
  for the interpretation of the results of ring-diagram analyses that
  the effects of shearing flows be assessed. Furthermore, the present
  analyses ignore any influence on the ring parameters of flows exterior
  to the region being studied. We present a progress report on the
  forward calculation of the modification of ring parameters produced
  by spatially varying flow fields. We examine effects of flow fields
  both inside and outside the region of observation. Additionally,
  we assess the influence of the non-uniform flow on the maps of the
  velocity field obtained by inverting the ring-parameter data. The
  effect of the inhomogeneous flow can be studied as a scattering
  problem. We have developed Green functions connecting an underlying
  inhomogeneous horizontal flow to the scattered wave field that results
  when an incident plane wave encounters the flow. By considering an
  ensemble of such incident waves, ring parameters can be inferred from
  the wave field. One application is to analyze artificial data sets,
  computed from models that contain horizontal shear flows. The scattered
  wave field produced by a prescribed 3-D shearing flow is computed,
  and the original and scattered wave fields are combined to generate an
  artificial helioseismic data set. The artificial data so produced should
  then be passed through a ring-diagram analysis and the deduced velocity
  field compared to the known imposed flow. Another application is to
  compute 3-D kernels relating the ring parameters to the underlying flow:
  these will in the future permit 3-D inversions for the flows within
  the solar convection zone, using mosaics of many ring-diagram samplings.

Title: Changes in High-Degree Oscillation Frequencies from 1996 to
    1999 Determined from Ring-Diagram Analysis
Authors: Bogart, R. S.; Schou, J.; Haber, D. A.; Hindman, B. W.;
   Toomre, J.; Hill, F.
Bibcode: 1999soho....9E..45B
Altcode:
  Ring-diagram analysis has traditionally been used primarily as a
  diagnostic for large-scale flows in the upper convection zone. It
  also yields values for the unperturbed (rest) frequencies of the
  local high-degree p-mode oscillations. These frequencies, positioned
  predominantly in a regime where ridge-fitting of traditional
  global modes is difficult, possess information about the average
  near-surface temperature profile in the region being analyzed. As
  the solar magnetic activity level increased from 1996 through 1999,
  we might expect these frequencies to have changed correspondingly. We
  present spatially and temporally averaged rest frequencies determined
  from ring-diagram analysis of full-disk Doppler data for selected
  intervals from each of the four annual SOI Dynamics campaigns covering
  the rise in solar activity from 1996 through 1999. These analyses are
  performed on a `dense-pack' mosaic of tracked tiles that oversample
  the spatial domain with a resolution of 15 heliographic degrees (180
  Mm). Tiles are individually tracked over time spans of 1664 minutes
  (27.7 hr), so a given physical region on the Sun is sampled from 7 to
  15 times depending on its latitude as it rotates across the visible
  hemisphere. We discuss the frequency changes seen for comparable areas
  on the disc over the years analyzed. This research is supported by
  NASA grant NAG5-3077 at Stanford University.

Title: Local p-Mode Frequency Shifts Used as Tracers of Solar Activity
Authors: Hindman, B. W.; Haber, D. A.; Toomre, J.
Bibcode: 1999soho....9E...5H
Altcode:
  The Dense-Pack data set from SOI-MDI was originally devised for
  ring-diagram analyses. Each day of data consists of 189 separately
  tracked tiles on the solar surface. Each tile is 16 degrees square
  and the tile centers are separated by 7.5 degrees in latitude and
  longitude. The tiling extends out to roughly 52.5 degrees from disk
  center. I have computed the local frequency of low order p modes in each
  of the Dense-Pack tiles. The frequencies were calculated once a day for
  a period of roughly two months during the 1996 dynamics campaign and
  for a period of more than week during the 1998 dynamics campaign. For
  each day of data and for each latitude and longitude in the Dense-Pack
  grid, I have computed the fractional frequency shift by subtracting
  the spatial and temporal average of the entire set of frequencies. The
  motion of active regions as they rotate across the solar disk is
  vividly tracked by these measurement of the local fractional frequency
  shift. Active regions are locations with a positive frequency shift,
  indicating a region of higher wave propagation speed. To demonstrate
  this correspondence, I will present animations of the fractional
  frequency shift overlaid with contemporaneous magnetograms.

Title: Solar Shear Flows Deduced From Helioseismic Dense-Pack
    Samplings of Ring Diagrams
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
   Schou, J.; Hill, F.
Bibcode: 1999soho....9E..62H
Altcode:
  Large-scale flows in the upper convection zone can be inferred
  by ring-diagram helioseismic analysis, permitting the study of
  both their daily variations and their longer temporal means. We use
  selected full-disk SOI-MDI velocity data from the 1996, 1997, and 1998
  Dynamics campaigns. We have tracked sets of regions (each 15 degrees
  in diameter and spaced 7.5 degrees apart in latitude and longitude),
  creating a `dense-pack' mosaic of such tiles that oversamples the
  spatial domain. The tiles cover the solar disc to a distance of up to
  52.5 degrees from center. A single dense-pack mosaic is prepared by
  tracking each of 189 regions for 1664 minutes (27.7 hrs). Such mosaics
  now cover more than two full Carrington rotations in 1996 and one-third
  of a rotation each in both 1997 and 1998. This is the best spatial and
  temporal coverage of any ring-diagram study carried out to date. We
  are able to compare the mean flows determined over 9-day averages
  for data from the different SOI-MDI Dynamics campaigns, as well as
  examine the daily flow maps, allowing us to study possible changes
  in the convection during the rising magnetic activity of the current
  solar cycle. We also present movies of the daily variations in the
  flows within this dense pack for given depths that show the evolution
  of the complex velocity field. The longitudinally-averaged meridional
  flow varies with latitude but remains relatively constant with depth
  below the upper shear layer at 2 Mm down to a depth of about 16 Mm. The
  averaged zonal flow increases with depth within this same layer and
  agrees well with the rotation rates found from global modes. However,
  with the high-degree wave-field data from this analysis we are better
  able to resolve the shear layer within the upper convection zone. We
  see bands of faster and slower average zonal flows in both hemispheres;
  these are present at all depths studied.

Title: Helioseismic Studies of Differential Rotation in the Solar
    Envelope by the Solar Oscillations Investigation Using the Michelson
    Doppler Imager
Authors: Schou, J.; Antia, H. M.; Basu, S.; Bogart, R. S.; Bush,
   R. I.; Chitre, S. M.; Christensen-Dalsgaard, J.; Di Mauro, M. P.;
   Dziembowski, W. A.; Eff-Darwich, A.; Gough, D. O.; Haber, D. A.;
   Hoeksema, J. T.; Howe, R.; Korzennik, S. G.; Kosovichev, A. G.;
   Larsen, R. M.; Pijpers, F. P.; Scherrer, P. H.; Sekii, T.; Tarbell,
   T. D.; Title, A. M.; Thompson, M. J.; Toomre, J.
Bibcode: 1998ApJ...505..390S
Altcode:
  The splitting of the frequencies of the global resonant acoustic modes
  of the Sun by large-scale flows and rotation permits study of the
  variation of angular velocity Ω with both radius and latitude within
  the turbulent convection zone and the deeper radiative interior. The
  nearly uninterrupted Doppler imaging observations, provided by the
  Solar Oscillations Investigation (SOI) using the Michelson Doppler
  Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft
  positioned at the L<SUB>1</SUB> Lagrangian point in continuous sunlight,
  yield oscillation power spectra with very high signal-to-noise ratios
  that allow frequency splittings to be determined with exceptional
  accuracy. This paper reports on joint helioseismic analyses of
  solar rotation in the convection zone and in the outer part of the
  radiative core. Inversions have been obtained for a medium-l mode set
  (involving modes of angular degree l extending to about 250) obtained
  from the first 144 day interval of SOI-MDI observations in 1996. Drawing
  inferences about the solar internal rotation from the splitting data
  is a subtle process. By applying more than one inversion technique
  to the data, we get some indication of what are the more robust
  and less robust features of our inversion solutions. Here we have
  used seven different inversion methods. To test the reliability and
  sensitivity of these methods, we have performed a set of controlled
  experiments utilizing artificial data. This gives us some confidence
  in the inferences we can draw from the real solar data. The inversions
  of SOI-MDI data have confirmed that the decrease of Ω with latitude
  seen at the surface extends with little radial variation through much
  of the convection zone, at the base of which is an adjustment layer,
  called the tachocline, leading to nearly uniform rotation deeper
  in the radiative interior. A prominent rotational shearing layer in
  which Ω increases just below the surface is discernible at low to
  mid latitudes. Using the new data, we have also been able to study the
  solar rotation closer to the poles than has been achieved in previous
  investigations. The data have revealed that the angular velocity
  is distinctly lower at high latitudes than the values previously
  extrapolated from measurements at lower latitudes based on surface
  Doppler observations and helioseismology. Furthermore, we have found
  some evidence near latitudes of 75° of a submerged polar jet which
  is rotating more rapidly than its immediate surroundings. Superposed
  on the relatively smooth latitudinal variation in Ω are alternating
  zonal bands of slightly faster and slower rotation, each extending
  some 10° to 15° in latitude. These relatively weak banded flows
  have been followed by inversion to a depth of about 5% of the solar
  radius and appear to coincide with the evolving pattern of ``torsional
  oscillations'' reported from earlier surface Doppler studies.

Title: Pumping of Magnetic Fields by Turbulent Penetrative Convection
Authors: Tobias, Steven M.; Brummell, Nicholas H.; Clune, Thomas L.;
   Toomre, Juri
Bibcode: 1998ApJ...502L.177T
Altcode:
  A plausible scenario for solar dynamo action is that the large-scale
  organized toroidal magnetic field is generated by the action of strong
  radial shear at the base of the solar convection zone, whereas the
  weaker poloidal field is regenerated by cyclonic convection throughout
  the convection zone. We show, using high-resolution three-dimensional
  numerical simulations, that the required transport of magnetic field
  from the convection zone to the overshoot region can be achieved on
  a convective rather than diffusive timescale by a pumping mechanism
  in turbulent penetrative compressible convection. A layer of magnetic
  field initially placed in the convection zone is swept down by strong
  sinking plumes, locally amplified, and deposited in the stable region
  at the base of the convection zone, despite the opposing action of
  magnetic buoyancy. The rate of transport is insensitive to the strength
  of the initial imposed field.

Title: Phase Inversion: Inferring Solar Subphotospheric Flow and
    Other Asphericity from the Distortion of Acoustic Waves
Authors: Gough, Douglas; Merryfield, William J.; Toomre, Juri
Bibcode: 1998ApJ...501..882G
Altcode:
  A method is proposed for analyzing an almost monochromatic train of
  waves propagating in a single direction in an inhomogenous medium that
  is not otherwise changing in time. An effective phase is defined in
  terms of the Hilbert transform of the wave function, which is related,
  via the JWKB approximation, to the spatial variation of the background
  state against which the wave is propagating. The contaminating effect
  of interference between the truly monochromatic components of the train
  is eliminated using its propagation properties. Measurement errors,
  provided they are uncorrelated, are manifest as rapidly varying noise;
  although that noise can dominate the raw phase-processed signal, it can
  largely be removed by low-pass filtering. The intended purpose of the
  analysis is to determine the distortion of solar oscillations induced by
  horizontal structural variation and material flow. It should be possible
  to apply the method directly to sectoral modes. The horizontal phase
  distortion provides a measure of longitudinally averaged properties
  of the Sun in the vicinity of the equator, averaged also in radius
  down to the depth to which the modes penetrate. By combining such
  averages from different modes, the two-dimensional variation can be
  inferred by standard inversion techniques. After taking due account
  of horizontal refraction, it should be possible to apply the technique
  also to locally sectoral modes that propagate obliquely to the equator
  and thereby build a network of lateral averages at each radius, from
  which the full three-dimensional structure of the Sun can, in principle,
  be determined as an inverse Radon transform.

Title: Subphotospheric Convective Flows Determined by Ring-Diagram
    Analyses of SOI-MDI Observations
Authors: Haber, D.; Hindman, B.; Toomre, J.; Bogart, R.; Schou, J.;
   Hill, F.
Bibcode: 1998ESASP.418..791H
Altcode: 1998soho....6..791H
  The variation of large-scale velocity flows with depth and location
  on the sun places important constraints on theoretical models of the
  solar convection zone and dynamo. High-degree oscillations can be
  viewed as nearly plane waves that are advected and distorted by the
  underlying flows. By conducting observations over limited regions
  of the solar surface to obtain `ring diagram' power spectra, we can
  deduce spatially-averaged horizontal flows with depth below that
  region. Previous analyses of ring diagrams have already suggested
  the presence of strong shearing flows below the surface. We have
  now implemented a highly efficient technique for determining these
  horizontal flows with depth and report here on a systematic analysis of
  full-disk Doppler velocity data taken continuously with a one-minute
  cadence during portions of the two-month dynamics observing program
  with SOI-MDI in 1996. The square regions examined span about 15-circ,
  and are studied for time intervals each of about 1536 mins (~25 hrs). A
  lattice of such squares is considered: their centers are spaced 15-circ
  apart in longitude and there are seven such regions across the solar
  disk at +20-circ, 0-circ, -20-circ latitude. Another set of regions
  is placed along the central meridian at 10-circ and 15-circ intervals
  in latitude. Properties of the underlying large-scale subphotospheric
  flows and their temporal variations so revealed are presented in detail.

Title: Slow Poles and Shearing Flows from Heliospheric Observations
    with MDI and GONG Spanning a Year
Authors: Schou, J.; Christensen-Dalsgaard, J.; Howe, R.; Larsen,
   R. M.; Thompson, M. J.; Toomre, J.
Bibcode: 1998ESASP.418..845S
Altcode: 1998soho....6..845S
  We invert one year of coeval high-resolution rotational splitting data
  (up to degree l 250) from GONG and SOI-MDI. The first 4 months of
  MDI data uncovered several new features in the rotation of the solar
  convective envelope: surface and subsurface zonal bands corresponding
  to the so-called torsional oscillations, superimposed on the overall
  smooth latitudinal surface rotation; a drop in the near-polar surface
  rotation rate below the rate extrapolated from lower latitudes; and an
  indication of a prograde jet-like feature at high latitudes at a depth
  of about 5 percent of the solar radius. Using the 1 year of data from
  the MDI and GONG instruments, we test the robustness and stationarity of
  these features. As an aid to testing the robustness of our inferences,
  we use two independent inversion methods (2-D regularized least squares
  and SOLA) and apply them to the splitting data obtained from both GONG
  and MDI.

Title: Helioseismology: What are We Learning About the Sun?
Authors: Toomre, Juri
Bibcode: 1998ASPC..154..275T
Altcode: 1998csss...10..275T
  Helioseismology studies the internal structure and dynamics of the
  Sun, utilizing very precise measurements of the frequencies of sound
  waves that propagate throughout the solar interior and are observed
  at the surface. Efforts to accurately and precisely measure the mode
  frequencies from a single observing site have met with fundamental
  limitations imposed by the day-night cycle. Such difficulties
  have recently been overcome as nearly uninterrupted Doppler imaged
  observations of the full solar disk have become available both from
  the ground-based six-station Global Oscillation Network Group (GONG)
  project and from the SOI Michelson Doppler Imager (SOI-MDI) aboard
  the SOHO spacecraft in continuous sunlight orbiting the Sun-Earth L_1
  Lagrangian point. Thus helioseismology has entered a major new phase
  of intensive scientific study as coordinated scientific teams have
  started to analyze both the GONG and SOI data. We review some of the
  basic principles and motivations of helioseismology, and then discuss
  some of the preliminary scientific results obtained by the teams through
  inversion of the global-mode frequencies and their splittings, dealing
  with the structure of the solar interior and the physics of stellar
  models, and an assessment of the differential rotation profile with
  depth and latitude. The inversions confirm that the surface latitudinal
  variation of the rotation rate carries through much of the convection
  zone. At the base of the convection zone there is a currently unresolved
  adjustment layer with latitudinally independent rotation at greater
  depths. A shearing layer just below the surface is discernible at low
  to mid latitudes. Such global investigations are supplemented by local
  area analyses via ring diagrams and time-distance methods, which enable
  one to probe the subsurface variation of large-scale flows and thermal
  structures with depth beneath selected regions of the Sun.

Title: Correlation Tracking of Mesogranules from SOI-MDI Doppler
    Images to Reveal Supergranular Flow Fields
Authors: De Rosa, Marc L.; Toomre, Juri
Bibcode: 1998ESASP.418..753D
Altcode: 1998soho....6..753D
  We present evidence that mesogranules on the sun are advected
  horizontally by the underlying supergranular flow field. Correlation
  tracking of mesogranules, as observed in full-disk SOI-MDI Doppler
  images, reveal that the flow field experienced by the mesogranules is
  composed of several long-lived regions of divergent fluid. These outflow
  regions correlate well with the locations of supergranules present on
  related Doppler images. The flow fields also contain regions where the
  fluid is converging or is moving slowly, both corresponding to areas of
  the related Doppler images where no organized supergranular outflows
  exist. Typical velocities are of order 200 m s<SUP>-1</SUP>. The data
  used in this study consist of 30-circ-square patches of the photospheric
  velocity field extracted from full-disk SOI-MDI Dopplergrams. Time
  series were created by tracking each patch in a frame corotating
  with the surface plasma. Images of mesogranulation superimposed on
  supergranulation were created by removing the velocity signals due
  to rotation and acoustic oscillations. The supergranular signal is
  isolated by spatially smoothing each image, while the mesogranular
  signal is isolated by taking the residual of the smoothed and unsmoothed
  images. The correlation tracking calculation was performed on the time
  series of mesogranulation, from which the surface flow-fields analyzed
  in this study were deduced.

