Author name code: steiner
ADS astronomy entries on 2022-09-14
author:"Steiner, Oskar" 
------------------------------------------------------------------------  

Title: Observation of a small-scale magnetic vortex associated with
a chromospheric swirl: signatures of a small-scale magnetic tornado
Authors: Milena Diaz Castillo, Saida; Steiner, Oskar; Fischer,
   Catherine; Berdyugina, Svetlana; Rezaei, Reza
Bibcode: 2022cosp...44.2521M
Altcode:
  \newcommand{\ion}[2]{#1\,{\textsc{#2}}} High-resolution solar
  observations revealed the existence of small-scale swirling vortices
  in chromospheric intensity maps and velocity diagnostics. These events
  are commonly localized in the quiet sun intergranular space and are
  often related to small-scale magnetic flux concentrations at the solar
  surface. Frequently, vortices have been observed in the vicinity of
  magnetic flux concentrations, indicating a link between swirls and the
  evolution of the small-scale magnetic fields. Vortices were also studied
  with MHD numerical simulations of the solar atmosphere, revealing
  their complexity, dynamics, and magnetic nature. In particular, it
  has been suggested that the chromospheric swirling plasma motion is
  due to a coherently rotating magnetic field structure, which again
  is driven by a photospheric vortex flow at its footpoint. In this
  contribution, we present a comprehensive description of the evolution
  of an isolated small-scale magnetic element interacting with a vortex
  flow, which in turn is related to a chromospheric swirl. We study
  observations taken with the CRisp Imaging SpectroPolarimeter (CRISP)
  instrument and the CHROMospheric Imaging Spectrometer (CHROMIS) at the
  1m Swedish Solar Telescope (SST) in April 2019 as part of a SOLARNET
  access program. The data were taken at quiet-Sun disk-center, recording
  full Stokes photospheric maps in the \ion{Fe}{i} line at 617\,nm, full
  Stokes data in the \ion{Ca}{ii} infrared triplet line at 854\,nm, and
  spectroscopic maps in the H$\alpha$ 656\,nm, \ion{Ca}{ii} K 393\,nm,
  and \ion{Ca}{ii} H 396\,nm lines. Utilizing the multi-wavelength
  data and applying height-dependent Stokes inversion and local
  correlation tracking methods, we are able to analyse the magnetic
  field dynamics in the presence of vortex structures at photospheric
  and chromospheric layers. The temporal evolution of the magnetic
  element shows an appreciable increase in the magnetic field strength
  during the interaction with the vortex flow, reaching kG values for
  a few minutes. We also find a clear evidence of a Rapid Blue-shift
  Excursion (RBE) associated with the magnetic field intensification
  event propagating along the chromospheric vortex. In addition, we
  explore the polarization signatures in the photosphere to reveal the
  intrinsic structure of the magnetic element. Marginal but consistent
  detection of linear polarization signals in the surroundings of the
  magnetic element before intensification suggests a magnetic field
  torsion. Our analysis indicates that we have observed a rotating
  magnetic object reaching from the photosphere to the chromosphere,
  resembling a small-scale magnetic tornado.

Title: Acoustic-gravity wave propagation characteristics in 3D
    radiation hydrodynamic simulations of the solar atmosphere
Authors: Fleck, Bernhard; Khomenko, Elena; Carlsson, Mats; Rempel,
   Matthias; Steiner, Oskar; Riva, Fabio; Vigeesh, Gangadharan
Bibcode: 2022cosp...44.2503F
Altcode:
  There has been tremendous progress in the degree of realism of
  three-dimensional radiation magneto-hydrodynamic simulations of the
  solar atmosphere in the past decades. Four of the most frequently
  used numerical codes are Bifrost, CO5BOLD, MANCHA3D, and MURaM. Here
  we test and compare the wave propagation characteristics in model
  runs from these four codes by measuring the dispersion relation
  of acoustic-gravity waves at various heights. We find considerable
  differences between the various models.

Title: Small scale Alfvénic vortices in the solar atmosphere
Authors: Canivete Cuissa, José Roberto; Steiner, Oskar; Battaglia,
   Andrea
Bibcode: 2022cosp...44.2551C
Altcode:
  Vortices are one of the fundamental small scale features present in the
  solar atmosphere. They are ubiquitous at photospheric and chromospheric
  levels and are often tightly coupled to small scale surface magnetic
  fields. Therefore, they potentially contribute to the transport of
  energy towards the upper layers of the solar atmosphere. We study
  the dynamics and the statistical properties of small scale swirls in
  realistic radiative magneto-hydrodynamical simulations of the solar
  atmosphere realized with the CO5BOLD code. To this aim, we employ the
  swirling strength criterion and its evolution equation to investigate
  the properties and dynamics of 9 identified swirl events. It is found
  that the studied photospheric and chromospheric swirls are the plasma
  response to self-consistently launched torsional Alfvén pulses that
  propagate vertically in the solar atmosphere. To infer the statistical
  properties of the swirl population in the numerical simulations, we
  apply a new algorithm for the automatic identification of vortices. This
  algorithm is based on a state-of-the-art method that combines the rigor
  of mathematical criteria and the global perspective of morphological
  techniques. Compared to previous studies, our analysis reveals more and
  smaller vortical motions in the simulated solar atmosphere. Moreover,
  it is found that the large majority of the identified swirls in the
  photosphere show twists in the magnetic field lines compatible with
  torsional Alfvén waves. Therefore we confirm that the small scale
  vortices in the lower solar atmosphere are Alfvénic in nature.

Title: Methodology for estimating the magnetic Prandtl number and
    application to solar surface small-scale dynamo simulations
Authors: Riva, F.; Steiner, O.
Bibcode: 2022A&A...660A.115R
Altcode: 2022arXiv220212115R
  Context. A crucial step in the numerical investigation of small-scale
  dynamos in the solar atmosphere consists of an accurate determination
  of the magnetic Prandtl number, Pr<SUB>m</SUB>, stemming from radiative
  magneto-hydrodynamic (MHD) simulations. <BR /> Aims: The aims are to
  provide a reliable methodology for estimating the effective Reynolds
  and magnetic Reynolds numbers, Re and Re<SUB>m</SUB>, and their ratio
  Pr<SUB>m</SUB> = Re<SUB>m</SUB>/Re (the magnetic Prandlt number),
  that characterise MHD simulations and to categorise small-scale
  dynamo simulations in terms of these dimensionless parameters. <BR />
  Methods: The methodology proposed for computing Re and Re<SUB>m</SUB>
  is based on the method of projection on proper elements and it relies
  on a post-processing step carried out using higher order accurate
  numerical operators than the ones in the simulation code. A number
  of radiative MHD simulations with different effective viscosities and
  plasma resistivities were carried out with the CO<SUP>5</SUP>BOLD code,
  and the resulting growth rate of the magnetic energy and saturated
  magnetic field strengths were characterised in terms of Re and
  Re<SUB>m</SUB>. <BR /> Results: Overall, the proposed methodology
  provides a solid estimate of the dissipation coefficients affecting
  the momentum and induction equations of MHD simulation codes, and
  consequently also a reliable evaluation of the magnetic Prandtl number
  characterising the numerical results. Additionally, it is found that
  small-scale dynamos are active and can amplify a small seed magnetic
  field up to significant values in CO<SUP>5</SUP>BOLD simulations with
  a grid spacing smaller than h = 12 km, even at Pr<SUB>m</SUB> ≃
  0.65. However, it is also evident that it is difficult to categorise
  dynamo simulations in terms of Pr<SUB>m</SUB> alone, because it
  is not only important to estimate the amplitude of the dissipation
  coefficients, but also at which scales energy dissipation takes place.

Title: Final Report for SAG 21: The Effect of Stellar Contamination
    on Space-based Transmission Spectroscopy
Authors: Rackham, Benjamin V.; Espinoza, Néstor; Berdyugina, Svetlana
   V.; Korhonen, Heidi; MacDonald, Ryan J.; Montet, Benjamin T.; Morris,
   Brett M.; Oshagh, Mahmoudreza; Shapiro, Alexander I.; Unruh, Yvonne C.;
   Quintana, Elisa V.; Zellem, Robert T.; Apai, Dániel; Barclay, Thomas;
   Barstow, Joanna K.; Bruno, Giovanni; Carone, Ludmila; Casewell, Sarah
   L.; Cegla, Heather M.; Criscuoli, Serena; Fischer, Catherine; Fournier,
   Damien; Giampapa, Mark S.; Giles, Helen; Iyer, Aishwarya; Kopp, Greg;
   Kostogryz, Nadiia M.; Krivova, Natalie; Mallonn, Matthias; McGruder,
   Chima; Molaverdikhani, Karan; Newton, Elisabeth R.; Panja, Mayukh;
   Peacock, Sarah; Reardon, Kevin; Roettenbacher, Rachael M.; Scandariato,
   Gaetano; Solanki, Sami; Stassun, Keivan G.; Steiner, Oskar; Stevenson,
   Kevin B.; Tregloan-Reed, Jeremy; Valio, Adriana; Wedemeyer, Sven;
   Welbanks, Luis; Yu, Jie; Alam, Munazza K.; Davenport, James R. A.;
   Deming, Drake; Dong, Chuanfei; Ducrot, Elsa; Fisher, Chloe; Gilbert,
   Emily; Kostov, Veselin; López-Morales, Mercedes; Line, Mike; Močnik,
   Teo; Mullally, Susan; Paudel, Rishi R.; Ribas, Ignasi; Valenti, Jeff A.
Bibcode: 2022arXiv220109905R
Altcode:
  Study Analysis Group 21 (SAG21) of the Exoplanet Exploration Program
  Analysis Group (ExoPAG) was organized to study the effect of stellar
  contamination on space-based transmission spectroscopy, a method for
  studying exoplanetary atmospheres by measuring the wavelength-dependent
  radius of a planet as it transits its star. Transmission spectroscopy
  relies on a precise understanding of the spectrum of the star being
  occulted. However, stars are not homogeneous, constant light sources
  but have temporally evolving photospheres and chromospheres with
  inhomogeneities like spots, faculae, and plages. This SAG has brought
  together an interdisciplinary team of more than 100 scientists, with
  observers and theorists from the heliophysics, stellar astrophysics,
  planetary science, and exoplanetary atmosphere research communities,
  to study the current needs that can be addressed in this context to
  make the most of transit studies from current NASA facilities like
  HST and JWST. The analysis produced 14 findings, which fall into
  three Science Themes encompassing (1) how the Sun is used as our best
  laboratory to calibrate our understanding of stellar heterogeneities
  ("The Sun as the Stellar Benchmark"), (2) how stars other than the Sun
  extend our knowledge of heterogeneities ("Surface Heterogeneities of
  Other Stars") and (3) how to incorporate information gathered for the
  Sun and other stars into transit studies ("Mapping Stellar Knowledge
  to Transit Studies").