Title: Turbulent Solar Convection and its Coupling with Rotation
Authors: Elliott, J. R.; Miesch, M. S.; Toomre, J.; Cluney, T. C.;
   Glatzmaier, G. A.
Bibcode: 1998ESASP.418..765E
Altcode: 1998soho....6..765E
  Previous numerical simulations of global-scale solar convection in
  rotating spherical shells of fluid have been restricted by computational
  resources to deal with nearly laminar flow regimes. Disparities between
  the differential rotation profiles that such models predict and those
  deduced from helioseismology, coupled with recent advances in high
  performance computing, encouraged us to begin pursuing numerical
  simulations of global-scale convection in turbulent parameter
  regimes. We anticipate that rotationally-constrained turbulence can
  possess inverse cascades that yield large-scale coherent vorticity
  structures and strong mean flows which coexist with less persistent
  smaller-scale turbulence, and yield angular velocity profiles that
  may be quite different than those obtained with laminar convection. We
  have developed a new code for studying penetrative anelastic convection
  in rotating spherical shells which is highly optimized for massively
  parallel supercomputer architechtures, and as a result, is capable
  of achieving more turbulent flow regimes than previously possible. We
  present results from such simulations, which are providing new insight
  into the nature of turbulent solar convection and its coupling to
  differential rotation.

Title: Some Comments on Phase Inversions
Authors: Gough, D. O.; Sekii, T.; Toomre, J.
Bibcode: 1998ESASP.418..789G
Altcode: 1998soho....6..789G
  The method of phase inversion have been proposed and tested for simple
  cases by Gough, Merryfield and Toomre(1991,1993,1998) for detection of
  inhomogeneity in media by observing wave propagation. We discuss some of
  the difficulties that are encountered with the procedure in practice,
  and what might be done to overcome them in transferring the technique
  to the solar case, such as in the study of horizontal inhomogeneity in
  the solar cavity along the equator using the MDI sectoral-mode data. A
  complication seems to arise, aside from observational problems, from
  the fact that the waves are not only scattered by inhomogeneity, but
  are also excited and damped, as is observed in the broadening of the
  ridges in the k-ω diagram.

Title: Turbulent Compressible Convection with Rotation. II. Mean
    Flows and Differential Rotation
Authors: Brummell, Nicholas H.; Hurlburt, Neal E.; Toomre, Juri
Bibcode: 1998ApJ...493..955B
Altcode:
  The effects of rotation on turbulent, compressible convection within
  stellar envelopes are studied through three-dimensional numerical
  simulations conducted within a local f-plane model. This work
  seeks to understand the types of differential rotation that can
  be established in convective envelopes of stars like the Sun, for
  which recent helioseismic observations suggest an angular velocity
  profile with depth and latitude at variance with many theoretical
  predictions. This paper analyzes the mechanisms that are responsible
  for the mean (horizontally averaged) zonal and meridional flows that are
  produced by convection influenced by Coriolis forces. The compressible
  convection is considered for a range of Rayleigh, Taylor, and Prandtl
  (and thus Rossby) numbers encompassing both laminar and turbulent flow
  conditions under weak and strong rotational constraints. <P />When the
  nonlinearities are moderate, the effects of rotation on the resulting
  laminar cellular convection leads to distinctive tilts of the cell
  boundaries away from the vertical. These yield correlations between
  vertical and horizontal motions that generate Reynolds stresses that
  can drive mean flows, interpretable as differential rotation and
  meridional circulations. Under more vigorous forcing, the resulting
  turbulent convection involves complicated and contorted fluid particle
  trajectories, with few clear correlations between vertical and
  horizontal motions, punctuated by an evolving and intricate downflow
  network that can extend over much of the depth of the layer. Within
  such networks are some coherent structures of vortical downflow that
  tend to align with the rotation axis. These yield a novel turbulent
  alignment mechanism, distinct from the laminar tilting of cellular
  boundaries, that can provide the principal correlated motions and thus
  Reynolds stresses and subsequently mean flows. The emergence of such
  coherent structures that can persist amidst more random motions is a
  characteristic of turbulence with symmetries broken by rotation and
  stratification. Such structure is here found to play a crucial role
  in defining the mean zonal and meridional flows that coexist with the
  convection. Though they are subject to strong inertial oscillations,
  the strength and type of the mean flows are determined by a combination
  of the laminar tilting and the turbulent alignment mechanisms. Varying
  the parameters produces a wide range of mean motions. Among these,
  some turbulent solutions exhibit a mean zonal velocity profile that
  is nearly constant with depth, much as deduced by helioseismology
  at midlatitudes within the Sun. The solutions exhibit a definite
  handedness, with the direction of the persistent mean flows often
  prescribing a spiral with depth near the boundaries, also in accord
  with helioseismic deductions. The mean helicity has a profile that is
  positive in the upper portion of the domain and negative in the lower
  portion, a property bearing on magnetic dynamo processes that may be
  realized within such rotating layers of turbulent convection.

Title: Differential rotation in turbulent compressible convection
Authors: Brummell, N. H.; Toomre, J.; Hurlburt, N.
Bibcode: 1997ASSL..225..223B
Altcode: 1997scor.proc..223B
  Numerical simulations of 3D compressible convection in a local
  rectilinear geometry show that zonal and meridional mean flows,
  $\overline{u}(z)$ and $\overline{v}(z)$, can be produced when rotation
  is included. A wide variety of mean profiles can be achieved depending
  upon the parameters, including behaviour equivalent (within the
  limitations of the model) to that inferred from helioseismic solar
  observations.

Title: Rotation and Zonal Flows in the Solar Envelope from the
    SOHO/MDI Observations
Authors: Scherrer, P. H.; Schou, J.; Bogart, R. S.; Bush, R. I.;
   Hoeksema, J. T.; Kosovichev, A. G.; Antia, H. M.; Chitre, S. M.;
   Christensen-Dalsgaard, J.; Larsen, R. M.; Pijpers, F. P.; Eff-Darwich,
   A.; Korzennik, S. G.; Gough, D. O.; Sekii, T.; Howe, R.; Tarbell,
   T.; Title, A. M.; Thompson, M. J.; Toomre, J.
Bibcode: 1997AAS...191.7310S
Altcode: 1997BAAS...29.1322S
  We report on the latest inferences concerning solar differential
  rotation that have been drawn from the helioseismic data that are now
  available from the Solar Oscillations Investigation (SOI) using the
  Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory
  (SOHO). That spacecraft is positioned in a halo orbit near the Sun-Earth
  Lagrangian point L_1, in order to obtain continuous Doppler-imaged
  observations of the sun with high spatial fidelity. Doppler velocity,
  intensity and magnetic field images are recorded, based on modulations
  of the 676.8 nm Ni I solar absorption line. The high spatial resolution
  of MDI thereby permits the study of many millions of global resonant
  modes of solar oscillation. Determination and subsequent inversion
  of the frequencies of these modes, including the degeneracy-splitting
  by the rotation of the sun, enables us to infer how the sun's angular
  velocity varies throughout much of the interior. The current MDI data
  are providing substantial refinements to the helioseismic deductions
  that can be made about differential rotation both within the convection
  zone and in its transition to the radiative interior. The shearing
  layer evident in the angular velocity Omega just below the solar
  surface is becoming better defined, as is the adjustment layer or
  tachocline near the base of the convection zone. The MDI data are also
  revealing a prominent decrease in Omega at high latitudes from the
  rotation rate expressed by a simple three-term expansion in latitude
  that was originally deduced from surface Doppler measurements. Further,
  there are indications that a submerged polar vortex involving somewhat
  faster Omega than its surroundings exists at about 75(deg) in latitudes.

Title: Global-scale numerical simulation of solar turbulent convection
    and its coupling to rotation
Authors: Elliott, J. R.; Miesch, M.; Toomre, J.; Clune, T. C.;
   Glatzmaier, G. A.
Bibcode: 1997AAS...191.7403E
Altcode: 1997BAAS...29.1324E
  The larger scales of convection in the sun are influenced by
  rotation, leading to a redistribution of angular momentum which
  is seen as differential rotation. Previous numerical simulations
  of such global-scale convection in rotating spherical shells of
  fluid have been restricted by computational resources to deal with
  nearly laminar flow regimes for the resolved scales of motion, though
  provisions were made for diffusive transport by nominally turbulent
  unresolved scales. The disparities between the differential rotation
  profiles that those models predict (angular velocity nearly constant on
  cylinders) and those deduced from the frequency splittings of p modes
  (nearly constant on radii in the convection zone), coupled with recent
  advances in high performance computing, encouraged us to begin pursuing
  numerical simulations of global-scale convection in turbulent parameter
  regimes. We anticipate that rotationally-constrained turbulence can
  possess inverse cascades that yield large-scale coherent vorticity
  structures and strong mean flows which coexist with less persistent
  smaller-scale turbulence, and yield angular velocity profiles that may
  be quite different than those obtained with laminar convection. The
  dominant challenge to all turbulence simulations is to be able to
  explicitly describe the dynamics over a broad enough range of length
  scales. To this end, we have developed a new code for studying rotating
  anelastic convection in spherical shells, employing expansions in
  spherical harmonics to resolve horizontal structures and in Chebyshev
  polynomials to resolve radial structures. Appropriate optimization
  techniques, including expedient use of inter-processor transposes
  and sophisticated load balancing, enable the code to achieve high
  performance on massively parallel architectures, and currently to reach
  a speed of around 100Mflop/s per node on the Cray T3E. The new code is
  enabling us to perform simulations of convection at spatial resolutions
  significantly higher than those of earlier studies, and thereby to
  begin to investigate fully turbulent parameter regimes. We present the
  results from such a simulation, which includes the important effects
  of penetration into the stable interior, and discuss the corresponding
  differential-rotation profile obtained.

Title: The Nature of Supergranulation from SOI-MDI Dopplergrams
Authors: De Rosa, Marc L.; Toomre, Juri
Bibcode: 1997SPD....28.0257D
Altcode: 1997BAAS...29..903D
  We discuss the distribution of supergranule cell areas and
  evolutionary characteristics as determined from a series of SOI-MDI
  dopplergrams. Patches of the photospheric velocity field 30(deg)
  x30(deg) (heliographic) in size were tracked as they rotated across the
  disk of the sun. Supergranule boundaries were identified on each tracked
  image by a pattern recognition algorithm, from which supergranule area
  distributions and evolutionary trends are found.

Title: Persistence of Large-Scale Flows Beneath Quiet Sun: Local-Area
    Analysis Using MDI Doppler Data
Authors: Haber, D.; Toomre, J.; Bogart, R.; Schou, J.; Gonzalez, I.;
   Hill, F.
Bibcode: 1997SPD....28.0201H
Altcode: 1997BAAS...29..893H
  Knowing the large-scale flows that occur in the upper convection zone
  is critical to our understanding of the processes that govern the
  solar cycle. Here we apply solar oscillation ring-diagram analysis to
  several small tracked regions on the sun, approximately 15(deg) on a
  side, as they rotate across the solar disk, in order to determine the
  persistence and depth variation of the large-scale flows beneath these
  regions. We use the Doppler velocity images from the Michelson Doppler
  Imager (MDI) instrument aboard the Solar Heliospheric Observatory
  (SOHO) satellite using quiet-sun data taken during the MDI Dynamics
  campaign of 1996. Three regions at different latitudes were extracted
  from full-disk Doppler images of 1024 x 1024 pixels (pixel size ~
  2'' square) with a one-minute temporal cadence. Eight sequential
  1536-minute time intervals were tracked, remapped onto great-circle
  grids, spatially and temporally filtered, and apodized in space and
  time. They were then Fourier transformed in two spatial dimensions
  and time. The resulting power spectra show characteristic rings at
  each frequency slice. Shifts in the center positions of the rings are
  caused by underlying flow fields and can be inverted to map these flows
  with depth. We use several techniques to fit these shifts in order to
  assess the stability of the results.

Title: Structure and Rotation of the Solar Interior: Initial Results
    from the MDI Medium-L Program
Authors: Kosovichev, A. G.; Schou, J.; Scherrer, P. H.; Bogart, R. S.;
   Bush, R. I.; Hoeksema, J. T.; Aloise, J.; Bacon, L.; Burnette, A.; de
   Forest, C.; Giles, P. M.; Leibrand, K.; Nigam, R.; Rubin, M.; Scott,
   K.; Williams, S. D.; Basu, Sarbani; Christensen-Dalsgaard, J.; Dappen,
   W.; Rhodes, E. J., Jr.; Duvall, T. L., Jr.; Howe, R.; Thompson, M. J.;
   Gough, D. O.; Sekii, T.; Toomre, J.; Tarbell, T. D.; Title, A. M.;
   Mathur, D.; Morrison, M.; Saba, J. L. R.; Wolfson, C. J.; Zayer, I.;
   Milford, P. N.
Bibcode: 1997SoPh..170...43K
Altcode:
  The medium-l program of the Michelson Doppler Imager instrument on board
  SOHO provides continuous observations of oscillation modes of angular
  degree, l, from 0 to ∽ 300. The data for the program are partly
  processed on board because only about 3% of MDI observations can be
  transmitted continuously to the ground. The on-board data processing,
  the main component of which is Gaussian-weighted binning, has been
  optimized to reduce the negative influence of spatial aliasing of the
  high-degree oscillation modes. The data processing is completed in a
  data analysis pipeline at the SOI Stanford Support Center to determine
  the mean multiplet frequencies and splitting coefficients. The initial
  results show that the noise in the medium-l oscillation power spectrum
  is substantially lower than in ground-based measurements. This enables
  us to detect lower amplitude modes and, thus, to extend the range of
  measured mode frequencies. This is important for inferring the Sun's
  internal structure and rotation. The MDI observations also reveal the
  asymmetry of oscillation spectral lines. The line asymmetries agree
  with the theory of mode excitation by acoustic sources localized in the
  upper convective boundary layer. The sound-speed profile inferred from
  the mean frequencies gives evidence for a sharp variation at the edge
  of the energy-generating core. The results also confirm the previous
  finding by the GONG (Gough et al., 1996) that, in a thin layer just
  beneath the convection zone, helium appears to be less abundant than
  predicted by theory. Inverting the multiplet frequency splittings from
  MDI, we detect significant rotational shear in this thin layer. This
  layer is likely to be the place where the solar dynamo operates. In
  order to understand how the Sun works, it is extremely important to
  observe the evolution of this transition layer throughout the 11-year
  activity cycle.

Title: Plane-wave analysis of 501 data
Authors: Bogart, R. S.; Discher de Sá, L. A.; González Hernández,
   I.; Patrón Recio, J.; Haber, D. A.; Toomre, J.; Hill, F.; Rhodes,
   E. J., Jr.; Xue, Y.; SOI Ring Diagrams Team
Bibcode: 1997IAUS..181..111B
Altcode:
  No abstract at ADS

Title: Internal structure and rotation of the Sun: First results
    from MDI data
Authors: Kosovichev, A. G.; Schou, J.; Scherrer, P. H.; Bogart, R. S.;
   Bush, R. I.; Hoeksema, J. T.; Aloise, J.; Bacon, L.; Burnette, A.;
   De Forest, C.; Giles, P. M.; Leibrand, K.; Nigam, R.; Rubin, M.;
   Scott, K.; Williams, S. D.; Basu, Sarbani; Christensen-Dalsgaard,
   J.; Däppen, W.; Rhodes, E. J., Jr.; Duvall, T. L., Jr.; Howe, R.;
   Thompson, M. J.; Gough, D. O.; Sekii, T.; Toomre, J.; Tarbell, T. D.;
   Title, A. M.; Mathur, D.; Morrison, M.; Saba, J. L. R.; Wolfson,
   C. J.; Zayer, I.; Milford, P. N.
Bibcode: 1997IAUS..181..203K
Altcode:
  No abstract at ADS

Title: Dynamics of the solar convection zone
Authors: Toomre, J.
Bibcode: 1997ppvs.conf..343T
Altcode:
  Introduction Multiple discrete scales of convection Probing of structure
  and flows with helioseismology Multitude of magnetic structures and
  dynamo action Structures and inverse cascades in turbulence Dynamical
  range of solar turbulence Local models of rotating compressible
  convection Formulation of local ƒ-plane models Nature of rotating
  turbulent convection Driving of mean flows and implications for
  differential rotation Penetrative convection and intermittency in
  transport of heat Global models of spherical convection Formulation
  of anelastic convection in rotating shells Nature of global convection
  and the mean flows Reflections

Title: Internal rotation and dynamics of the Sun from GONG data
Authors: Korzennik, S.; Thompson, M. J.; Toomre, J.; GONG Internal
   Rotation Team
Bibcode: 1997IAUS..181..211K
Altcode:
  No abstract at ADS

Title: The seismic structure of the Sun from GONG
Authors: Anderson, E.; Antia, H. M.; Basu, S.; Chaboyer, B.; Chitre,
   S. M.; Christensen-Dalsgaard, J.; Eff-Darwich, A.; Elliott, J. R.;
   Giles, P. M.; Gough, D. O.; Guzik, J. A.; Harvey, J. W.; Hill,
   F.; Leibacher, J. W.; Kosovichev, A. G.; Monteiro, M. J. P. F. G.;
   Richard, O.; Sekii, T.; Shibahashi, H.; Takata, M.; Thompson, M. J.;
   Toomre, J.; Vauclair, S.; Vorontsov, S. V.
Bibcode: 1997IAUS..181..151A
Altcode:
  No abstract at ADS

Title: Turbulent Compressible Convection with Rotation. I. Flow
    Structure and Evolution
Authors: Brummell, Nicholas H.; Hurlburt, Neal E.; Toomre, Juri
Bibcode: 1996ApJ...473..494B
Altcode:
  The effects of Coriolis forces on compressible convection are studied
  using three-dimensional numerical simulations carried out within a
  local modified f-plane model. The physics is simplified by considering
  a perfect gas occupying a rectilinear domain placed tangentially to a
  rotating sphere at various latitudes, through which a destabilizing
  heat flux is driven. The resulting convection is considered for a
  range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers,
  evaluating conditions where the influence of rotation is both weak
  and strong. Given the computational demands of these high-resolution
  simulations, the parameter space is explored sparsely to ascertain
  the differences between laminar and turbulent rotating convection. The
  first paper in this series examines the effects of rotation on the flow
  structure within the convection, its evolution, and some consequences
  for mixing. Subsequent papers consider the large-scale mean shear flows
  that are generated by the convection, and the effects of rotation on
  the convective energetics and transport properties. <P />It is found
  here that the structure of rotating turbulent convection is similar to
  earlier nonrotating studies, with a laminar, cellular surface network
  disguising a fully turbulent interior punctuated by vertically coherent
  structures. However, the temporal signature of the surface flows is
  modified by inertial motions to yield new cellular evolution patterns
  and an overall increase in the mobility of the network. The turbulent
  convection contains vortex tubes of many scales, including large-scale
  coherent structures spanning the full vertical extent of the domain
  involving multiple density scale heights. Remarkably, such structures
  align with the rotation vector via the influence of Coriolis forces on
  turbulent motions, in contrast with the zonal tilting of streamlines
  found in laminar flows. Such novel turbulent mechanisms alter the
  correlations which drive mean shearing flows and affect the convective
  transport properties. In contrast to this large-scale anisotropy,
  small-scale vortex tubes at greater depths are randomly orientated by
  the rotational mixing of momentum, leading to an increased degree of
  isotropy on the medium to small scales of motion there. Rotation also
  influences the thermodynamic mixing properties of the convection. In
  particular, interaction of the larger coherent vortices causes a loss of
  correlation between the vertical velocity and the temperature leaving
  a mean stratification which is not isentropic.