Title: A novel fourth-order WENO interpolation technique. A possible
    new tool designed for radiative transfer
Authors: Janett, Gioele; Steiner, Oskar; Alsina Ballester, Ernest;
   Belluzzi, Luca; Mishra, Siddhartha
Bibcode: 2021arXiv211011885J
Altcode:
  Context. Several numerical problems require the interpolation of
  discrete data that present various types of discontinuities. The
  radiative transfer is a typical example of such a problem. This
  calls for high-order well-behaved techniques to interpolate both
  smooth and discontinuous data. Aims. The final aim is to propose
  new techniques suitable for applications in the context of numerical
  radiative transfer. Methods. We have proposed and tested two different
  techniques. Essentially non-oscillatory (ENO) techniques generate
  several candidate interpolations based on different substencils. The
  smoothest candidate interpolation is determined from a measure for
  the local smoothness, thereby enabling the essential non-oscillatory
  property. Weighted ENO (WENO) techniques use a convex combination of
  all candidate substencils to obtain high-order accuracy in smooth
  regions while keeping the essentially non-oscillatory property. In
  particular, we have outlined and tested a novel well-performing
  fourth-order WENO interpolation technique for both uniform and
  nonuniform grids. Results. Numerical tests prove that the fourth-order
  WENO interpolation guarantees fourth-order accuracy in smooth regions
  of the interpolated functions. In the presence of discontinuities, the
  fourth-order WENO interpolation enables the non-oscillatory property,
  avoiding oscillations. Unlike Bézier and monotonic high-order Hermite
  interpolations, it does not degenerate to a linear interpolation near
  smooth extrema of the interpolated function. Conclusions. The novel
  fourth-order WENO interpolation guarantees high accuracy in smooth
  regions, while effectively handling discontinuities. This interpolation
  technique might be particularly suitable for several problems, including
  a number of radiative transfer applications such as multidimensional
  problems, multigrid methods, and formal solutions.

Title: The Alfvénic nature of chromospheric swirls
Authors: Battaglia, Andrea Francesco; Canivete Cuissa, José Roberto;
   Calvo, Flavio; Bossart, Aleksi Antoine; Steiner, Oskar
Bibcode: 2021A&A...649A.121B
Altcode: 2021arXiv210307366B
  Context. Observations show that small-scale vortical plasma motions
  are ubiquitous in the quiet solar atmosphere. They have received
  increasing attention in recent years because they are a viable
  candidate mechanism for the heating of the outer solar atmospheric
  layers. However, the true nature and the origin of these swirls, and
  their effective role in the energy transport, are still unclear. <BR />
  Aims: We investigate the evolution and origin of chromospheric swirls
  by analyzing numerical simulations of the quiet solar atmosphere. In
  particular, we are interested in finding their relation with magnetic
  field perturbations and in the processes driving their evolution. <BR
  /> Methods: The radiative magnetohydrodynamic code CO5BOLD is used
  to perform realistic numerical simulations of a small portion of the
  solar atmosphere, ranging from the top layers of the convection zone
  to the middle chromosphere. For the analysis, the swirling strength
  criterion and its evolution equation are applied in order to identify
  vortical motions and to study their dynamics. As a new criterion,
  we introduce the magnetic swirling strength, which allows us to
  recognize torsional perturbations in the magnetic field. <BR />
  Results: We find a strong correlation between swirling strength and
  magnetic swirling strength, in particular in intense magnetic flux
  concentrations, which suggests a tight relation between vortical
  motions and torsional magnetic field perturbations. Furthermore,
  we find that swirls propagate upward with the local Alfvén speed as
  unidirectional swirls driven by magnetic tension forces alone. In the
  photosphere and low chromosphere, the rotation of the plasma co-occurs
  with a twist in the upwardly directed magnetic field that is in the
  opposite direction of the plasma flow. All together, these are clear
  characteristics of torsional Alfvén waves. Yet, the Alfvén wave is
  not oscillatory but takes the form of a unidirectional pulse. The
  novelty of the present work is that these Alfvén pulses naturally
  emerge from realistic numerical simulations of the solar atmosphere. We
  also find indications of an imbalance between the hydrodynamic and
  magnetohydrodynamic baroclinic effects being at the origin of the
  swirls. At the base of the chromosphere, we find a mean net upwardly
  directed Poynting flux of 12.8 ± 6.5 kW m<SUP>−2</SUP>, which is
  mainly due to swirling motions. This energy flux is mostly associated
  with large and complex swirling structures, which we interpret as the
  superposition of various small-scale vortices. <BR /> Conclusions:
  We conclude that the ubiquitous swirling events observed in numerical
  simulations are tightly correlated with perturbations of the magnetic
  field. At photospheric and chromospheric levels, they form Alfvén
  pulses that propagate upward and may contribute to chromospheric
  heating. <P />Movie associated to Fig. C.1 is available at <A
  href="https://www.aanda.org/10.1051/0004-6361/202040110/olm">https://www.aanda.org</A>