Title: Angular Momentum Transport in Turbulent Compressible Convection
Authors: Hurlburt, N. E.; Brummell, N. H.; Toomre, J.
Bibcode: 1996AAS...188.6907H
Altcode: 1996BAAS...28R.936H
  We consider the dynamics of compressible convection within a curved
  local segment of a rotating spherical shell, aiming to resolve the
  disparity between the differential rotation profiles predicted by
  previous laminar simulations (angular velocity constant on cylinders)
  and those deduced from helioseismic inversion of the observed frequency
  splitting of p modes. By limiting the horizontal extent of the domain
  under study, we can utilize the available spatial degrees of freedom
  on current supercomputers to attain more turbulent flows than in the
  full shell. Our previous study of three-dimensional convection within
  a slab geometry of an f-plane neglected the effects of curvature,
  and thus did not admit the generation of Rossby waves. These waves
  propagate in the longitudinal direction and thus produce rather
  different spectral characteristics and mean flows in the north-south
  and east-west directions. By considering motions in a curvilinear
  geometry in which the Coriolis parameter varies with latitude, we
  admit the possibility of Rossby waves which couple to the turbulent
  convection. Here we present simulations with Rayleigh numbers in excess
  of 10(6) , and Prandtl numbers less than 0.1 in such a curved local
  segment of a spherical shell using a newly developed code based on
  compact finite differences. This computational domain takes the form of
  a curved, periodic channel in longitude with stress-free sidewalls in
  latitude and radius. Despite the differences in geometry and boundary
  conditions, the flows maintain similarities with those of our previous
  f-plane simulations. The surface flows form broad, laminar networks
  which mask the much more turbulent flows of the interior. The dynamics
  within this turbulent region is controlled by the interactions of a
  tangled web of strong vortex tubes. These interactions are further
  complicated by the effects of curvature. The differential rotation
  generated by the turbulent convection typically increases with depth
  and attains a maximum at the base of the layer of about 10 % over the
  imposed rotation rate.

Title: Perspectives in Helioseismology
Authors: Gough, D. O.; Leibacher, J. W.; Scherrer, P. H.; Toomre, J.
Bibcode: 1996Sci...272.1281G
Altcode:
  Helioseismology is probing the interior structure and dynamics of
  the sun with ever-increasing precision, providing a well-calibrated
  laboratory in which physical processes can be studied under conditions
  that are unattainable on Earth. Nearly 10 million resonant modes
  of oscillation are observable in the solar atmosphere, and their
  frequencies need to be known with great accuracy in order to gauge the
  sun's interior. The advent of nearly continuous imaged observations
  from the complementary ground-based Global Oscillation Network Group
  (GONG) observatories and the space-based Solar and Heliospheric
  Observatory instruments augurs a new era of discovery. The flow of
  early results from GONG resolves some issues and raises a number of
  theoretical questions whose answers are required for understanding
  how a seemingly ordinary star actually operates.

Title: Preliminary Ring-Diagram Analysis of Doppler Velocity Fields
    Observed with MDI on SOHO
Authors: Haber, D. A.; Bogart, R. S.; Sa, L. A. D.; Hill, F.; Toomre,
   J.; Duvall, T. L., Jr.
Bibcode: 1996AAS...188.3710H
Altcode: 1996BAAS...28Q.879H
  We analyze properties of high-degree acoustic wave fields over small
  patches of the sun using high-resolution Doppler velocity observations
  with the Michelson Doppler Imager (MDI) on the Solar Heliospheric
  Observatory (SOHO). By studying asymmetric frequency shifts in the
  acoustic waves that propagate in different horizontal directions,
  we can make inferences about the underlying large-scale flows which
  contribute to these shifts. We here analyze two different sets of
  data obtained from early observations with MDI. One is a continuous
  80-hour sequence of full-disk Doppler images with a 60 s cadence and 4''
  resolution, the other is an 8-hour sequence of high-resolution images
  that have 1.2'' resolution. Both sets have 1024 x 1024 pixels but the
  second set only covers about 36deg on the sun and is centered on the
  central meridian and somewhat above disk center. In both cases we remap
  a number of smaller areas of the data and compute three-dimensional
  Fourier transforms (two in space, one in time) over each patch. The
  resulting power diagrams have cross-sections in frequency that exhibit
  power distributed along rings. The detailed shapes and displacements
  of the rings depend upon the averaged velocities and their gradients,
  which can be estimated by theory. We measure the displacements of the
  rings using two different analysis techniques, thereby determining
  the frequency splittings which are then used in inversion procedures
  to deduce the underlying smoothed flow fields in each region. The
  results from the various patches provide preliminary estimates of the
  flow structures present in the upper convection zone.

Title: The Seismic Structure of the Sun
Authors: Gough, D. O.; Kosovichev, A. G.; Toomre, J.; Anderson,
   E.; Antia, H. M.; Basu, S.; Chaboyer, B.; Chitre, S. M.;
   Christensen-Dalsgaard, J.; Dziembowski, W. A.; Eff-Darwich, A.;
   Elliott, J. R.; Giles, P. M.; Goode, P. R.; Guzik, J. A.; Harvey,
   J. W.; Hill, F.; Leibacher, J. W.; Monteiro, M. J. P. F. G.; Richard,
   O.; Sekii, T.; Shibahashi, H.; Takata, M.; Thompson, M. J.; Vauclair,
   S.; Vorontsov, S. V.
Bibcode: 1996Sci...272.1296G
Altcode:
  Global Oscillation Network Group data reveal that the internal
  structure of the sun can be well represented by a calibrated standard
  model. However, immediately beneath the convection zone and at the
  edge of the energy-generating core, the sound-speed variation is
  somewhat smoother in the sun than it is in the model. This could be a
  consequence of chemical inhomogeneity that is too severe in the model,
  perhaps owing to inaccurate modeling of gravitational settling or to
  neglected macroscopic motion that may be present in the sun. Accurate
  knowledge of the sun's structure enables inferences to be made about
  the physics that controls the sun; for example, through the opacity,
  the equation of state, or wave motion. Those inferences can then be
  used elsewhere in astrophysics.

Title: The Global Oscillation Network Group (GONG) Project
Authors: Harvey, J. W.; Hill, F.; Hubbard, R. P.; Kennedy, J. R.;
   Leibacher, J. W.; Pintar, J. A.; Gilman, P. A.; Noyes, R. W.; Title,
   A. M.; Toomre, J.; Ulrich, R. K.; Bhatnagar, A.; Kennewell, J. A.;
   Marquette, W.; Patron, J.; Saa, O.; Yasukawa, E.
Bibcode: 1996Sci...272.1284H
Altcode:
  Helioseismology requires nearly continuous observations of the
  oscillations of the solar surface for long periods of time in
  order to obtain precise measurements of the sun's normal modes of
  oscillation. The GONG project acquires velocity images from a network
  of six identical instruments distributed around the world. The GONG
  network began full operation in October 1995. It has achieved a duty
  cycle of 89 percent and reduced the magnitude of spectral artifacts by
  a factor of 280 in power, compared with single-site observations. The
  instrumental noise is less than the observed solar background.

Title: Differential Rotation and Dynamics of the Solar Interior
Authors: Thompson, M. J.; Toomre, J.; Anderson, E. R.; Antia, H. M.;
   Berthomieu, G.; Burtonclay, D.; Chitre, S. M.; Christensen-Dalsgaard,
   J.; Corbard, T.; De Rosa, M.; Genovese, C. R.; Gough, D. O.; Haber,
   D. A.; Harvey, J. W.; Hill, F.; Howe, R.; Korzennik, S. G.; Kosovichev,
   A. G.; Leibacher, J. W.; Pijpers, F. P.; Provost, J.; Rhodes, E. J.,
   Jr.; Schou, J.; Sekii, T.; Stark, P. B.; Wilson, P. R.
Bibcode: 1996Sci...272.1300T
Altcode:
  Splitting of the sun's global oscillation frequencies by large-scale
  flows can be used to investigate how rotation varies with radius
  and latitude within the solar interior. The nearly uninterrupted
  observations by the Global Oscillation Network Group (GONG) yield
  oscillation power spectra with high duty cycles and high signal-to-noise
  ratios. Frequency splittings derived from GONG observations confirm
  that the variation of rotation rate with latitude seen at the surface
  carries through much of the convection zone, at the base of which is
  an adjustment layer leading to latitudinally independent rotation at
  greater depths. A distinctive shear layer just below the surface is
  discernible at low to mid-latitudes.

Title: High Resolution Numerical Simulations of Global Solar
    Convection
Authors: Miesch, M.; Clune, T.; Toomre, J.; Glatzmaier, G.
Bibcode: 1996AAS...188.6908M
Altcode: 1996BAAS...28..936M
  We present a new computer code for simulating anelastic stellar
  convection in a rotating spherical shell which is based on an existing
  algorithm, but redesigned to take full advantage of the higher
  resolution possible on currently available parallel super-computing
  platforms. Similar previous studies have led to important insights into
  the dynamics of the solar convection zone, but are unable to reproduce
  several important features, in particular the latitudinal and radial
  angular velocity profile inferred from helioseismological inversion. The
  results from helioseismology imply a differential rotation which is
  constant on radial lines at mid latitudes in the convection zone,
  while numerical simulations generally exhibit profiles which tend
  to be constant on cylindrical surfaces aligned with the rotation
  axis. Spherical shell simulations by Glatzmaier and other results from
  convection in plane-parallel geometries suggest that the answer may
  lie in increasing the spatial resolution of the model. The relatively
  low resolutions of previous simulations only admit predominantly
  laminar flows, which are known to exhibit significantly different
  transport properties than turbulent flows, and which are therefore
  less applicable to the highly turbulent conditions in solar convection
  zone. To achieve the highest possible resolution, and therefore the most
  turbulent flows, on current (and near future) computational resources,
  our new implementation of Glatzmaier's earlier code is specifically
  suited to the hierarchical memories characteristic of MPPs, with
  careful consideration given to achieving both good serial performance
  as well as good scalability on this class of machines. The former is
  largely achieved through an extremely efficient implementation of the
  Legendre transform which constitutes the majority of the computational
  workload, while the latter is achieved primarily by a relatively complex
  load-balancing scheme. We discuss the implementation as well as the
  flow characteristics and transport properties of several simulations
  achieved on our initial target platform, the IBM SP-2 at the Cornell
  Theory Center, with spatial resolutions of up to 768 x 1536 x 129
  (latitude, longitude, radial).

Title: First Helioseismic Results from the Global Oscillation
    Network Group
Authors: Toomre, Juri
Bibcode: 1996AAS...188.2901T
Altcode: 1996BAAS...28..861T
  Helioseismology studies the internal structure and dynamics of the
  sun, utilizing very precise measurements of the frequencies of sound
  waves that propagate throughout the solar interior and are observed
  at the surface. Efforts to accurately and precisely measure the mode
  frequencies from a single observing site have met with fundamental
  limitations imposed by the inevitable interruptions arising from the
  day-night cycle. To address such problems, the NSF-sponsored Global
  Oscillation Network Group (GONG) project has developed a network of
  six identical instruments around the world providing velocity images
  nearly continuously, a data processing system that can keep up with the
  massive data flow, and is supported by a vigorous scientific community
  structured around GONG teams that have shared in all aspects of the
  development of the project. Though the primary helioseismic data deals
  with the frequencies and their splittings for the nearly half-million
  global acoustic modes detectable with the GONG instruments, the
  data also allows study of how wave fields are locally influenced by
  flows and magnetic structures below the solar surface, and further
  provides direct measures of larger-scale flows at the surface. We
  shall briefly describe the network, instruments, and data analysis,
  and then review some of the preliminary scientific results obtained
  by the teams through inversion of the frequency data, dealing with
  the structure of the solar interior and the physics of stellar models,
  and an assessment of the differential rotation profile with depth and
  latitude. Early results will also be presented concerning nearly steady
  surface flows of the solar surface.

Title: Solar Internal Rotation and Dynamics from GONG Frequency
    Splittings
Authors: Thompson, M. J.; Toomre, J.; GONG Dynamics Inversion Team
Bibcode: 1996AAS...188.5305T
Altcode: 1996BAAS...28..903T
  The splitting of the Sun's global mode frequencies by large-scale flows
  can be used to investigate the rotation profile in both radius and
  latitude within the convection zone and deeper radiative interior. The
  inversion of GONG data confirms that the surface latitudinal variation
  of the rotation rate carries through much of the convection zone. At the
  base of the convection zone there is a currently unresolved adjustment
  layer with latitudinally independent rotation at greater depths. A
  shearing layer just below the surface is discernable at low to mid
  latitudes. Such global investigations are supplemented by local area
  analyses via ring diagrams, which enable us to probe the subsurface
  variation of rotation with depth beneath selected regions of the Sun.

Title: First Scientific Results from the GONG Helioseismology Network
Authors: Toomre, Juri
Bibcode: 1995AAS...18711402T
Altcode: 1995BAAS...27.1447T
  The GONG helioseismology project involves a broad international
  collaboration among experimentalists and theoreticians keenly
  interested in studying the internal dynamics and structure of our
  nearest star. Much of the scientific work is being done by teams of GONG
  members working together to assess the scientific inferences that can be
  drawn from the nearly continuous Doppler imaging of the sun that is now
  available from this network of identical instruments. Though the primary
  helioseismic data deals with the frequencies and their splittings for
  the nearly half-million global acoustic modes detectable with the GONG
  instruments, the data also allows study of how wave fields are locally
  influenced by flows and magnetic structures below the solar surface,
  and further provides direct measures of larger-scale flows at the
  surface. We shall review some of the preliminary scientific results
  obtained by the teams through inversion of the frequency data obtained
  from the early operation of the full network, dealing with assessment
  of differential rotation profiles with depth and latitude deduced from
  inversion of frequency splittings and of the sound speed profiles,
  and thus mean structure deduced from the basic mode frequencies. Early
  results will also be presented concerning nearly steady surface flows,
  and of magnetic effects seen in the wave fields.

Title: Turbulent Dynamics in the Solar Convection Zone
Authors: Brummell, Nicholas; Cattaneo, Fausto; Toomre, Juri
Bibcode: 1995Sci...269.1370B
Altcode:
  Observations of the sun reveal highly complex flows and magnetic
  structures that must result from turbulent convection in the solar
  envelope. A remarkable degree of large-scale coherence emerges
  from the small-scale turbulent dynamics, as seen in the cycles of
  magnetic activity and in the differential rotation profile of this
  star. High-performance computing now permits numerical simulations
  of compressible turbulence and magnetohydrodynamics with sufficient
  resolution to show that compact structures of vorticity and magnetic
  fields can coexist with larger scales. Such structured turbulence
  is yielding transport properties for heat and angular momentum at
  considerable variance with earlier models. These simulations are
  elucidating the coupling of turbulent fluid motions with rotation
  and magnetic fields, which must control the interlinked differential
  rotation and magnetic dynamo action.

Title: Local-Area Simulations of Rotating Compressible Convection
    and Associated Mean Flows
Authors: Hurlburt, N. E.; Brummel, N. H.; Toomre, J.
Bibcode: 1995ESASP.376b.245H
Altcode: 1995soho....2..245H; 1995help.confP.245H
  No abstract at ADS

Title: The Sensitivity of Various Mode Sets for Probing Differential
    Rotation Shear Zones
Authors: Christensen-Dalsgaard, J.; Schou, J.; Thompson, M. J.;
   Toomre, J.
Bibcode: 1995ESASP.376b..41C
Altcode: 1995soho....2...41C; 1995help.confP..41C
  The potential of forthcoming datasets from GONG and SOI for resolving
  long-lived azimuthal jets and shearing flows is investigated. The
  authors construct various artificial datasets, containing noise
  resembling that for a one-year observing run. These are then inverted,
  using a 2-D regularized least squares (RLS) inversion. In particular,
  the authors investigate the ability of the RLS method to form
  well-localized averages of the rotation rate, as measured by the
  averaging kernels, using an extensive mode set as well as subsets
  thereof. The authors show that it is possible to keep the noise in
  the solution down to a few nanohertz in much of the solar interior,
  while obtaining very reasonable resolution, for a GONG-like dataset.

Title: Analysis of Helioseismic Wave Fields to Examine Horizontal
    Structures
Authors: Julien, K. A.; Gough, D. O.; Toomre, J.
Bibcode: 1995ESASP.376b.155J
Altcode: 1995help.confP.155J; 1995soho....2..155J
  Presents and evaluates a preliminary inversion procedure for carrying
  out a local area analysis on simulated oscillation data to deduce
  two-dimensional subsurface structures in the horizontal, representative
  of thermal variations, potentially as function of depth.