Title: On the effect of oscillatory phenomena on Stokes inversion
    results
Authors: Keys, P. H.; Steiner, O.; Vigeesh, G.
Bibcode: 2021RSPTA.37900182K
Altcode: 2020arXiv200805539K
  Stokes inversion codes are crucial in returning properties of the solar
  atmosphere, such as temperature and magnetic field strength. However,
  the success of such algorithms to return reliable values can be
  hindered by the presence of oscillatory phenomena within magnetic
  wave guides. Returning accurate parameters is crucial to both
  magnetohydrodynamics (MHD) studies and solar physics in general. Here,
  we employ a simulation featuring propagating MHD waves within a flux
  tube with a known driver and atmospheric parameters. We invert the
  Stokes profiles for the 6301 Å and 6302 Å line pair emergent from
  the simulations using the well-known Stokes Inversions from Response
  functions code to see if the atmospheric parameters can be returned
  for typical spatial resolutions at ground-based observatories. The
  inversions return synthetic spectra comparable to the original input
  spectra, even with asymmetries introduced in the spectra from wave
  propagation in the atmosphere. The output models from the inversions
  match closely to the simulations in temperature, line-of-sight magnetic
  field and line-of-sight velocity within typical formation heights of the
  inverted lines. Deviations from the simulations are seen away from these
  height regions. The inversions results are less accurate during passage
  of the waves within the line formation region. The original wave period
  could be recovered from the atmosphere output by the inversions, with
  empirical mode decomposition performing better than the wavelet approach
  in this task. <P />This article is part of the Theo Murphy meeting issue
  `High-resolution wave dynamics in the lower solar atmosphere'.

Title: Acoustic-gravity wave propagation characteristics in
    three-dimensional radiation hydrodynamic simulations of the solar
    atmosphere
Authors: Fleck, B.; Carlsson, M.; Khomenko, E.; Rempel, M.; Steiner,
   O.; Vigeesh, G.
Bibcode: 2021RSPTA.37900170F
Altcode: 2020arXiv200705847F
  There has been tremendous progress in the degree of realism of
  three-dimensional radiation magneto-hydrodynamic simulations of the
  solar atmosphere in the past decades. Four of the most frequently
  used numerical codes are Bifrost, CO5BOLD, MANCHA3D and MURaM. Here
  we test and compare the wave propagation characteristics in model
  runs from these four codes by measuring the dispersion relation of
  acoustic-gravity waves at various heights. We find considerable
  differences between the various models. The height dependence of
  wave power, in particular of high-frequency waves, varies by up to
  two orders of magnitude between the models, and the phase difference
  spectra of several models show unexpected features, including ±180°
  phase jumps. <P />This article is part of the Theo Murphy meeting issue
  `High-resolution wave dynamics in the lower solar atmosphere'.