Title: Non-Local Transport in Turbulent MHD Convection
Authors: Miesch, M.; Brandenburg, A.; Zweibel, E.; Toomre, J.
Bibcode: 1995ESASP.376b.253M
Altcode: 1995help.confP.253M; 1995soho....2..253M
  No abstract at ADS

Title: Plane-Wave Analysis of Solar Acoustic-Gravity Waves: a
    (slightly) New Approach
Authors: Bogart, R. S.; Sá, L. A. D.; Duvall, T. L.; Haber, D. A.;
   Toomre, J.; Hill, F.
Bibcode: 1995ESASP.376b.147B
Altcode: 1995soho....2..147B; 1995help.confP.147B
  Plane-wave decomposition of acoustic-gravity wave effects observed
  in the photosphere provides a computationally efficient technique for
  probing the structure of the upper convective zone and boundary, where
  the flat-Sun approximation is reasonably accurate. The authors describe
  the technique to be used for systematic plane-wave analysis of MDI
  data as part of the SOI data analysis pipeline, and the SOI analysis
  plan. The authors present estimates of sensitivity and discuss the
  effects of using different planar mappings. The technique is compared
  with previous approaches to the 3-dimensional plane-wave problem.

Title: Local-Area Analysis of High-Degree Solar Oscillations: New
    Ring-Fitting Procedures
Authors: Haber, D. A.; Toomre, J.; Hill, F.; Gough, D. O.
Bibcode: 1995ESASP.376b.141H
Altcode: 1995help.confP.141H; 1995soho....2..141H
  Local-area analysis of five-minute solar oscillations using ring
  diagrams to determine subphotospheric velocity flows is on the brink
  of becoming an important tool in understanding convective zone
  dynamics. One of the main problems up to this point has been the
  large computational burden of fitting the rings. The authors present a
  faster method for carrying out the ring fits using data obtained with
  the High-l Helioseismometer at Kitt Peak. The authors first eliminate
  serious sources of noise, then use a perturbation approach to fit the
  azimuthally averaged spectrum. The parameters so determined are held
  constant while fitting the entire ring diagram.

Title: Turbulent Rotating Compressible Convection in Spherical Domains
Authors: Hurlburt, N. E.; Brummell, N. H.; Toomre, J.
Bibcode: 1995SPD....26..406H
Altcode: 1995BAAS...27..955H
  No abstract at ADS

Title: Inversion for Background Inhomogeneity from Phase Distortion
    of Two-Dimensional Wave Fields
Authors: Julien, K.; Gough, D.; Toomre, J.
Bibcode: 1995ASPC...76..196J
Altcode: 1995gong.conf..196J
  No abstract at ADS

Title: Global-Scale Solar Turbulent Convection and its Coupling
    to Rotation
Authors: Glatzmaier, G. A.; Toomre, J.
Bibcode: 1995ASPC...76..200G
Altcode: 1995gong.conf..200G
  No abstract at ADS

Title: Spherical Core Convection in Rotating A-Type Stars
Authors: Dolez, N.; Glatzmaier, G. A.; Toomre, J.
Bibcode: 1995ASPC...76..653D
Altcode: 1995gong.conf..653D
  No abstract at ADS

Title: Maintenance of Differential Rotation in Turbulent Compressible
    Convection with Rotation
Authors: Brummell, N. H.; Xie, X.; Toomre, J.; Baillie, C.
Bibcode: 1995ASPC...76..192B
Altcode: 1995gong.conf..192B
  No abstract at ADS

Title: Modelling Astrophysical Turbulent Convection
Authors: Brummell, N.; Toomre, J.
Bibcode: 1995ASPC...77...15B
Altcode: 1995adass...4...15B
  Numerical simulations of highly turbulent flows in astrophysics
  benefit greatly from recent advances in high performance computing. Yet
  such three-dimensional modelling raises major problems in capturing,
  moving, and analyzing the resulting massive data sets necessary to
  sample the evolving intricate dynamics. Thus archiving, networking,
  and visualization are as essential as the actual act of computing when
  it comes to real scientific progress.

Title: Solar Convection Zone Dynamics and Rotation
Authors: Toomre, J.; Brummell, N. H.
Bibcode: 1995ESASP.376a..47T
Altcode: 1995soho....1...47T; 1995heli.conf...47T
  Reviews a range of approaches to study the basic dynamics of convection,
  along with its ability to redistribute angular momentum in rotating
  systems. The authors then describe results of three-dimensional
  simulations of turbulent compressible convection constrained by
  effects of rotation, both within spherical shells and within local
  area f-planes. The turbulence possesses intense vortex tubes with
  intricate interactions and instabilities, and more persistent and
  spatially-coherent downflow networks, along with strong mean flows
  when the rotational constraint is prominent. These theoretical
  studies reveal that transition to turbulent states have associated
  with them significant changes in flow asymmetries and transports,
  and that such turbulent convection can drive substantial mean flows
  which are distinctly different from those in which the convection is
  dominantly laminar.

Title: Hunting for Azimuthal Jets and Shearing Flows in the Solar
    Convection Zone
Authors: Christensen-Dalsgaard, J.; Schou, J.; Thompson, M. J.;
   Toomre, J.
Bibcode: 1995ASPC...76..212C
Altcode: 1995gong.conf..212C
  No abstract at ADS

Title: Solar Oscillation Ring Diagrams: Benefits of Great Circle
    Remapping
Authors: Haber, D.; Toomre, J.; Hill, F.; Gough, D.
Bibcode: 1995ASPC...76..272H
Altcode: 1995gong.conf..272H
  No abstract at ADS

Title: Astrophysical Convection and Turbulence
Authors: Toomre, J.
Bibcode: 1994AAS...184.5002T
Altcode: 1994BAAS...26..942T
  The vigorous turbulence that results from convective instability
  within rotating stars serves to not only transport heat but also
  redistribute angular momentum and chemical species, and can yield
  magnetic dynamo action. A hallmark of such turbulence constrained by
  rotation and stratification is that large-scale coherent structures
  and strong mean flows can coexist with the intense smaller-scale
  turbulence. Helioseismology is suggesting that the resulting
  differential rotation within the convection zone of a star like the
  sun yields serious puzzles about the interaction of convection and
  rotation. Understanding such nonlinear dynamics at a fundamental
  level raises formidable challenges because of the broad range of
  scales of motion that must be resolved. High-performance computing
  offers the opportunity to make substantial inroads in studying the
  properties of such astrophysical turbulence. An interdisciplinary team
  of researchers at several institutions is working jointly on problems
  in geophysical and astrophysical fluid dynamics (GAFD) turbulence
  to utilize massively parallel architectures to increase the spatial
  resolution in three-dimensional simulations employing variously
  pseudo-spectral, finite-difference, multi-grid and PPM approaches
  in studying the intense turbulence encountered in both planetary and
  stellar settings. The scale of these simulations requires corresponding
  progress in the computational sciences, both in order to develop and
  optimize software for massively-parallel computers and to capture and
  visualize the resulting massive data sets. A selection of highlights
  from our turbulence research will be presented, turning for instance to
  local-area models of turbulent compressible convection within stellar
  envelopes. The turbulence possesses both intense vortex filaments
  with intricate interactions and instabilities, and more persistent
  and spatially-coherent downflow networks, along with strong mean
  flows when the rotational constraint is prominent. We also consider
  the convective turbulence and mixing achieved within the full nuclear
  burning cores of rotating A-type stars, finding that such penetrative
  convection drives substantial differential rotation.

Title: Penetration below a Convection Zone
Authors: Hurlburt, Neal E.; Toomre, Juri; Massaguer, Josep M.; Zahn,
   Jean-Paul
Bibcode: 1994ApJ...421..245H
Altcode:
  Two-dimensional numerical simulations are used to investigate how fully
  compressible nonlinear convection penetrates into a stably stratified
  zone beneath a stellar convection zone. Estimates are obtained of the
  extent of penetration as the relative stability S of the stable to
  the unstable zone is varied over a broad range. The model deals with
  a perfect gas possessing a constant dynamic viscosity. The dynamics
  is dominated by downward-directed plumes which can extend far into
  the stable material and which can lead to the excitation of a broad
  spectrum of internal gravity waves in the lower stable zone. The
  convection is highly time dependent, with the close coupling between
  the lateral swaying of the plumes and the internal gravity waves they
  generate serving to modulate the strength of the convection. The depth
  of penetration delta, determined by the position where the time-averaged
  kinetic flux has its first zero in the stable layer, is controlled by
  a balance between the kinetic energy carried into the stable layer by
  the plumes and the buoyancy braking they experience there. A passive
  scalar is introduced into the unstable layer to evaluate the transport
  of chemical species downward. Such a tracer is effectively mixed
  within a few convective overturning times down to a depth of delta
  within the stable layer. Analytical estimates based on simple scaling
  laws are used to interpret the variation of delta with S, showing that
  it first involves an interval of adiabatic penetration if the local
  Peclet number of the convection exceeds unity, followed by a further
  thermal adjustment layer, the depths of each interval scaling in turn
  as S<SUP>-1</SUP> and S<SUP>-1/4</SUP>. These estimates are in accord
  with the penetration results from the simulations.

Title: Seismology of the Sun
Authors: Christensen-Dalsgaard, J.; Gough, D. O.; Toomre, J.
Bibcode: 1994snft.book..418C
Altcode:
  No abstract at ADS

Title: Compressible Convection with Ionization. II. Thermal
    Boundary-Layer Instability
Authors: Rast, Mark P.; Toomre, Juri
Bibcode: 1993ApJ...419..240R
Altcode:
  Rast &amp; Toomre (1993, Paper I) examined the effects of
  ionization-state changes on the stability, flow asymmetry,
  and flux transport properties of two-dimensional compressible
  convection. Here we employ the same single-atomic-level hydrogen model
  and analyze vigorously time-dependent nonlinear solutions. Ionization-
  state-dependent variations in thermal diffusivity of the fluid can
  result in thermal boundary-layer instability and plume formation. The
  interval between pluming events depends on the growth rate of the
  instability and both the scale and the velocity of the underlying
  convective motions. Such instabilities can occur at either boundary,
  depending on the positioning of the partially ionized region within the
  domain. Here we concentrate on simulations in which the instability is
  manifest in the upper thermal boundary layer, and results in cool plume
  formation. Temperature fluctuations and associated buoyancy forces in
  the plumes are maintained as long as heat exchange and compressional
  heating result primarily in ionization of the fluid rather than in
  temperature equilibration, and this can lead to supersonic vertical
  flows in an otherwise subsonic flow field. These flows serve to excite
  acoustic oscillations, the phase of which can be abruptly altered
  by subsequent plume events. For high rates of plume initiation, the
  fundamental acoustic period of the domain is greater than the time
  span between two descents. Such ionization effects are expected to
  influence the dynamics of granulation and acoustic mode excitation
  in the Sun and other stars, and likewise the coupling of convection
  with pulsations that occurs in stars such as white dwarfs and Cepheid
  variables. Additionally, it is possible that thermal instabilities
  analogous to those seen in these simulations occur not only in the
  photosphere but also at the base of stellar convective envelopes owing
  to temperature-sensitive variations in the radiative conductivity of
  fluid there.

Title: Compressible Convection with Ionization. I. Stability, Flow
    Asymmetries, and Energy Transport
Authors: Rast, Mark P.; Toomre, Juri
Bibcode: 1993ApJ...419..224R
Altcode:
  The influence of nonideal effects associated with ionization
  upon the dynamics and thermodynamics of compressible convection
  is studied. Linear and finite-amplitude analyses and fully
  nonlinear two-dimensional simulations of a plane-parallel layer
  of single-atomic-level hydrogen fluid are undertaken. Ionization
  significantly influences both the global transport properties and
  the local dynamics of convective flows by modifying the particle
  number density, specific heat, and internal energy content of the
  fluid. Strong temperature fluctuations and corresponding buoyancy
  forces develop locally in the fluid wherever rapid changes in
  ionization state occur. These can result in narrow regions of
  intense vertical flow. The flow asymmetries seen in simulations of
  compressible ideal-gas convection can either be enhanced or diminished
  depending on the vertical positioning of the partially ionized
  region within the domain. Additionally, the enthalpy flux achieved
  by ionizing convection is dominated in regions of partial ionization
  by latent-heat transport. The enthalpy carried by downflow plumes can
  be considerably elevated, and the cancellation between kinetic energy
  and enthalpy fluxes observed in the downflows in some simulations of
  ideal gas turbulence may thus be offset by partial ionization of the
  fluid. Such ionization effects are likely to influence the character
  of convective motions within stellar envelopes. Convective transport
  properties may differ substantially between the partially ionized and
  the deeper fully ionized regions of a star, and since ionization zone
  placement also varies with respect to both the photosphere and the
  lower thermal boundary, between stellar types and during the course
  of stellar evolution.

Title: Turbulent Compressible Convection with Rotation
Authors: Brummell, N. H.; Toomre, J.; Hurlburt, N. E.
Bibcode: 1993BAAS...25.1192B
Altcode:
  No abstract at ADS

Title: Ionization Effects in Three-dimensional Solar Granulation
    Simulations
Authors: Rast, Mark P.; Nordlund, Ake; Stein, Robert F.; Toomre, Juri
Bibcode: 1993ApJ...408L..53R
Altcode:
  These numerical studies show that ionization influences both the
  transport and dynamical properties of compressible convection
  near the surface of the Sun. About two-thirds of the enthalpy
  transported by convective motions in the region of partial hydrogen
  ionization is carried as latent heat. The role of fast downflow
  plumes in total convective transport is substantially elevated
  by this contribution. Instability of the thermal boundary layer
  is strongly enhanced by temperature sensitive variations in the
  radiative properties of the fluid, and this provides a mechanism for
  plume initiation and cell fragmentation in the surface layers. As
  the plumes descend, temperature fluctuations and associated buoyancy
  forces are maintained because of the increased specific heat of the
  partially ionized material. This can result is supersonic vertical
  flows. At greater depths, ionization effects diminish, and the plumes
  are decelerated by significant entrainment of surrounding fluid.

Title: Large-Eddy Simulations of Compressible Convection on Massively
    Parallel Computers
Authors: Xie, Xin; Toomre, Juri
Bibcode: 1993ApJ...405..747X
Altcode:
  We report preliminary implementation of the large-eddy simulation (LES)
  technique in 2D simulations of compressible convection carried out
  on the CM-2 massively parallel computer. The convective flow fields
  in our simulations possess structures similar to those found in a
  number of direct simulations, with roll-like flows coherent across the
  entire depth of the layer that spans several density scale heights. Our
  detailed assessment of the effects of various subgrid scale (SGS) terms
  reveals that they may affect the gross character of convection. Yet,
  somewhat surprisingly, we find that our LES solutions, and another in
  which the SGS terms are turned off, only show modest differences. The
  resulting 2D flows realized here are rather laminar in character,
  and achieving substantial turbulence may require stronger forcing and
  less dissipation.

Title: Interaction of Externally-Driven Acoustic Waves with
    Compressible Convection
Authors: Jones, P.; Merryfield, W.; Toomre, J.
Bibcode: 1993ASPC...42...45J
Altcode: 1993gong.conf...45J
  No abstract at ADS

Title: Inversion for Background Inhomogeneity from Phase Distortions
    of One-Dimensional Wave Trains
Authors: Gough, D. O.; Merryfield, W. J.; Toomre, J.
Bibcode: 1993ASPC...42..257G
Altcode: 1993gong.conf..257G
  No abstract at ADS

Title: Acoustic Excitation by Thermal Boundary Layer Instability in
    a Partially Ionized Convecting Fluid
Authors: Rast, M. P.; Toomre, J.
Bibcode: 1993ASPC...42...41R
Altcode: 1993gong.conf...41R
  No abstract at ADS

Title: Thermal convection and penetration.
Authors: Toomre, J.
Bibcode: 1993afd..conf..325T
Altcode:
  Contents: 1. Introduction. 2. Boussinesq convection in simple
  geometries. 3. Anelastic modal convection. 4. Two-dimensional fully
  compressible convection. 5. Three-dimensional fully compressible
  convection. 6. Final reflections.

Title: Ionization Effects on Solar Granulation Dynamics
Authors: Rast, M. P.; Nordlund, A.; Stein, R. F.; Toomre, J.
Bibcode: 1993ASPC...42...57R
Altcode: 1993gong.conf...57R
  No abstract at ADS

Title: Turbulent Compressible Convection with Rotation
Authors: Brummell, N. H.; Hurlburt, N. E.; Toomre, J.
Bibcode: 1993ASPC...42...61B
Altcode: 1993gong.conf...61B
  No abstract at ADS

Title: Laboratory and theoretical models of planetary-scale
    instabilities and waves
Authors: Hart, John E.; Toomre, Juri
Bibcode: 1991gsap.rept...47H
Altcode:
  Meteorologists and planetary astronomers interested in large-scale
  planetary and solar circulations recognize the importance of rotation
  and stratification in determining the character of these flows. The
  two outstanding problems of interest are: (1) the origins and nature
  of chaos in baroclinically unstable flows; and (2) the physical
  mechanisms responsible for high speed zonal winds and banding on
  the giant planets. The methods used to study these problems, and the
  insights gained, are useful in more general atmospheric and climate
  dynamic settings. Because the planetary curvature or beta-effect
  is crucial in the large scale nonlinear dynamics, the motions of
  rotating convecting liquids in spherical shells were studied using
  electrohydrodynamic polarization forces to generate radial gravity and
  centrally directed buoyancy forces in the laboratory. The Geophysical
  Fluid Flow Cell (GFFC) experiments performed on Spacelab 3 in 1985 were
  analyzed. The interpretation and extension of these results have led to
  the construction of efficient numerical models of rotating convection
  with an aim to understand the possible generation of zonal banding on
  Jupiter and the fate of banana cells in rapidly rotating convection as
  the heating is made strongly supercritical. Efforts to pose baroclinic
  wave experiments for future space missions using a modified version of
  the 1985 instrument have led us to develop theoretical and numerical
  models of baroclinic instability. Some surprising properties of both
  these models were discovered.