Title: On the influence of magnetic topology on the propagation of
    internal gravity waves in the solar atmosphere
Authors: Vigeesh, G.; Roth, M.; Steiner, O.; Fleck, B.
Bibcode: 2021RSPTA.37900177V
Altcode: 2020arXiv201006926V
  The solar surface is a continuous source of internal gravity waves
  (IGWs). IGWs are believed to supply the bulk of the wave energy for
  the lower solar atmosphere, but their existence and role for the energy
  balance of the upper layers is still unclear, largely due to the lack
  of knowledge about the influence of the Sun's magnetic fields on
  their propagation. In this work, we look at naturally excited IGWs
  in realistic models of the solar atmosphere and study the effect
  of different magnetic field topographies on their propagation. We
  carry out radiation-magnetohydrodynamic simulations of a magnetic
  field free and two magnetic models-one with an initial, homogeneous,
  vertical field of 100 G magnetic flux density and one with an initial
  horizontal field of 100 G flux density. The propagation properties
  of IGWs are studied by examining the phase-difference and coherence
  spectra in the k<SUB>h</SUB> - ω diagnostic diagram. We find that IGWs
  in the upper solar atmosphere show upward propagation in the model with
  predominantly horizontal field similar to the model without magnetic
  field. In contrast to that the model with predominantly vertical fields
  show downward propagation. This crucial difference in the propagation
  direction is also revealed in the difference in energy transported by
  waves for heights below 0.8 Mm. Higher up, the propagation properties
  show a peculiar behaviour, which require further study. Our analysis
  suggests that IGWs may play a significant role in the heating of
  the chromospheric layers of the internetwork region where horizontal
  fields are thought to be prevalent. <P />This article is part of the
  Theo Murphy meeting issue `High-resolution wave dynamics in the lower
  solar atmosphere'.

Title: Interaction of Magnetic Fields with a Vortex Tube at Solar
    Subgranular Scale
Authors: Fischer, C. E.; Vigeesh, G.; Lindner, P.; Borrero, J. M.;
   Calvo, F.; Steiner, O.
Bibcode: 2020ApJ...903L..10F
Altcode: 2020arXiv201005577F
  Using high-resolution spectropolarimetric data recorded with the
  Swedish 1 m Solar Telescope, we have identified several instances of
  granular lanes traveling into granules. These are believed to be the
  observational signature of underlying tubes of vortical flow with
  their axis oriented parallel to the solar surface. Associated with
  these horizontal vortex tubes, we detect in some cases a significant
  signal in linear polarization, located at the trailing dark edge of
  the granular lane. The linear polarization appears at a later stage of
  the granular lane development, and is flanked by patches of circular
  polarization. Stokes inversions show that the elongated patch of linear
  polarization signal arises from the horizontal magnetic field aligned
  with the granular lane. We analyze snapshots of a magnetohydrodynamic
  numerical simulation and find cases in which the horizontal vortex
  tube of the granular lane redistributes and transports the magnetic
  field to the solar surface causing a polarimetric signature similar to
  what is observed. We thus witness a mechanism capable of transporting
  magnetic flux to the solar surface within granules. This mechanism is
  probably an important component of the small-scale dynamo supposedly
  acting at the solar surface and generating the quiet-Sun magnetic field.

Title: Vortices evolution in the solar atmosphere. A dynamical
    equation for the swirling strength
Authors: Canivete Cuissa, José R.; Steiner, Oskar
Bibcode: 2020A&A...639A.118C
Altcode: 2020arXiv200512871C
  <BR /> Aims: We study vortex dynamics in the solar atmosphere by
  employing and deriving the analytical evolution equations of two
  vortex identification criteria. <BR /> Methods: The two criteria used
  are vorticity and the swirling strength. Vorticity can be biased
  in the presence of shear flows, but its dynamical equation is well
  known; the swirling strength is a more precise criterion for the
  identification of vortical flows, but its evolution equation is not
  known yet. Therefore, we explore the possibility of deriving a dynamical
  equation for the swirling strength. We then apply the two equations
  to analyze radiative magneto-hydrodynamical simulations of the solar
  atmosphere produced with the CO<SUP>5</SUP>BOLD code. <BR /> Results:
  We present a detailed review of the swirling strength criterion and
  the mathematical derivation of its evolution equation. This equation
  did not exist in the literature before and it constitutes a novel
  tool that is suitable for the analysis of a wide range of problems in
  (magneto-)hydrodynamics. By applying this equation to numerical models,
  we find that hydrodynamical and magnetic baroclinicities are the
  driving physical processes responsible for vortex generation in the
  convection zone and the photosphere. Higher up in the chromosphere,
  the magnetic terms alone dominate. Moreover, we find that the
  swirling strength is produced at small scales in a chaotic fashion,
  especially inside magnetic flux concentrations. <BR /> Conclusions:
  The swirling strength represents an appropriate criterion for the
  identification of vortices in turbulent flows, such as those in the
  solar atmosphere. Moreover, its evolution equation, which is derived
  in this paper, is pivotal for obtaining precise information about the
  dynamics of these vortices and the physical mechanisms responsible
  for their production and evolution. Since this equation is available,
  the swirling strength is now the ideal quantity to study the dynamics
  of vortices in (magneto-)hydrodynamics.