Title: Simulation of Effects of Atmospheric Seeing on the Observation
    of High-Degree Solar Oscillations
Authors: Hill, Frank; Gough, Douglas; Merryfield, William J.;
   Toomre, Juri
Bibcode: 1991ApJ...369..237H
Altcode:
  Numerical simulations of the effects of atmospheric seeing distortions
  on observations of solar oscillations of intermediate and high degree
  are performed. The simulations involve a representation of about 100
  p-modes of oscillation, with degrees l = 50-150 (intermediate-degree)
  and 150-450 (high-degree), formed from the complement of a sexated mode
  set. These modes are superposed on a steady large-scale convective
  background, and projected onto the plane of the sky. Image motion is
  modeled by displacement maps generated from two-dimensional turbulence
  power spectra; the maps are scaled so that the rms amplitude of the
  displacements has values of 2-5 arcsec. The distorted velocity field is
  then Fourier analyzed to produce simulated (l, nu) power diagrams, where
  nu is the temporal cyclic frequency. The results show that power in the
  mode ridges is diminished as atmospheric seeing worsens, particularly
  at high degrees. Redistribution of power produces an apparent decrease
  in the frequencies of the oscillations as measured by the centroids
  of the ridges in the power spectra. It is found that time-averaging
  the observations is quite effective in reducing the noise.

Title: Turbulent Compressible Convection
Authors: Cattaneo, Fausto; Brummell, Nicholas H.; Toomre, Juri;
   Malagoli, Andrea; Hurlburt, Neal E.
Bibcode: 1991ApJ...370..282C
Altcode:
  Numerical simulations with high spatial resolution (up to 96-cubed
  gridpoints) are used to study three-dimensional, compressible
  convection. A sequence of four models with decreasing viscous
  dissipation is considered in studying the changes in the flow structure
  and transport properties as the convection becomes turbulent.

Title: Nonlinear Behavior of Solar Gravity Modes Driven by 3He in
    the Core. II. Numerical Simulations
Authors: Merryfield, William J.; Toomre, Juri; Gough, Douglas
Bibcode: 1991ApJ...367..658M
Altcode:
  The nonlinear behavior of gravity-mode oscillations driven by
  He-3-destroying reactions in the solar core has been examined
  by numerically integrating equations describing a very simplified
  model. The results of a previous bifurcation analysis, which suggest
  that such oscillations are unlikely to attain amplitudes sufficient
  to trigger core convection, are verified. These results are extended
  to models whose nuclear reaction rates and thermal stratification
  represent the core somewhat more accurately. Nonlinear processes give
  rise to a preference for the oscillations to develop as standing waves
  rather than traveling waves, thus breaking the degeneracy between
  these two types of motion which exists in linearized theory. Study
  of the large-amplitude behavior of the oscillations is hindered by a
  tendency for the model to become thermally unstable.

Title: On the Analysis of Physical Wave Trains
Authors: Gough, D. O.; Merryfield, W. J.; Toomre, J.
Bibcode: 1991LNP...388..265G
Altcode: 1991ctsm.conf..265G
  When a wave train whose constituent frequencies and wave numbers are
  unresolved by observation propagates through an inhomogeneous medium,
  beating between the components can contaminate deductions one might
  naively draw about the inhomogeneous background. This is a severe
  problem to anyone confronted with analysing helioseismic data with
  a view to determining the structure of giant convective cells. We
  propose a procedure for analysing wave trains, based on approximating
  a packet as a single representative pure wave. We present some
  preliminary results of analysing artificial data. For simplicity, we
  have deliberately excluded some of the effects of wave interference,
  which must be faced by any means of analysis. Therefore we do not
  claim to have found a complete procedure for analysing real data.

Title: Challenges to Theories of the Structure of Moderate-Mass Stars
Authors: Gough, Douglas; Toomre, Juri
Bibcode: 1991LNP...388.....G
Altcode: 1991ctsm.conf.....G
  No abstract at ADS

Title: The Organization of Turbulent Convection
Authors: Brummell, Nicholas; Cattaneo, Fausto; Malagoli, Andrea;
   Toomre, Juri; Hurlburt, Neal E.
Bibcode: 1991LNP...388..187B
Altcode: 1991ctsm.conf..187B
  Highly resolved numerical simulations are used to study
  three-dimensional, compressible convection. The viscous dissipation is
  sufficiently low that the flow divides itself in depth into two distinct
  regions: (i) an upper thermal boundary layer containing a smooth flow
  with a granular appearance, and (ii) a turbulent interior pierced
  by the strongest downflows from the surface layer. Such downflows
  span the whole depth of the unstable layer, are temporally coherent,
  and are thermodynamically well correlated. A remarkable property of
  such convection, once it becomes turbulent, is that the enthalpy and
  kinetic fluxes carried by the strong downflows nearly cancel, for they
  are of opposite sense and nearly equal in amplitude. Thus, although the
  downflows serve to organize the convection and are the striking feature
  that emerges from effects of compressibility, it is the small-scale,
  disorganized turbulent motions (between the coherent downflow structures
  that serve as the principal carriers of net convected flux.

Title: The role of f modes in the inversion of high-ℓ rotational
    splittings
Authors: Haber, Deborah A.; Hill, Frank; Toomre, Juri
Bibcode: 1991LNP...388...87H
Altcode: 1991ctsm.conf...87H
  The contribution of the solar f modes of oscillation to the inversion
  of high-degree rotational splitting data is examined. We find that
  the f modes play an important role in such inversions as revealed
  by the magnitude of their weighting coefficients c i . This may be
  attributed to the single-peaked structure of the f-mode kernels,
  which is similar to that of the desired averaging kernels and in
  contrast to the many-peaked shape of the higher-order kernels. The
  high weight placed on the f modes in the inversions raises issues for
  observational techniques since the f modes possess modest power levels
  and their detection is influenced by the choice of spatial filtering.

Title: Program at ITP: Helioseismology — Probing the interior of
    a star
Authors: Gough, Douglas; Toomre, Juri
Bibcode: 1991LNP...388....1G
Altcode: 1991ctsm.conf....1G
  The research program in helioseismology carried out at the Institute
  for Theoretical Physics (ITP) at the University of California, Santa
  Barbara during the six-month interval from January to June 1990
  involved 61 scientists of diverse disciplines: theorists, observers
  and instrumentalists in physics, astrophysics and geophysics. The main
  topics of research and joint discussion included mode excitation and
  decay, the internal structure of the sun and its sensitivity to the
  physics of the equation of state and opacity, seismological inverse
  procedures, and solar rotation and convection-zone dynamics.

Title: Vertically Coherent Compressible Convective Flows in a Layer
    with a High Density Contrast
Authors: Xie, Xin; Toomre, Juri
Bibcode: 1991LNP...388..171X
Altcode: 1991ctsm.conf..171X
  Two-dimensional simulations are used to study compressible convection
  in a plane-parallel layer of ideal gas with a high density contrast
  across the layer. The convective flows are found to consist of rolls
  which are coherent throughout the entire vertical domain, similar to the
  results of a number of earlier investigations. Motions near the upper
  boundary are supersonic, though the Rayleigh number is moderate. The
  major effect of a high density stratification is to significantly
  rarefy the fluid in the upper part of the domain, hence increase its
  thermal diffusivity. The consequence appears to be twofold: Firstly,
  enhanced thermal diffusion makes non-adiabatic cooling more efficient,
  thus helps the flows to become supersonic more easily. Secondly,
  sufficient diffusion can broaden shocks to such an extent that it
  actually turns them into smooth transition regions.

Title: Effects of spatial filtering on high-ℓ power spectra and
    rotational splitting inversions
Authors: Haber, Deborah A.; Hill, Frank; Toomre, Juri
Bibcode: 1991LNP...388..259H
Altcode: 1991ctsm.conf..259H
  The effects of the spatial filtering algorithm on the results of an
  inversion of high-degree solar oscillation data are examined. In
  attempting to isolate sectoral modes, the Fourier transforms in
  longitude are accompanied by three different spatial filterings in
  the orthogonal direction. The filters are: simple averaging in the
  plane of the sky, averaging along lines of constant heliographic
  longitude with uniform weighting, and another with weighting based
  on appropriate Legendre functions. The choice of spatial filter
  changes the distribution of power in the two-dimensional spectrum
  of the oscillations, particularly in the f and p 1 ridges. These
  variations in the power distribution affect the determination of the
  rotational splittings, thereby influencing the results of inversions
  which emphasize information contained in the low-order ridges.

Title: Seismic observations of the solar interior.
Authors: Gough, Douglas; Toomre, Juri
Bibcode: 1991ARA&A..29..627G
Altcode:
  Contents: 1. Introduction. 2. Solar evolution. 3. Properties of
  modes. 4. Observational principles. 5. Inversion of data. 6. Inference
  of hydrostatic structure. 7. The neutrino problem. 8. Rotation and
  other subsurface flows. 9. Mode excitation and decay. 10. Solar cycle
  variations. 11. Asteroseismology.

Title: Interaction of Acoustic Oscillations with Time-Dependent
    Compressible Convection
Authors: Jones, P. W.; Merryfield, W. J.; Toomre, J.
Bibcode: 1991LNP...388..213J
Altcode: 1991ctsm.conf..213J
  We present the results of numerical simulations in which acoustic waves
  are driven into a two-dimensional layer of compressible fluid which
  is undergoing convection. The energetics of the waves are analyzed by
  computing the work integrals associated with the modulation of the
  gas and turbulent pressures. We find that the relative importance
  of the turbulent pressure component of the work integral increases
  prominently with increasing wave frequency. Also, the time dependence
  of the convection leads to temporal irregularity in the component
  of wave driving and damping associated with the convection-pulsation
  coupling. We speculate that such irregularity may contribute to the
  aperiodicity observed in the light curves of Mira variables and other
  pulsating red giant stars.

Title: Large Eddy Simulations of Compressible Convection
Authors: Xie, Xin; Toomre, Juri
Bibcode: 1991LNP...388..147X
Altcode: 1991ctsm.conf..147X
  Large-eddy simulation (LES) technique has been applied to
  two-dimensional compressible convection in a plane-parallel layer
  of ideal gas with intermediate density contrast. The general flow
  patterns consist of a series of rolls in the horizontal which are
  coherent throughout the entire vertical domain, much like findings by a
  number of investigators. The horizontal component of the subgrid-scale
  (SGS) force appears to enhance fluctuations of pressure and density,
  which in turn cause the resultant force, say f pg arising from pressure
  gradient and gravity terms, to increase in magnitude in such a way that
  f pg, besides balancing the inertial terms, can essentially offset
  the vertical component of the SGS force. Consequently, compared to a
  solution obtained omitting the SGS terms, the flow field of the LES
  solution only shows moderate differences. There is some indication
  that the overall SGS effect tends to reduce the asymmetry between the
  vertical flows in the interior of the domain while enhancing it in
  the base region.

Title: Three-dimensional compressible convection at low Prandtl
    numbers.
Authors: Toomre, Juri; Brummell, Nicholas; Cattaneo, Fausto; Hurlburt,
   Neal E.
Bibcode: 1990CoPhC..59..105T
Altcode:
  Numerical simulations are used to study fully compressible thermal
  convection at large Rayleigh numbers. The authors present results from a
  sequence of three-dimensional simulations that reveal a transition from
  gradually-evolving laminar convection to nearly turbulent convection
  as the Prandtl number is reduced from a value of unity to one-tenth.

Title: Nonlinear Behavior of Solar Gravity Modes Driven by 3He in
    the Core. I. Bifurcation Analysis
Authors: Merryfield, William J.; Toomre, Juri; Gough, Douglas
Bibcode: 1990ApJ...353..678M
Altcode:
  The nonlinear development of solar gravity modes driven by He-3 burning
  in the solar core is investigated by means of an idealized dynamical
  model. Possible outcomes that have been suggested in the literature
  include the triggering of subcritical direct convection, leading to
  core mixing, and the saturation of the excitation processes, leading
  to sustained finite-amplitude oscillations. The present simple model
  suggests that the latter is the more likely. The limiting amplitude
  of the oscillations is estimated, ignoring possible resonances with
  other gravity modes, to be of order 10 km/s at the solar surface. Such
  oscillations would be easily observable. That large-amplitude gravity
  modes have not been observed suggests either that these modes are not
  unstable in the present era or that they are limited to much smaller
  amplitudes by resonant coupling.

Title: Supersonic Convection
Authors: Cattaneo, Fausto; Hurlburt, Neal E.; Toomre, Juri
Bibcode: 1990ApJ...349L..63C
Altcode:
  Numerical simulations with high spatial resolution are used to study
  that the combined effects of stratification, pressure gradients,
  and nonadiabatic processes can lead to the formation of regions of
  supersonic motions near the upper thermal boundary layer. Within
  these regions, the dynamics is dominated by nonstationary shock
  structures. These form near the downflow sites and propagate upstream
  along the boundary layer to the upflow regions where they weaken and
  eventually disappear. The shock cycle, consisting of the formation,
  propagation, and disappearance of shock structures, has a time scale
  comparable to the sound crossing time over a portion of the convective
  cell, giving rise to vigorous time dependence in the convection.

Title: Laboratory and theoretical models of planetary-scale
    instabilities and waves
Authors: Hart, John E.; Toomre, Juri
Bibcode: 1989gsap.rept...59H
Altcode:
  The continuous low-g environment of the orbiting space shuttle provided
  a setting for conducting geophysical fluid model experiments with a
  completely consistent representation of sphericity and the resultant
  radial gravity found on astrogeophysical objects. This is possible
  because in zero gravity an experiment can be constructed that has
  its own radial buoyancy forces. The dielectric forces in a liquid,
  which are linearly dependent on fluid temperature, give rise to an
  effectively radial buoyancy force when a radial electrostatic field
  is applied. The Geophysical Fluid Flow Cell (GFFC) experiment is an
  implementation of this idea in which fluid is contained between two
  rotating hemispheres that are differentially heated and stressed with a
  large ac voltage. The GFFC flew on Spacelab 3 in May 1985. Data in the
  form of global Schlieren images of convective patterns were obtained
  for a large variety of configurations. These included situations of
  rapid rotation (large Taylor numbers), low rotation, large and small
  thermal forcing, and situations with applied meridional temperature
  gradients. The analysis and interpretation of the GFFC-85 data are
  being conducted. Improvements were developed to the GFFC instrument
  that will allow for real-time (TV) display of convection data and for
  near-real-time interactive experiments. These experiments, on the
  transition to global turbulence, the breakdown of rapidly rotating
  convective planforms and other phenomena, are scheduled to be carried
  out on the International Microgravity Laboratory (IML-1) aboard the
  shuttle in June 1990.

Title: Preflare activity.
Authors: Priest, E. R.; Gaizauskas, V.; Hagyard, M. J.; Schmahl, E. J.;
   Webb, D. F.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson,
   R. S.; Chapman, G. A.; Deloach, A. C.; Gary, G. A.; Jones, H. P.;
   Karpen, J. T.; Martres, M. -J.; Porter, J. G.; Schmieder, B.; Smith,
   J. B., Jr.; Toomre, J.; Woodgate, B.; Waggett, P.; Bentley, R.;
   Hurford, G.; Schadee, A.; Schrijver, J.; Harrison, R.; Martens, P.
Bibcode: 1989epos.conf....1P
Altcode:
  Contents: 1. Introduction. 2. Magnetohydrodynamic
  instability. 3. Preflare magnetic and velocity fields. 4. Coronal
  manifestations of preflare activity.

Title: Two and Three-Dimensional Simulations of Compressible
    Convection
Authors: Cattaneo, F.; Hurlburt, N. E.; Toomre, J.
Bibcode: 1989ASIC..263..415C
Altcode: 1989ssg..conf..415C
  No abstract at ADS

Title: Nonlinear studies of solar gravity modes driven by nuclear
    burning of the <SUP>3</SUP>He in the core.
Authors: Merryfield, W. J.; Toomre, J.; Gough, Douglas O.
Bibcode: 1988ESASP.286...21M
Altcode: 1988ssls.rept...21M
  The finite-amplitude behavior of gravity-mode oscillations driven
  within the deep interior of the sun has been studied by means of a
  simple idealized model. Such g modes may be self-excited by their
  ability to extract energy from the nuclear burning of <SUP>3</SUP>He
  in the core. Both a nonlinear bifurcation analysis and numerical
  simulations of the behavior of this instability suggest that the
  growth of <SUP>3</SUP>He-driven oscillations is likely be limited to
  an amplitude which is insufficient to induce convective instability
  in the core, a process which has been proposed as a mechanism for core
  mixing. The numerical results also indicate that if the oscillations are
  linarly unstable then the degeneracy in linear theory between standing
  and travelling g modes is broken by nonlinear effects. The oscillations
  thus develop into a left- or right-travelling wave rather than a
  standing wave or other superposition of horizontally propagating waves.

Title: Local effects of a major flare on solar five-minute
    oscillations.
Authors: Haber, D. A.; Toomre, J.; Hill, Frank; Gough, Douglas O.
Bibcode: 1988ESASP.286..301H
Altcode: 1988ssls.rept..301H
  Doppler velocity images of the full Sun were obtained both during and
  after a major white-light flare. These velocities were interpolated onto
  a cylindrical coordinate system centered on the flare and decomposed
  into radially propagating waves defined by Hankel functions. For
  a similar analysis of quiet Sun regions the authors find fairly
  comparable power in incoming and outgoing waves irrespective of the
  presence of the flare. However, for the flaring region, there is 14%
  greater power in incoming as opposed to outgoing waves when there
  is no flare, but 5% greater power in outgoing than in incoming waves
  during the flare. This result suggests that the flare may have excited
  outgoing waves which counteracted the more usual absorption of incoming
  acoustic waves by sunspots.

Title: Whirlpool traced by granulation
Authors: Toomre, Juri
Bibcode: 1988Natur.335..202T
Altcode:
  No abstract at ADS

Title: Magnetic Fields Interacting with Nonlinear Compressible
    Convection
Authors: Hurlburt, Neal E.; Toomre, Juri
Bibcode: 1988ApJ...327..920H
Altcode:
  Two-dimensional numerical simulations are used to study fully
  compressible convection in the presence of an imposed magnetic
  field. Highly nonlinear flows are considered that span multiple density
  scale heights. The convection tends to sweep the initially uniform
  vertical magnetic field into concentrated flux sheets with significant
  magnetic pressures. These flux sheets are partially evacuated, and
  effects of buoyancy and Lorentz forces there can serve to suppress
  motions. The flux sheets can be surrounded by a sheath of descending
  flow. If the imposed magnetic field is sufficiently strong, the
  convection can become oscillatory. The unstably stratified fluid layer
  has an initial density ratio (bottom to top of layer) of 11. Surveys of
  solutions at fixed Rayleigh number sample Chandrasekhar numbers from 1
  to 1000 and magnetic Prandtl numbers from 1/16 to 1. These nonlinear
  simulations utilize a two-dimensional numerical scheme based on a
  modified two-step Lax-Wendroff method.