Title: Numerical Methods for the Radiative Transfer Equation of
    Polarized Light
Authors: Janett, G.; Steiner, O.; Belluzzi, L.
Bibcode: 2019ASPC..526..133J
Altcode:
  The quest of the "best formal solver" available is still open and the
  lack of a clear comparison between the different numerical methods
  proposed by the community does not facilitate a conclusion. This work
  presents a reference paradigm for the characterization of formal
  solvers, based on the concepts of order of accuracy, stability and
  computational cost. This overview aims to facilitate the comprehension
  of the advantages and weaknesses of the already existing formal solvers
  and of those yet to come.

Title: A novel fourth-order WENO interpolation technique. A possible
    new tool designed for radiative transfer
Authors: Janett, Gioele; Steiner, Oskar; Alsina Ballester, Ernest;
   Belluzzi, Luca; Mishra, Siddhartha
Bibcode: 2019A&A...624A.104J
Altcode:
  Context. Several numerical problems require the interpolation of
  discrete data that present at the same time (i) complex smooth
  structures and (ii) various types of discontinuities. The radiative
  transfer in solar and stellar atmospheres is a typical example of such
  a problem. This calls for high-order well-behaved techniques that are
  able to interpolate both smooth and discontinuous data. <BR /> Aims:
  This article expands on different nonlinear interpolation techniques
  capable of guaranteeing high-order accuracy and handling discontinuities
  in an accurate and non-oscillatory fashion. The final aim is to propose
  new techniques which could be suitable for applications in the context
  of numerical radiative transfer. <BR /> Methods: We have proposed
  and tested two different techniques. Essentially non-oscillatory
  (ENO) techniques generate several candidate interpolations based
  on different substencils. The smoothest candidate interpolation is
  determined from a measure for the local smoothness, thereby enabling the
  essentially non-oscillatory property. Weighted ENO (WENO) techniques
  use a convex combination of all candidate substencils to obtain
  high-order accuracy in smooth regions while keeping the essentially
  non-oscillatory property. In particular, we have outlined and tested a
  novel well-performing fourth-order WENO interpolation technique for both
  uniform and nonuniform grids. <BR /> Results: Numerical tests prove that
  the fourth-order WENO interpolation guarantees fourth-order accuracy
  in smooth regions of the interpolated functions. In the presence
  of discontinuities, the fourth-order WENO interpolation enables the
  non-oscillatory property, avoiding oscillations. Unlike Bézier and
  monotonic high-order Hermite interpolations, it does not degenerate
  to a linear interpolation near smooth extrema of the interpolated
  function. Conclusion. The novel fourth-order WENO interpolation
  guarantees high accuracy in smooth regions, while effectively handling
  discontinuities. This interpolation technique might be particularly
  suitable for several problems, including a number of radiative transfer
  applications such as multidimensional problems, multigrid methods,
  and formal solutions.

Title: Internal Gravity Waves in the Magnetized Solar
    Atmosphere. II. Energy Transport
Authors: Vigeesh, G.; Roth, M.; Steiner, O.; Jackiewicz, J.
Bibcode: 2019ApJ...872..166V
Altcode: 2019arXiv190108871V
  In this second paper of the series on internal gravity waves (IGWs),
  we present a study of the generation and propagation of IGWs in a
  model solar atmosphere with diverse magnetic conditions. A magnetic
  field-free and three magnetic models that start with an initial,
  vertical, homogeneous field of 10, 50, and 100 G magnetic flux density,
  are simulated using the CO<SUP>5</SUP>BOLD code. We find that the
  IGWs are generated in similar manner in all four models in spite of
  the differences in the magnetic environment. The mechanical energy
  carried by IGWs is significantly larger than that of the acoustic
  waves in the lower part of the atmosphere, making them an important
  component of the total wave energy budget. The mechanical energy flux
  (10<SUP>6</SUP>-10<SUP>3</SUP> W m<SUP>-2</SUP>) is a few orders of
  magnitude larger than the Poynting flux (10<SUP>3</SUP>-10<SUP>1</SUP>
  W m<SUP>-2</SUP>). The Poynting fluxes show a downward component in
  the frequency range corresponding to the IGWs, which confirm that
  these waves do not propagate upward in the atmosphere when the fields
  are predominantly vertical and strong. We conclude that, in the upper
  photosphere, the propagation properties of IGWs depend on the average
  magnetic field strength and therefore these waves can be potential
  candidates for magnetic field diagnostics of these layers. However,
  their subsequent coupling to Alfvénic waves is unlikely in a magnetic
  environment permeated with predominantly vertical fields, and therefore
  they may not directly or indirectly contribute to the heating of layers
  above plasma-β less than 1.

Title: Formal Solutions for Polarized Radiative
    Transfer. IV. Numerical Performances in Practical Problems
Authors: Janett, Gioele; Steiner, Oskar; Belluzzi, Luca
Bibcode: 2018ApJ...865...16J
Altcode: 2018arXiv180906604J
  The numerical computation of reliable and accurate Stokes profiles
  is of great relevance in solar physics. In the synthesis process,
  many actors play a relevant role: among them the formal solver, the
  discrete atmospheric model, and the spectral line. This paper tests
  the performances of different numerical schemes in the synthesis
  of polarized spectra for different spectral lines and atmospheric
  models. The hierarchy between formal solvers is enforced, stressing the
  peculiarities of high-order and low-order formal solvers. The density
  of grid points necessary for reaching a given accuracy requirement is
  quantitatively described for specific situations.