Title: Simulations of the Interaction of Radial Stellar Pulsations
    with Compressible Convection
Authors: Merryfield, W. J.; Toomre, J.
Bibcode: 1988BAAS...20..702M
Altcode:
  No abstract at ADS

Title: Topology of Plumes in Nonlinear Compressible Convection
Authors: Toomre, J.; Cattaneo, F.; Hurlburt, N. E.
Bibcode: 1988BAAS...20..678T
Altcode:
  No abstract at ADS

Title: Helioseismology: Theoretical Background and Challenges
Authors: Toomre, J.
Bibcode: 1988BAAS...20..729T
Altcode:
  No abstract at ADS

Title: Solar Equatorial Rotation Rate Inferred from Inversion of
    Frequency Splitting of High-Degree Modes
Authors: Hill, F.; Gough, D. O.; Toomre, J.; Haber, D. A.
Bibcode: 1988IAUS..123...45H
Altcode:
  The equatorial rotation rate has been inferred as a function of depth
  through the outer 16 Mm of the Sun from observations of high-degree
  five-minute oscillations. The results imply that the solar rotation
  rate increases with depth by 0.023 μHz reaching a maximum at about
  2 Mm below the surface, then decreases by 0.037 μHz down to 16 Mm.

Title: Response of the Solar 5-MINUTE Oscillations to a Major Flare
Authors: Haber, D. A.; Toomre, J.; Hill, F.
Bibcode: 1988IAUS..123...59H
Altcode:
  Solar five-minute oscillations of intermediate-degree l were observed
  both before and after a very strong white-light flare. The data
  were projected onto both equatorial and polar sectoral modes and
  Fourier transformed in time. Comparing the resulting power spectra,
  the authors find a substantial increase in power in the p<SUB>5</SUB>
  ridge of the equatorial modes on the day after the flare. When data
  from all the ridges are considered, there is an average increase in
  power of only a few percent the day after the flare.

Title: Traveling waves and chaos in thermosolutal convection
Authors: Deane, A. E.; Knobloch, E.; Toomre, J.
Bibcode: 1987PhRvA..36.2862D
Altcode:
  Numerical experiments on two-dimensional thermosolutal convection reveal
  oscillations in the form of traveling, standing, modulated, and chaotic
  waves. Transitions between these wave forms and steady convection are
  investigated and compared with theory. Such rich nonlinear behavior
  is possible in fluid layers of wide horizontal extent, and provides
  an explanation for waves observed in recent laboratory experiments
  with binary fluid mixtures.

Title: Solar oscillations and convective flows as probes of structure
    in the subphotosphere
Authors: Toomre, Juri; Gebbie, Katharine B.
Bibcode: 1987jila.rept.....T
Altcode:
  Application of inverse theory to the observation of high-degree
  five-minute solar oscillations has led to the detection of horizontal
  flows below the solar surface that are a combination of solar
  rotation and giant convection cells. The distinctive displacements
  in the centroids of the ridges evident in the power diagrams of the
  oscillations from one observing day to the next arise from different
  patterns of giant cells being rotated into view. Such observation
  of frequency splittings for the high degree oscillation modes,
  combined with refinements in the inversion of the data using optimal
  averaging and spectral expansions, has shown that helioseismology
  should permit detailed mapping of velocity and thermal structures
  below the solar surface. Extensive theoretical studies of fully
  compressible magnetoconvection have shown that flows are indeed able
  to concentrate magnetic fields into concentrated flux sheets that are
  substantially evacuated of gas. The magnetic buoyancy instabilities
  have been extensively studied.

Title: A laboratory model of planetary and stellar convection
Authors: Hart, J. E.; Toomre, J.; Deane, A. E.; Hurlburt, N. E.;
   Glatzmaier, G. A.; Fichtl, G. H.; Leslie, F.; Fowlis, W. W.; Gilman,
   P. A.
Bibcode: 1987STIN...8722108H
Altcode:
  Experiments on thermal convection in a rotating, differentially-heated
  spherical shell with a radial buoyancy force were conducted in an
  orbiting microgravity laboratory. A variety of convective structures,
  or planforms, were observed depending on the magnitude of the rotation
  and the nature of the imposed heating distribution. The results are in
  agreement with numerical simulations that can be conducted at modest
  parameter values, and suggest possible regimes of motion in rotating
  planets and stars.

Title: Vector array processor computer equipment
Authors: Toomre, Juri
Bibcode: 1987colo.rept.....T
Altcode:
  To support the on-going research on Solar Oscillations and Convective
  Flows as Probes of Structure in the Subphotosphere, a vector array
  processor system was acquired to augment the existing DEC VAX-11/750
  computer system. The fifty-fold average increase in computing speed
  offered by the array processor would make it feasible to invert
  solar oscillation data on a regular basis, and thereby permit us to
  use the five-minutes oscillations of the Sun to probe the turbulent
  convection zone below the surface of this star. The array processor
  would also permit us to carry out detailed numerical experiments
  with compressible convection in the presence of magnetic fields,
  for the speed and memory of the machine makes it a formidable tool
  for direct numerical simulations of two- and three-dimensional fluid
  dynamics. Such theoretical simulations are also needed to study the
  solar dynamo and its ability to build and transform magnetic fields,
  an issue central to solar-terrestrial variability and predictions of
  solar activity. Attached as Appendix A is a cover article in Science
  Magazine that describes the importance of the work on the Seismology of
  the Sun that is beginning to emerge from the class of array processors.

Title: Spacelab experiments on convection in a rotating spherical
    shell with radial gravity
Authors: Toomre, J.; Hart, J. E.; Glatzmaier, G. A.
Bibcode: 1987ASSL..137...27T
Altcode: 1987isav.symp...27T
  Experiments on thermal convection in a rotating, differentially-heated
  hemispherical shell of fluid with a radial gravity field were carried
  out in the microgravity environment of Spacelab 3 which was flown on the
  space shuttle Challenger in May 1985. Schlieren visualizations of these
  laboratory flows are compared briefly to three-dimensional nonlinear
  simulations that can be conducted at the more modest heating rates.

Title: Nonlinear Compressible Convection Penetrating into Stable
    Layers and Producing Internal Gravity Waves
Authors: Hurlburt, Neal E.; Toomre, Juri; Massaguer, Josep M.
Bibcode: 1986ApJ...311..563H
Altcode:
  Penetrative convection spanning multiple scale heights is studied
  within a simple stellar envelope consisting of three layers: a
  convectively unstable middle layer bounded above and below by stably
  stratified polytropes. Two-dimensional numerical simulations are
  used to investigate the fully compressible nonlinear motions that
  ensue. The cellular flows display prominent downward-directd plumes
  surrounded by broader regions of upflow. Such asymmetry arises because
  pressure fluctuations accentuate buoyancy driving in the concentrated
  plumes and can even lead to weak buoyancy braking in the surrounding
  ascending flows. As the plumes plunge downward into a region of stable
  stratification, they serve to excite a broad spectrum of internal
  gravity waves there. The induced waves are not passive, for they feed
  back upon the plumes by deflecting them sideways, thereby modulating
  the amplitude of the convection in time even in the unstable layer. The
  penetrative motions that billow upward into the upper stable zone are
  distinctly weaker, and they cascade back downward toward the unstable
  zone over a broad horizontal scale. The strong excitation of gravity
  waves by the convection has implications for gradual mixing deep within
  a star.

Title: Space-laboratory and numerical simulations of thermal
    convection in arotating hemispherical shell with radial gravity.
Authors: Hart, John E.; Glatzmaier, Gary A.; Toomre, Juri
Bibcode: 1986JFM...173..519H
Altcode:
  The flight of the Spacelab 3 microgravity laboratory onboard the
  Space Shuttle Challenger in May 1985 enabled electroconvection
  experiments to be conducted using the goephysical fluid flow cell
  instrument. Experimental results are presented which illustrate the
  variety of convection achieved by varying the imposed radial and
  latitudinal temperature gradients, rotation rates, and the strength
  of the electrostatic gravity. These results are compared with those
  obtained from nonlinear three-dimensional simulations and good agreement
  is found.

Title: Laboratory Experiments on Planetary and Stellar Convection
    Performed on Spacelab 3
Authors: Hart, J. E.; Toomre, J.; Deane, A. E.; Hurlburt, N. E.;
   Glatzmaier, G. A.; Fichtl, G. H.; Leslie, F.; Fowlis, W. W.; Gilman,
   P. A.
Bibcode: 1986Sci...234...61H
Altcode:
  Experiments on thermal convection in a rotating, differentially heated
  hemispherical shell with a radial buoyancy force were conducted in an
  orbiting microgravity laboratory. A variety of convective structures,
  or planforms, were observed, depending on the magnitude of the rotation
  and the nature of the imposed heating distribution. The results are
  compared with numerical simulations that can be conducted at the more
  modest heating rates, and suggest possible regimes of motion in rotating
  planets and stars.

Title: Local Response of the Five-Minute Oscillations to a Major
    Solar Flare
Authors: Haber, D. A.; Toomre, J.; Hill, F.; Gough, D. O.
Bibcode: 1986BAAS...18Q1011H
Altcode:
  No abstract at ADS

Title: Preflare activity.
Authors: Priest, E. R.; Gaizauskas, V.; Hagyard, M. J.; Schmahl, E. J.;
   Webb, D. F.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson,
   R. S.; Chapman, G. A.; Deloach, A. C.; Gary, G. A.; Jones, H. P.;
   Karpen, J. T.; Martres, M. -J.; Porter, J. G.; Schmieder, B.; Smith,
   J. B., Jr.; Toomre, J.; Woodgate, B.; Waggett, P.; Bentley, R.;
   Hurford, G.; Schadee, A.; Schrijver, J.; Harrison, R.; Martens, P.
Bibcode: 1986NASCP2439....1P
Altcode:
  Contents: 1. Introduction: the preflare state - a review of previous
  results. 2. Magnetohydrodynamic instability: magnetic reconnection,
  nonlinear tearing, nonlinear reconnection experiments, emerging flux and
  moving satellite sunspots, main phase reconnection in two-ribbon flares,
  magnetic instability responsible for filament eruption in two-ribbon
  flares. 3. Preflare magnetic and velocity fields: general morphology of
  the preflare magnetic field, magnetic field shear, electric currents in
  the preflare active region, characterization of the preflare velocity
  field, emerging flux. 4. Coronal manifestations of preflare activity:
  defining the preflare regime, specific illustrative events, comparison
  of preflare X-rays and ultraviolet, preflare microwave intensity and
  polarization changes, non-thermal precursors, precursors of coronal
  mass ejections, short-lived and long-lived HXIS sources as possible
  precursors.

Title: Influence of spatial filtering on possible anisotropies in
    solar oscillations.
Authors: Hill, Frank; Haber, Deborah A.; Toomre, Juri; November,
   Laurence J.
Bibcode: 1986ASIC..169...85H
Altcode: 1986ssds.proc...85H
  The authors have used full disk Doppler observations of solar
  oscillations to compare the amplitudes of sectoral modes propagating
  along the equator with those of similar modes propagating along a
  great circle aligned with the poles. They find that the amplitudes are
  generally not equal for the two classes of modes, but the results are
  sensitive to analysis procedures attempting to isolate the different
  modes of oscillation. Spatial filtering of the data using spherical
  harmonics suggests that greater amplitudes are associated with "polar"
  sectoral modes than with "equatorial" sectoral modes.

Title: Properties of solar oscillations.
Authors: Toomre, Juri
Bibcode: 1986ASIC..169....1T
Altcode: 1986ssds.proc....1T
  Many of the oscillations that can be observed in the atmosphere of the
  Sun are resonant acoustic or gravity modes of the interior. Accurate
  measurement of the frequencies of these p and g modes permits deductions
  about the internal structure and dynamics of this star. Some of
  the methods of interpretation, involving a close interplay between
  observation and theory, can be carried over to the study of more
  distant stars.

Title: Theoretical and experimental studies in support of the
    geophysical fluid flow experiment
Authors: Hart, J.; Toomre, J.
Bibcode: 1985aprr.nasa.....H
Altcode:
  Meteorologists and astrophysicists interested in large scale planetary
  and solar circulations have come to recognize the importance of
  rotation and stratification in determining the character of these
  flows. In particular, the effect of latitude-dependent Coriolis force on
  nonlinear convection is thought to play a crucial role in such phenomena
  as differential rotation on the Sun, cloud band orientation on Jupiter,
  and the generation of magnetic fields in thermally driven dynamos. The
  continuous low-gravity environment of the orbiting space shuttle offers
  a unique opportunity to make laboratory studies of such large-scale
  thermally driven flows under the constraint imposed by rotation
  and sphericity. This is possible because polarization forces in a
  dielectric liquid, which are linearly dependent on fluid temperature,
  give rise to an effectively radial buoyancy force when a radial
  electrostatic field is imposed. The Geophysical Fluid Flow Cell (GFFC)
  is an implementation of this ideal in which fluid is contained between
  two rotating hemispheres that are differentially heated and stressed
  with a large a-c voltage. The experiment, to be flown on Spacelab III
  (currently set for launch April 29, 1985), will explore non-linear mode
  selection and high Rayleigh number turbulence in a rotating convecting
  spherical shell of liquid. Experiments will be carried out in a low
  driving parameter range where some limited numerical experimentation
  is currently feasible, as well as in a parameter range significantly
  beyond numerical computation for many years.

Title: Seismology of the Sun
Authors: Christensen-Dalsgaard, J.; Gough, D.; Toomre, J.
Bibcode: 1985Sci...229..923C
Altcode:
  Oscillations of the sun make it possible to probe the inside of a
  star. The frequencies of the oscillations have already provided measures
  of the sound speed and the rate of rotation throughout much of the solar
  interior. These quantities are important for understanding the dynamics
  of the magnetic cycle and have a bearing on testing general relativity
  by planetary precession. The oscillation frequencies yield a helium
  abundance that is consistent with cosmology, but they reinforce the
  severity of the neutrino problem. They should soon provide an important
  standard by which to calibrate the theory of stellar evolution.

Title: Helioseismology
Authors: Leibacher, J. W.; Noyes, R. W.; Toomre, J.; Ulrich, R. K.
Bibcode: 1985SciAm.253c..48L
Altcode: 1985SciAm.253...48L
  Oscillations of the sun's surface are due to sound waves resonating in
  the solar interior. In actual observations, such surface displacements
  are evidenced in the form of Doppler shifts in the wavelengths of
  light that are absorbed by the moving gases, and as variations in
  brightness. The spatial pattern and period of surface oscillation
  allows investigators to deduce the three-dimensional structure of the
  resonance, and to infer properties of the solar interior. Reflection
  and refraction below the solar surface confine sound waves within
  acoustic cavities. Such trapped waves interfere constructively with
  themselves as they circle the sun, creating the resonances that are
  detectable as solar surface oscillations.

Title: Helioseismology.
Authors: Leibacher, J. W.; Noyes, R. W.; Toomre, J.; Ulrich, R. K.
Bibcode: 1985SciAm.253c..34L
Altcode: 1985SciAm.253...34L
  Acoustic waves within the sun are visible as oscillations on the solar
  surface. Their pattern and period hold clues to structure, composition
  and dynamics in the sun's interior.

Title: Frequent Ultraviolet Brightenings in Solar Active Regions
Authors: Porter, J. G.; Toomre, J.; Gebbie, K. B.
Bibcode: 1985BAAS...17..629P
Altcode:
  No abstract at ADS

Title: Changes in Subsurface Horizontal Velocities Inferred from
    Observations of High Degree 5-Minute Solar Oscillations
Authors: Hill, F.; Toomre, J.; Gough, D. O.
Bibcode: 1985BAAS...17..643H
Altcode:
  No abstract at ADS

Title: Turbulence and wave particle interactions in solar-terrestrial
    plasmas
Authors: Dulk, G. A.; Goldman, M. V.; Toomre, J.
Bibcode: 1985colo.reptQ....D
Altcode:
  Activities in the following study areas are reported: (1) particle and
  wave processes in solar flares; (2) solar convection zone turbulence;
  and (3) solar radiation emission. To investigate the amplification of
  cyclotron maser radiation in solar flares, a radio frequency. (RF)
  heating model was developed for the corona surrounding the energy
  release site. Then nonlinear simulations of compressible convection
  display prominent penetration by plumes into regions of stable
  stratification at the base of the solar convection zone, leading to the
  excitation of internal gravity waves there. Lastly, linear saturation
  of electron-beam-driven Langmuir waves by ambient density fluctuations,
  nonlinear saturation by strong turbulence processes, and radiation
  emission mechanisms are examined. An additional section discusses
  solar magnetic fields and hydromagnetic waves in inhomogeneous media,
  and the effect of magnetic fields on stellar oscillation.

Title: Sensitivity of inferred subphotospheric velocity field to
    mode selection, analysis technique and noise.
Authors: Hill, F.; Gough, D.; Toomre, J.
Bibcode: 1984sses.nasa...95H
Altcode: 1984sss..conf...95H
  The horizontal velocity immediately below the photosphere can be
  inferred from observations of high-degree solar oscillations by an
  optimal-averaging inversion technique. The authors investigate the
  sensitivity of the results to various details of both the inversion
  and the determination of the frequencies. The results are shown to be
  quite stable to the choice of most parameters, suggesting that this
  procedure produces reliable estimates of the subsurface velocity.

Title: Solar Seismology From Space. A conference at Snowmass, Colorado
Authors: Ulrich, R. K.; Harvey, J.; Rhodes, E. J., Jr.; Toomre, J.
Bibcode: 1984sses.nasa.....U
Altcode: 1984sss..conf.....U
  No abstract at ADS

Title: Overview of solar seismology: oscillations as probes of
    internal structure and dynamics in the Sun.
Authors: Toomre, J.
Bibcode: 1984sses.nasa....7T
Altcode: 1984sss..conf....7T
  The physical nature of solar oscillations is reviewed. The nomenclature
  of the subject and the techniques used to interpret the oscillations
  are discussed. Many of the acoustic and gravity waves that can be
  observed in the atmosphere of the Sun are actually resonant or standing
  modes of the interior; precise measurements of the frequencies of
  such modes allow deductions of the internal structure and dynamics of
  this star. The scientific objectives of such studies of solar seismic
  disturbances, or of solar seismology, will be outlined. The reasons
  for why it would be very beneficial to carry out further observations
  of solar oscillations both from ground-based networks and from space
  will be discussed.

Title: Penetrative cellular convection in a stratified atmosphere
Authors: Massaguer, J. M.; Latour, J.; Toomre, J.; Zahn, J. -P.
Bibcode: 1984A&A...140....1M
Altcode:
  In the present investigation of penetrative convection within a simple
  compressible model, the middle one of the three layers of differing
  stratification prior to the onset of convection is a convectively
  unstable polytrope bounded above and below by two stably stratified
  polytropes. One- and two-mode steady solutions with hexagonal planforms
  have been studied for Rayleigh numbers up to aobut 1000 times critical,
  and for a range of Prandtl numbers, horizontal wavenumbers, and
  stratifications. These indicate that the penetration into the lower
  stable layer by downward plumes is substantially larger in a stratified
  medium than in a Boussinesq fluid, and produces an extended region
  of adiabatic stratification. The strong asymmetry between upward and
  downward penetration in compressible media has major implications for
  the mixing of stable regions above and below stellar convection zones.

Title: Frequent ultraviolet brightenings observed in a solar active
    region with solar maximum mission
Authors: Porter, J. G.; Toomre, J.; Gebbie, K. B.
Bibcode: 1984ApJ...283..879P
Altcode:
  Observations of the temporal behavior of ultraviolet emission from
  bright points within an active region of the sun are reported. Frequent
  and rapid brightenings in Si IV and O IV line emission are seen. The
  observations suggest that intermittent heating events of modest
  amplitude are occurring at many sites within an active region. By
  selecting the brightest site at any given time within an active region
  and then sampling its behavior in detail within a 120 s interval, it
  is found that about two-thirds of the samples show variations of the
  Si IV line intensity. The brightenings typically last about 40-60 s;
  intensity increases of about 20-100 percent are frequently observed. The
  results suggest that heating due to magnetic field reconnection within
  an active region is proceeding almost stochastically. Events involving
  only a modest release of energy occur the most frequently.

Title: Two-dimensional compressible convection extending over multiple
    scale heights
Authors: Hurlburt, N. E.; Toomre, J.; Massaguer, J. M.
Bibcode: 1984ApJ...282..557H
Altcode:
  The theoretical description of the dynamics of a stellar convection
  zone is considered, taking into account one of the most basic issues
  by studying compressible convection extending over multiple scale
  heights. A revised version of a code reported by Graham (1975) is
  employed. Two-dimensional simulations show that nonlinear compressible
  convection possesses cellular structures with strong localized
  downward-directed plumes and broader upflows. The horizontal flows
  which close the circulation within the cell satisfy an approximate
  Bernoulli integral along a considerable portion of the horizontal
  trajectory. Attention is given to details regarding the numerical
  methods, the properties of the numerical solutions, the overall effects
  of compressibility on nonlinear convection, and a comparison with
  anelastic modal solutions.

Title: Attempt to measure the solar subsurface velocity
Authors: Hill, F.; Gough, D.; Toomre, J.
Bibcode: 1984MmSAI..55..153H
Altcode:
  Five-minute oscillation modes are advected by horizontal velocities
  below the solar surface, and thus can be used as probes of rotation
  and large-scale convective flows. Results of inverse theory applied
  to observations of high-degree modes carried out on six separate days
  reveal variations in horizontal velocities with depth from day to day
  that may be the result of giant convection cells, through noise in
  the data makes this interpretation somewhat tentative.

Title: Solar convection
Authors: Toomre, J.; Gebbie, K. B.
Bibcode: 1984colo.rept.....T
Altcode:
  A thorough study of convective penetration into the solar atmosphere
  and convective motions in sub-atmospheric layers on the sun was
  made. Non-linear anelastic and Boussinesq modal equations were developed
  and solved to describe solar and stellar convection. An explanation was
  developed for the lack of penetration of large-scale convective motions
  into the observable solar atmosphere through the discovery of buoyancy
  braking near the top of a supposedly unstable layer. Observations
  of motions in the solar atmosphere led to the discovery of a new
  scale of solar motion, the so-called mesogranulation. A technique was
  developed to use changes in the solar five-minute oscillations as a
  probe of internal solar structure. Using this technique, large-scale,
  subatmospheric convective eddies were discovered.

Title: Simulation of Effects of Atmospheric Seeing on Observations
    of Solar Five-Minute Oscillations
Authors: Merryfield, W. J.; Toomre, J.; Hill, F.; Gough, D. O.
Bibcode: 1984BAAS...16..532M
Altcode:
  No abstract at ADS

Title: Horizontal Velocities in the Solar Convection Zone Inferred
    from High Degree 5-Minute Oscillations
Authors: Hill, F.; Toomre, J.; Gough, D. O.
Bibcode: 1984BAAS...16R.451H
Altcode: 1984BAAS...16..451H
  No abstract at ADS

Title: Effects of Spherical Harmonic Filtering on Analysis of
    Five-Minute Solar Oscillations of High-Degree
Authors: Haber, D.; Toomre, J.; Hill, F.
Bibcode: 1984BAAS...16Q.533H
Altcode:
  No abstract at ADS

Title: Strong Downward Plumes Resulting from Compressibility in
    Nonlinear Convection and Their Coupling to Gravity Waves
Authors: Toomre, J.; Hurlburt, N. E.; Massaguer, J. M.
Bibcode: 1984ssdp.conf..222T
Altcode:
  Two-dimensional numerical simulations are used to model fully
  compressible nonlinear convection spanning multiple scale heights
  within a stellar envelope.

Title: Solar seismology from space. A conference at Snowmass,
    Colorado, August 17 - 19, 1983.
Authors: Ulrich, R. K.; Harvey, J.; Rhodes, E. J., Jr.; Toomre, J.
Bibcode: 1984ssfs.book.....U
Altcode:
  No abstract at ADS

Title: On the Detection of Subphotospheric Convective Velocities
    and Temperature Fluctuations
Authors: Gough, D. O.; Toomre, J.
Bibcode: 1983SoPh...82..401G
Altcode: 1983IAUCo..66..401G
  A procedure is outlined for estimating the influence of large-scale
  convective eddies on the wave patterns of five-minute oscillations
  of high degree. The method is applied to adiabatic oscillations, with
  frequency ω and wave number k, of a plane-parallel polytropic layer
  upon which is imposed a low-amplitude convective flow. The distortion to
  the k - ω relation has two constituents: one depends on the horizontal
  component of the convective velocity and has a sign which depends on
  the sign of ω/k; the other depends on temperature fluctuations and
  is independent of the sign of ω/k. The magnitude of the distortion
  is just at the limit of present observational sensitivity. Thus there
  is reasonable hope that it will be possible to reveal some aspects of
  the large-scale flow in the solar convection zone.

Title: Nonlinear Anelastic Modal Theory for Solar Convection
Authors: Latour, J.; Toomre, J.; Zahn, J. -P.
Bibcode: 1983SoPh...82..387L
Altcode: 1983IAUCo..66..387L
  Preliminary solar envelope models have been computed using the
  single-mode anelastic equations as a description of turbulent
  convection. This approach provides estimates for the variation
  with depth of the largest convective cellular flows, akin to giant
  cells, with horizontal sizes comparable to the total depth of the
  convection zone. These modal nonlinear treatments are capable of
  describing compressible motions occurring over many density scale
  heights. Single-mode anelastic solutions have been constructed for a
  solar envelope whose mean stratification is nearly adiabatic over most
  of its vertical extent because of the enthalpy (or convective) flux
  explicitly carried by the big cell; a sub-grid scale representation of
  turbulent heat transport is incorporated into the treatment near the
  surface. The single-mode equations admit two solutions for the same
  horizontal wavelength, and these are distinguished by the sense of
  the vertical velocity at the center of the three-dimensional cell. It
  is striking that the upward directed flows experience large pressure
  effects when they penetrate into regions where the vertical scale height
  has become small compared to their horizontal scale. The fluctuating
  pressure can modify the density fluctuations so that the sense of the
  buoyancy force is changed, with buoyancy braking actually achieved near
  the top of the convection zone. The pressure and buoyancy work in the
  shallow but unstable H<SUP>+</SUP> and He<SUP>+</SUP> ionization regions
  can serve to decelerate the vertical motions and deflect them laterally,
  leading to strong horizontal shearing motions. It appears that such
  dynamical processes may explain why the amplitudes of flows related to
  the largest scales of convection are so feeble in the solar atmosphere.

Title: Variability in the power spectrum of solar five-minute
    oscillations
Authors: Hill, F.; Toomre, J.; November, L. J.
Bibcode: 1983SoPh...82..411H
Altcode: 1983IAUCo..66..411H
  Two-dimensional power spectra of solar five-minute oscillations
  display prominent ridge structures in (k, ω) space, where k is the
  horizontal wavenumber and ω is the temporal frequency. The positions
  of these ridges in k and ω can be used to probe temperature and
  velocity structures in the subphotosphere. We have been carrying out a
  continuing program of observations of five-minute oscillations with the
  diode array instrument on the vacuum tower telescope at Sacramento Peak
  Observatory (SPO). We have sought to establish whether power spectra
  taken on separate days show shifts in ridge locations; these may arise
  from different velocity and temperature patterns having been brought
  into our sampling region by solar rotation. Power spectra have been
  obtained for six days of observations of Doppler velocities using the
  MgIλ5173 and FeIλ5434 spectral lines. Each data set covers 8 to 11
  hr in time and samples a region 256″ × 1024″ in spatial extent,
  with a spatial resolution of 2″ and temporal sampling of 65 s. We have
  detected shifts in ridge locations between certain data sets which are
  statistically significant. The character of these displacements when
  analyzed in terms of eastward and westward propagating waves implies
  that changes have occurred in both temperature and horizontal velocity
  fields underlying our observing window. We estimate the magnitude of
  the velocity changes to be on the order of 100 m s<SUP>-1</SUP>; we may
  be detecting the effects of large-scale convection akin to giant cells.

Title: Search for Solar Giant Cells Using Five-Minute Oscillations
    as Probes of Velocity Structures
Authors: Toomre, J.
Bibcode: 1983EOSTr..64..303T
Altcode:
  No abstract at ADS

Title: Time-dependent solutions of multimode convection equations
Authors: Toomre, J.; Gough, D. O.; Spiegel, E. A.
Bibcode: 1982JFM...125...99T
Altcode:
  Truncated modal equations are used to study the time evolution of
  thermal convection. In the Boussinesq approximation these nonlinear
  equations are obtained by expanding the fluctuating velocity and
  temperature fields in a finite set of planforms of the horizontal
  coordinates. Numerical studies dealing with two or three modes with
  triad interactions are discussed. Rich time dependence was found
  in these cases: periodic and aperiodic solutions can be obtained,
  along with various steady solutions. Three-mode solutions reproduce
  the qualitative appearance of spoke-pattern convection as observed in
  experiments at high Prandtl numbers. Though the values of the periods of
  the time-dependent solutions do not agree with those of the experiments,
  their variation with Rayleigh number compares favorably. Except at
  the highest Rayleigh number considered (10,000,000), the theoretical
  Nusselt numbers agree well with experiment.

Title: Internal gravity waves in the solar atmosphere. II - Effects
    of radiative damping
Authors: Mihalas, B. W.; Toomre, J.
Bibcode: 1982ApJ...263..386M
Altcode:
  In the solar photosphere, temperature fluctuations associated
  with acoustic-gravity waves may be rapidly smoothed by the transfer
  mechanism of radiation between hotter and cooler regions. The present
  investigation of the radiative effects on internal gravity waves takes
  into account the parameterization of the radiative energy, employing the
  Newtonian cooling approximation. A linear analysis of the propagation of
  internal gravity waves is carried out in a model of the solar atmosphere
  which is taken to be homogeneous in the horizontal coordinates. Linear
  wave properties both with and without radiative cooling are summarized,
  and the variation with height of energy fluxes and of nonlinearities
  in the waves is discussed. Attention is given to the significance of
  the obtained results in terms of energy balance in the chromosphere
  and in relation to spectral line observations.

Title: Single-mode theory of diffusive layers in thermohaline
    convection
Authors: Gough, D. O.; Toomre, J.
Bibcode: 1982JFM...125...75G
Altcode:
  A two-layer configuration of thermohaline convection is studied,
  with the principal aim of explaining the observed independence of
  the buoyancy-flux ratio on the stability parameter when the latter is
  large. Temperature is destabilizing and salinity is stabilizing, so
  diffusive interfaces separate the convecting layers. The convection is
  treated in the single-mode approximation, with a prescribed horizontal
  planform and wavenumber. Surveys of numerical solutions are presented
  for a selection of Rayleigh numbers R, stability parameters lambda
  and horizontal wavenumbers. The solutions yield a buoyancy flux
  ratio chi that is insensitive to lambda, in accord with laboratory
  experiments. However chi increases with increasing R, in contradiction
  to laboratory observations.

Title: Nonlinear modal analysis of penetrative convection
Authors: Zahn, J. -P.; Toomre, J.; Latour, J.
Bibcode: 1982GApFD..22..159Z
Altcode:
  It is pointed out that thermal convection in many astrophysical and
  geophysical settings occurs in an unstable layer bounded above and
  below by regions which are stably stratified. The convective motions
  may extend a substantial distance into the adjacent stable zones. If
  the motions have little direct effect upon the mean stratification
  of the stable zone, then they are usually referred to as convective
  overshooting. The primary objective of the present investigation is
  to study the dynamics of overshooting at very large Rayleigh numbers,
  mainly with stellar applications in mind. Numerically this is only
  feasible if severe simplifications are made in the description of
  what are likely to be turbulent motions. The approach employed in the
  investigation utilizes nonlinear modal equations in which the vertical
  and temporal structure of the convection is described accurately at
  the expense of the horizontal structure. A summary of the salient
  properties of penetrative convection is provided on the basis of the
  results of the conducted studies.

Title: Relation of Ephemeral Magnetic Regions to the Low Amplitude
    Branch of Persistent Vertical Velocities
Authors: Gebbie, K. B.; Toomre, J.; Haber, D. A.; Hill, F.; Simon,
   G. W.; November, L. J.; Gurman, J. B.; Shine, R. A.
Bibcode: 1982BAAS...14R.939G
Altcode: 1982BAAS...14..939G
  No abstract at ADS

Title: The Lateral Deflection of Large-Scale Convective Flows by
    Scale Height Effects below the Solar Surface
Authors: Hurlburt, N.; Toomre, J.
Bibcode: 1982BAAS...14..938H
Altcode:
  No abstract at ADS

Title: Solar Five-Minute Oscillations, Subsurface Velocities and
    Inverse Theory
Authors: Gough, D. O.; Hill, F.; Toomre, J.
Bibcode: 1982BAAS...14..938G
Altcode:
  No abstract at ADS

Title: Vertical flows of supergranular and mesogranular scale observed
    on the sun with OSO 8
Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.
Bibcode: 1982ApJ...258..846N
Altcode:
  A program of observations was carried out in order to study the
  penetration of supergranular flows over a broad range of heights in
  the solar atmosphere. Steady Doppler velocities are determined from
  observations of a Si II spectral line using the Ultraviolet Spectrometer
  on the Orbiting Solar Observatory 8 (OSO 8) satellite and Fe I and
  Mg I lines with the diode-array instrument on the vacuum telescope at
  Sacramento Peak Observatory (SPO). The heights of formation of these
  spectral lines span about 1400 km or nearly 11 density scale heights
  from the photosphere to the middle chromosphere. Steady vertical flows
  on spatial scales typical of supergranulation and mesogranulation have
  been detected in the middle chromosphere with OSO 8. The patterns of
  intensity and steady velocity of granular scale are reproducible in
  successive data sets. The patterns appear to evolve slowly over the
  9 hr period spanned by six orbits.

Title: University of Colorado, Boulder, Colorado 80309. Report.
Authors: Dulk, G. A.; Shull, J. M.; Toomre, J.
Bibcode: 1982BAAS...14..122D
Altcode:
  No abstract at ADS

Title: Solar 5-MINUTE Oscillations as Probes of Structure in the
    Subphotosphere
Authors: Hill, F.; Toomre, J.; November, L. J.
Bibcode: 1982pccv.conf..139H
Altcode:
  No abstract at ADS

Title: Review of Time-Dependent Convection and Attempts to Couple
    it to Pulsation in Stars
Authors: Toomre, J.
Bibcode: 1982pccv.conf..170T
Altcode:
  No abstract at ADS

Title: Steady flows in the solar transition region observed with SMM
Authors: Gebbie, K. B.; Hill, F.; November, L. J.; Gurman, J. B.;
   Shine, R. A.; Woodgate, B. E.; Athay, R. G.; Tandberg-Hanssen, E. A.;
   Toomre, J.; Simon, G. W.
Bibcode: 1981ApJ...251L.115G
Altcode:
  Steady flows in the quiet solar transition region have been observed
  with the Ultraviolet Spectrometer and Polarimeter experiment on the
  Solar Maximum Mission (SMM) satellite. The persistent vertical motions
  seen at disk center have spatial rms amplitudes of 1.4 km/s in the C
  II line, 3.9 km/s in Si IV, and 4.2 km/s in C IV. The amplitudes of
  the more horizontal flows seen toward the limb tend to be somewhat
  higher. Plots of steady vertical velocity versus intensity seen at
  disk center in Si IV and C IV show two distinct branches.