Title: Structure of the Balmer jump. The isolated hydrogen atom
Authors: Calvo, F.; Belluzzi, L.; Steiner, O.
Bibcode: 2018A&A...613A..55C
Altcode: 2019arXiv190110241C
  Context. The spectrum of the hydrogen atom was explained by Bohr
  more than one century ago. We revisit here some of the aspects of the
  underlying quantum structure, with a modern formalism, focusing on the
  limit of the Balmer series. <BR /> Aims: We investigate the behaviour
  of the absorption coefficient of the isolated hydrogen atom in the
  neighbourhood of the Balmer limit. <BR /> Methods: We analytically
  computed the total cross-section arising from bound-bound and bound-free
  transitions in the isolated hydrogen atom at the Balmer limit, and
  established a simplified semi-analytical model for the surroundings of
  that limit. We worked within the framework of the formalism of Landi
  Degl'Innocenti &amp; Landolfi (2004, Astrophys. Space Sci. Lib.,
  307), which permits an almost straight-forward generalization of
  our results to other atoms and molecules, and which is perfectly
  suitable for including polarization phenomena in the problem. <BR />
  Results: We analytically show that there is no discontinuity at the
  Balmer limit, even though the concept of a "Balmer jump" is still
  meaningful. Furthermore, we give a possible definition of the location
  of the Balmer jump, and we check that this location is dependent
  on the broadening mechanisms. At the Balmer limit, we compute the
  cross-section in a fully analytical way. <BR /> Conclusions: The Balmer
  jump is produced by a rapid drop of the total Balmer cross-section,
  yet this variation is smooth and continuous when both bound-bound and
  bound-free processes are taken into account, and its shape and location
  is dependent on the broadening mechanisms.

Title: Simulation of the small-scale magnetism in main-sequence
    stellar atmospheres
Authors: Salhab, R. G.; Steiner, O.; Berdyugina, S. V.; Freytag, B.;
   Rajaguru, S. P.; Steffen, M.
Bibcode: 2018A&A...614A..78S
Altcode:
  Context. Observations of the Sun tell us that its granular and
  subgranular small-scale magnetism has significant consequences for
  global quantities such as the total solar irradiance or convective
  blueshift of spectral lines. <BR /> Aims: In this paper, properties
  of the small-scale magnetism of four cool stellar atmospheres,
  including the Sun, are investigated, and in particular its effects
  on the radiative intensity and flux. <BR /> Methods: We carried out
  three-dimensional radiation magnetohydrodynamic simulations with the
  CO<SUP>5</SUP>BOLD code in two different settings: with and without
  a magnetic field. These are thought to represent states of high and
  low small-scale magnetic activity of a stellar magnetic cycle. <BR
  /> Results: We find that the presence of small-scale magnetism
  increases the bolometric intensity and flux in all investigated
  models. The surplus in radiative flux of the magnetic over the magnetic
  field-free atmosphere increases with increasing effective temperature,
  T<SUB>eff</SUB>, from 0.47% for spectral type K8V to 1.05% for the solar
  model, but decreases for higher effective temperatures than solar. The
  degree of evacuation of the magnetic flux concentrations monotonically
  increases with T<SUB>eff</SUB> as does their depression of the visible
  optical surface, that is the Wilson depression. Nevertheless, the
  strength of the field concentrations on this surface stays remarkably
  unchanged at ≈1560 G throughout the considered range of spectral
  types. With respect to the surrounding gas pressure, the field strength
  is close to (thermal) equipartition for the Sun and spectral type F5V
  but is clearly sub-equipartition for K2V and more so for K8V. The
  magnetic flux concentrations appear most conspicuous for model K2V
  owing to their high brightness contrast. <BR /> Conclusions: For mean
  magnetic flux densities of approximately 50 G, we expect the small-scale
  magnetism of stars in the spectral range from F5V to K8V to produce a
  positive contribution to their bolometric luminosity. The modulation
  seems to be most effective for early G-type stars.

Title: Formal Solutions for Polarized Radiative
    Transfer. II. High-order Methods
Authors: Janett, Gioele; Steiner, Oskar; Belluzzi, Luca
Bibcode: 2017ApJ...845..104J
Altcode: 2017arXiv170901280J
  When integrating the radiative transfer equation for polarized light,
  the necessity of high-order numerical methods is well known. In fact,
  well-performing high-order formal solvers enable higher accuracy and
  the use of coarser spatial grids. Aiming to provide a clear comparison
  between formal solvers, this work presents different high-order
  numerical schemes and applies the systematic analysis proposed by
  Janett et al., emphasizing their advantages and drawbacks in terms of
  order of accuracy, stability, and computational cost.