Title: Internal gravity waves in the solar atmosphere. I - Adiabatic
    waves in the chromosphere
Authors: Mihalas, B. W.; Toomre, J.
Bibcode: 1981ApJ...249..349M
Altcode:
  The properties of adiabatic and linear internal gravity waves
  propagating in a solar wind model are discussed, using nonlinearity
  criteria unique to gravity waves to estimate wave-breaking heights. The
  results are used to deduce information on the possible role of gravity
  waves in the chromospheric energy balance. Maximum vertical velocity
  amplitudes for gravity waves are estimated to be on the order of 2
  km/sec or less, and maximum horizontal velocity amplitudes are less than
  6 km/sec, with temperature perturbations as large as 1000-2000 K. It
  is also estimated that gravity waves with an incident energy flux of
  one million ergs/sq cm-sec can propagate upward to a maximum height
  of 900-1000 km above the visible surface before nonlinearities lead
  to wave breaking, while those with an energy flux of 100,000 ergs/sq
  cm-sec can reach maximum heights of 1400-1600 km.

Title: Stellar convection theory. III - Dynamical coupling of the
    two convection zones in A-type stars by penetrative motions
Authors: Latour, J.; Toomre, J.; Zahn, J. -P.
Bibcode: 1981ApJ...248.1081L
Altcode:
  The thermal convection occurring over many density scale heights in an
  A-type star outer envelope, encompassing both the hydrogen and helium
  convectively unstable zones, is examined by means of anelastic modal
  equations. The single-mode anelastic equations for such compressible
  convection display strong overshooting of the motions into adjacent
  radiative zones, which would preclude diffusive separation of
  elements in the supposedly quiescent region between the two unstable
  zones. In addition, the anelastic solutions reveal that the two zones
  of convective instability are dynamically coupled by the overshooting
  motions. The two solutions that the nonlinear single-mode equations
  admit for the same horizontal wavelength are distinguished by the
  sense of the vertical velocity at the center of the three-dimensional
  cell. It is suggested that strong horizontal shear flows should be
  present just below the surface of the star, and that the large-scale
  motions extending into the stable atmosphere would appear mainly as
  horizontal flows.

Title: The detection of mesogranulation on the sun.
Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.
Bibcode: 1981ApJ...245L.123N
Altcode:
  Time averages of velocity measurements at disk center on the quiet sun
  reveal the presence of a fairly stationary pattern of cellular flow
  with a spatial scale of 5-10 Mm. Such mesogranulation has a spatial rms
  vertical velocity amplitude of about 60 m/s superposed on the larger
  scale supergranular flows. The lifetimes of mesogranules appear to be
  at least 2 hr.

Title: Nonlinear Penetrative Convection in a Compressible Medium
Authors: Hurlburt, N.; Toomre, J.; Massaguer, J. M.
Bibcode: 1981BAAS...13..912H
Altcode:
  No abstract at ADS

Title: Solar Five-Minute Oscillations as Probes of Velocity and
    Temperature Fields
Authors: Hill, F.; Toomre, J.; November, L. J.
Bibcode: 1981BAAS...13Q.860H
Altcode: 1981BAAS...13..860H
  No abstract at ADS

Title: Nonlinear Anelastic Models of Solar Convection
Authors: Toomre, J.; Latour, J.; Zahn, J. -P.
Bibcode: 1981BAAS...13Q.907T
Altcode:
  No abstract at ADS

Title: Height Dependence of Steady Flows Determined from Coordinated
    SMM and SPO Observations
Authors: Gebbie, K. B.; Hill, F.; Toomre, J.; November, L. J.; Simon,
   G. W.; Gurman, J. B.; Shine, R. A.; Woodgate, B. E.
Bibcode: 1981BAAS...13..914G
Altcode:
  No abstract at ADS

Title: OSO 8 Observations of Coherent Chromospheric Oscillations
Authors: Hill, F.; Toomre, J.; November, L. J.
Bibcode: 1980BAAS...12R.894H
Altcode:
  No abstract at ADS

Title: Nonlinear Simulations of Rotational Effects in Supergranules
Authors: Hathaway, D. H.; Toomre, J.
Bibcode: 1980BAAS...12Q.894H
Altcode:
  No abstract at ADS

Title: Steady Flows in the Solar Transition Region Observed with
    the UVSP Experiment on SMM
Authors: Gebbie, K. B.; Hill, F.; Toomre, J.; November, L. J.; Simon,
   G. W.; Athay, R. G.; Bruner, E. C.; Rehse, R.; Gurman, J. B.; Shine,
   R. A.; Woodgate, B. E.; Tandberg-Hanssen, E. A.
Bibcode: 1980BAAS...12..907G
Altcode:
  No abstract at ADS

Title: Two Dimensional Compressible Convection Extending Over Multiple
    Scale Heights
Authors: Hurlburt, N. E.; Toomre, J.; Massaguer, J. M.; Graham, E.
Bibcode: 1980BAAS...12S.894H
Altcode:
  No abstract at ADS

Title: Anelastic Modal Theory Applied to the Solar Convection Zone
Authors: Toomre, J.; Latour, J.; Zahn, J. P.
Bibcode: 1980BAAS...12..895T
Altcode:
  No abstract at ADS

Title: The Lifetime of Solar Mesogranulation
Authors: November, L. J.; Gebbie, K. B.; Hill, F.; Toomre, J.; Simon,
   G. W.
Bibcode: 1980BAAS...12..895N
Altcode:
  No abstract at ADS

Title: Axisymmetric Convection Driven by Latitudinal Temperature
    Gradients in Rotating Spherical Shells.
Authors: Hathaway, D. H.; Gilman, P. A.; Miller, J.; Toomre, J.
Bibcode: 1980BAAS...12..686H
Altcode:
  No abstract at ADS

Title: Overshooting Motions from the Convection Zone and Their Role
    in Atmospheric Heating
Authors: Toomre, J.
Bibcode: 1980HiA.....5..571T
Altcode:
  No abstract at ADS

Title: Convective instability when the temperature gradient and
    rotation vector are oblique to gravity. II. Real fluids with effects
    of diffusion
Authors: Hathaway, D. H.; Toomre, J.; Gilman, P. A.
Bibcode: 1980GApFD..15....7H
Altcode:
  The linear stability analysis of Hathaway, Gilman and Toomre (1979)
  (hereafter referred to as Paper I) is repeated for Boussinesq fluids
  with viscous and thermal diffusion. As in Paper I the fluid is confined
  between plane parallel boundaries and the rotation vector is oblique
  to gravity. This tilted rotation vector introduces a preference
  for roll-like disturbances whose axes are oriented north-south;
  the preference is particularly strong in the equatorial region. The
  presence of a latitudinal temperature gradient produces a thermal
  wind shear which favors axisymmetric convective rolls if the gradient
  exceeds some critical value. For vanishingly small diffusivities the
  value of this transition temperature gradient approaches the inviscid
  value found in Paper I. For larger diffusivities larger gradients are
  required particularly in the high latitudes. These results are largely
  independent of the Prandtl number. Diffusion tends to stabilize the
  large wavenumber rolls with the result that a unique wavenumber can
  be found at which the growth rate is maximized. These preferred rolls
  have widths comparable to the depth of the layer and tend to be broader
  near the equator. The axisymmetric rolls are similar in many respects
  to the cloud bands on Jupiter provided they extend to a depth of about
  15,000 km.

Title: Mesogranulation -- An Intermediate Scale of Motion on the Sun
Authors: Toomre, J.; November, L. J.; Gebbie, K. B.; Simon, G. W.
Bibcode: 1979BAAS...11..641T
Altcode:
  No abstract at ADS

Title: Convective Instability in Rotating Layers with Thermal Winds
    and Application to Jupiter
Authors: Hathaway, D. H.; Gilman, P. A.; Toomre, J.
Bibcode: 1979BAAS...11Q.618H
Altcode:
  No abstract at ADS

Title: The height variation of supergranular velocity fields
    determined from simultaneous OSO 8 satellite and ground-based
    observations.
Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.
Bibcode: 1979ApJ...227..600N
Altcode:
  Results are reported for simultaneous satellite and ground-based
  observations of supergranular velocities in the sun, which were made
  using a UV spectrometer aboard OSO 8 and a diode-array instrument
  operating at the exit slit of an echelle spectrograph attached to a
  vacuum tower telescope. Observations of the steady Doppler velocities
  seen toward the limb in the middle chromosphere and the photosphere
  are compared; the observed spectral lines of Si II at 1817 A and Fe
  I at 5576 A are found to differ in height of formation by about 1400
  km. The results show that supergranular motions are able to penetrate
  at least 11 density scale heights into the middle chromosphere, that
  the patterns of motion correlate well with the cellular structure seen
  in the photosphere, and that the motion increases from about 800 m/s in
  the photosphere to at least 3000 m/s in the middle chromosphere. These
  observations imply that supergranular velocities should be evident
  in the transition region and that strong horizontal shear layers in
  supergranulation should produce turbulence and internal gravity waves.

Title: Convective Instability when the Temperature Gradient and
    Rotation Vector are Oblique to Gravity. I. Fluids without Diffusion
Authors: Hathaway, D. H.; Toomre, J.; Gilman, P. A.
Bibcode: 1979GApFD..13..289H
Altcode:
  No abstract at ADS

Title: Compressible Convection in the Outer Envelope of A-type Stars
Authors: Toomre, J.; Latour, J.; Zahn, J. -P.
Bibcode: 1978BAAS...10..677T
Altcode:
  No abstract at ADS

Title: The Variation with Height of Supergranular Velocity Fields
Authors: Gebbie, K. B.; November, L. J.; Toomre, J.; Simon, G. W.
Bibcode: 1978BAAS...10Q.672G
Altcode:
  No abstract at ADS

Title: Vertical and Horizontal Components of Supergranulation Velocity
    Fields Observed with OSO-8
Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.
Bibcode: 1977BAAS....9..337N
Altcode:
  No abstract at ADS

Title: Anelastic Stellar Convection Theory Applied to A-type Stars.
Authors: Toomre, J.; Latour, J.; Zahn, J. -P.
Bibcode: 1977BAAS....9..337T
Altcode:
  No abstract at ADS

Title: Violent Tides Between Galaxies
Authors: Toomre, Alar; Toomre, Juri
Bibcode: 1977nass.book..271T
Altcode:
  No abstract at ADS

Title: Numerical solutions of single-mode convection equations
Authors: Toomre, J.; Gough, D. O.; Spiegel, E. A.
Bibcode: 1977JFM....79....1T
Altcode:
  In the Boussinesq approximation, single-mode equations describing
  thermal convection are constructed by expanding the fluctuating velocity
  and temperature fields in a complete set of functions (or planforms)
  of the horizontal coordinates and retaining just one term. Numerical
  solutions of the single-mode equations are investigated, chief
  consideration being given to hexagonal planforms. Extensive surveys of
  steady solutions are presented for various Rayleigh numbers, Prandtl
  numbers, and horizontal wavenumbers. The dependences on Rayleigh number
  and Prandtl number at very large Rayleigh number are in satisfactory
  agreement with the results of asymptotic expansions.

Title: Stellar convection theory. II. Single-mode study of the second
    convection zone in an A-type star.
Authors: Toomre, J.; Zahn, J. -P.; Latour, J.; Spiegel, E. A.
Bibcode: 1976ApJ...207..545T
Altcode:
  The anelastic modal equations presented in Paper I are considered
  in their simplest version: only one mode is retained in the
  representation of the fluctuating dynamic and thermodynamic variables
  of convection theory. These single-mode equations are used to examine
  the structure of the second convection zone of an A-type star. Two-
  and three-dimensional numerical solutions are obtained for a range of
  parameters in the theory, and a simple analysis is provided for their
  interpretation. The principal results are for three-dimensional motions,
  since these are most likely to be relevant to stellar convection. Such
  motions produce a convective heat flux several orders of magnitude
  greater than predicted by standard mixing-length theory for the same
  situation; we find that convection carries up to 6 percent of the
  total flux. The most significant astrophysical implication of our
  results is that they suggest strong overshooting into the adjacent
  radiative zones. We anticipate that mixing will extend to the overlying
  hydrogen convection zone. This would rule out some interpretations of
  metallic-line stars which invoke diffusive element separation between
  the two convection zones. Subject headings: convection - stars:
  interiors - stars: metallic-line

Title: Stellar convection theory. I. The anelastic modal equations.
Authors: Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J. -P.
Bibcode: 1976ApJ...207..233L
Altcode:
  Methods are developed for dealing with the various dynamical
  problems that arise because of convective zones in stars. A system
  of equations for stellar convection is derived from the full
  equations of compressible fluid dynamics with the aid of two major
  approximations. The first of these is the anelastic approximation,
  which involves both the filtering out of acoustic waves and a suitable
  linearization of the fluctuating thermodynamic variables. The second
  one approximates the horizontal structure of convection by expanding
  the motion in a set of horizontal cellular platforms and severely
  truncating the expansion. The resulting system of partial differential
  equations, referred to as the anelastic modal equations, is outlined
  along with suggested boundary conditions and techniques for solving
  the equations. Ways of assessing the overall validity of the present
  treatment are discussed.

Title: Supergranulation Velocity Fields Observed in the Solar
    Transition Region with OSO-8
Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.;
   Bruner, E. C., Jr.; Chipman, E. G.; Lites, B. W.; Shine, R. A.;
   Orrall, F. Q.; Athay, R. G.; White, O. R.
Bibcode: 1976BAAS....8..311N
Altcode:
  No abstract at ADS

Title: The Second Convection Zone in an A-type Star
Authors: Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J. P.
Bibcode: 1975BAAS....7..526L
Altcode:
  No abstract at ADS

Title: Modal equations for cellular convection
Authors: Gough, D. O.; Spiegel, E. A.; Toomre, J.
Bibcode: 1975JFM....68..695G
Altcode:
  We expand the fluctuating flow variables of Boussinesq convection in
  the planform functions of linear theory. Our proposal is to consider a
  drastic truncation of this expansion as a possible useful approximation
  scheme for studying cellular convection. With just one term included,
  we obtain a fairly simple set of equations which reproduces some of the
  qualitative properties of cellular convection and whose steady-state
  form has already been derived by Roberts (1966). This set of 'modal
  equations' is analyzed at slightly supercritical and at very high
  Rayleigh numbers. In the latter regime the Nusselt number varies
  with Rayleigh number just as in the mean-field approximation with one
  horizontal scale when the boundaries are rigid. However, the Nusselt
  number now depends also on the Prandtl number in a way that seems
  compatible with experiment. The chief difficulty with the approach is
  the absence of a deductive scheme for deciding which planforms should
  be retained in the truncated expansion.

Title: What Velocities are Consistent with the Interpretation of
    Supergranulation as Penetrative Convection?
Authors: Gebbie, K. B.; Toomre, J.
Bibcode: 1975BAAS....7Q.363G
Altcode:
  No abstract at ADS

Title: Highly stretched meshes as functionals of solutions
Authors: Gough, D. O.; Spiegel, E. A.; Toomre, J.
Bibcode: 1975LNP....35..191G
Altcode:
  No abstract at ADS

Title: Violent tides between galaxies.
Authors: Toomre, A.; Toomre, J.
Bibcode: 1973SciAm.229f..38T
Altcode: 1973SciAm.229...38T
  No abstract at ADS

Title: Violent Tides between Galaxies
Authors: Alar; Toomre, Juri
Bibcode: 1973SciAm.229f..38A
Altcode:
  No abstract at ADS

Title: Radial Velocities in the Tail of NGC 4676A
Authors: Theys, J. C.; Spiegel, E. A.; Toomre, Juri
Bibcode: 1972PASP...84..851T
Altcode:
  A spectrum of ffie long tail of NGC 4676A shows [011] x3727 in
  emission. The radial velocity measured from one plate varies by about
  400 km sec-1 along the length of the tail. Key words: peculiar galaxy -
  radial velocities

Title: Galactic Bridges and Tails
Authors: Toomre, Alar; Toomre, Juri
Bibcode: 1972ApJ...178..623T
Altcode:
  This paper argues that the bridges and tails seen in some multiple
  galaxies are just tidal relics of close encounters. These consequences
  of the brief but violent tidal forces are here studied in a deliberately
  simple-minded fashion: Each encounter is considered to involve only two
  galaxies and to be roughly parabolic; each galaxy is idealized as just
  a disk of noninteracting test particles which initially orbit a central
  mass point. As shown here, the two-sided distortions provoked by gravity
  alone in such circumstances can indeed evolve kinematically into some
  remarkably narrow and elongated features: (i) After a relatively direct
  passage of a small companion, the outer portions of the primary disk
  often deform both into a near-side spiral arm or "bridge" extending
  toward this satellite, and into a far-side "counterarm." (ii) A similar
  encounter with an equal or more massive partner results typically in
  a long and curving "tail" of escaping debris from the far side of the
  victim disk, and in an avalanche of near-side particles, most of which
  are captured by the satellite. Besides extensive pictorial surveys of
  such tidal damage, this paper offers reconstructions of the orbits
  and outer shapes of four specific interacting pairs: Arp 295, M51 +
  NOC 5195, NGC 4676, and NOC 4038/9. Those models can be found in the
  fairly self-explanatory figures 19, 21, 22, and 23. Also discussed are
  some closely related issues of eccentric bound orbits, orbital decay,
  accretion, and forced spiral waves.

Title: Spectra of Extragalactic Rings.
Authors: Theys, J. C.; Spiegel, E. A.; Toomre, J.
Bibcode: 1972BAAS....4..213T
Altcode:
  No abstract at ADS

Title: Model of the Encounter Between NGC 5194 and 5195.
Authors: Toomre, A.; Toomre, J.
Bibcode: 1972BAAS....4..214T
Altcode:
  No abstract at ADS

Title: Theorectical Model of NGC 4038/39.
Authors: Toomre, Alar; Toomre, Juri
Bibcode: 1971BAAS....3..390T
Altcode:
  No abstract at ADS

Title: On Intergalactic Bridges.
Authors: Toomre, Alar; Toomre, Juri
Bibcode: 1970BAAS....2R.350T
Altcode:
  No abstract at ADS