Title: On the effect of vorticity on the propagation of internal
    gravity waves.
Authors: Vigeesh, G.; Steiner, O.; Calvo, F.; Roth, M.
Bibcode: 2017MmSAI..88...54V
Altcode:
  We compare different models of solar surface convection to study
  vorticity and how it can influence the propagation of internal
  gravity waves. We conclude that simulations performed with higher grid
  resolution may have a reduced gravity wave flux in the lower part of
  the atmosphere due to strong vorticity. We also show that the vertical
  extent of the allowed region of propagation depends on the magnetic
  field inclination.

Title: Formal Solutions for Polarized Radiative Transfer. I. The
    DELO Family
Authors: Janett, Gioele; Carlin, Edgar S.; Steiner, Oskar; Belluzzi,
   Luca
Bibcode: 2017ApJ...840..107J
Altcode: 2017arXiv170901274J
  The discussion regarding the numerical integration of the polarized
  radiative transfer equation is still open and the comparison between
  the different numerical schemes proposed by different authors in the
  past is not fully clear. Aiming at facilitating the comprehension of
  the advantages and drawbacks of the different formal solvers, this
  work presents a reference paradigm for their characterization based
  on the concepts of order of accuracy, stability, and computational
  cost. Special attention is paid to understand the numerical methods
  belonging to the Diagonal Element Lambda Operator family, in an attempt
  to highlight their specificities.

Title: High-frequency Oscillations in Small Magnetic Elements Observed
    with Sunrise/SuFI
Authors: Jafarzadeh, S.; Solanki, S. K.; Stangalini, M.; Steiner,
   O.; Cameron, R. H.; Danilovic, S.
Bibcode: 2017ApJS..229...10J
Altcode: 2016arXiv161109302J
  We characterize waves in small magnetic elements and investigate
  their propagation in the lower solar atmosphere from observations at
  high spatial and temporal resolution. We use the wavelet transform to
  analyze oscillations of both horizontal displacement and intensity
  in magnetic bright points found in the 300 nm and the Ca II H 396.8
  nm passbands of the filter imager on board the Sunrise balloon-borne
  solar observatory. Phase differences between the oscillations at the
  two atmospheric layers corresponding to the two passbands reveal
  upward propagating waves at high frequencies (up to 30 mHz). Weak
  signatures of standing as well as downward propagating waves are also
  obtained. Both compressible and incompressible (kink) waves are found
  in the small-scale magnetic features. The two types of waves have
  different, though overlapping, period distributions. Two independent
  estimates give a height difference of approximately 450 ± 100 km
  between the two atmospheric layers sampled by the employed spectral
  bands. This value, together with the determined short travel times of
  the transverse and longitudinal waves provide us with phase speeds of 29
  ± 2 km s<SUP>-1</SUP> and 31 ± 2 km s<SUP>-1</SUP>, respectively. We
  speculate that these phase speeds may not reflect the true propagation
  speeds of the waves. Thus, effects such as the refraction of fast
  longitudinal waves may contribute to an overestimate of the phase speed.

Title: Internal Gravity Waves in the Magnetized Solar
    Atmosphere. I. Magnetic Field Effects
Authors: Vigeesh, G.; Jackiewicz, J.; Steiner, O.
Bibcode: 2017ApJ...835..148V
Altcode: 2016arXiv161204729V
  Observations of the solar atmosphere show that internal gravity
  waves are generated by overshooting convection, but are suppressed
  at locations of magnetic flux, which is thought to be the result of
  mode conversion into magnetoacoustic waves. Here, we present a study
  of the acoustic-gravity wave spectrum emerging from a realistic,
  self-consistent simulation of solar (magneto)convection. A magnetic
  field free, hydrodynamic simulation and a magnetohydrodynamic (MHD)
  simulation with an initial, vertical, homogeneous field of 50 G flux
  density were carried out and compared with each other to highlight the
  effect of magnetic fields on the internal gravity wave propagation
  in the Sun’s atmosphere. We find that the internal gravity waves
  are absent or partially reflected back into the lower layers in the
  presence of magnetic fields and argue that the suppression is due to
  the coupling of internal gravity waves to slow magnetoacoustic waves
  still within the high-β region of the upper photosphere. The conversion
  to Alfvén waves is highly unlikely in our model because there is no
  strongly inclined magnetic field present. We argue that the suppression
  of internal waves observed within magnetic flux concentrations may also
  be due to nonlinear breaking of internal waves due to vortex flows that
  are ubiquitously present in the upper photosphere and the chromosphere.

Title: CO5BOLD for MHD: progresses and deficiencies .
Authors: Steiner, O.; Calvo, F.; Salhab, R.; Vigeesh, G.
Bibcode: 2017MmSAI..88...37S
Altcode:
  The magnetohydrodynamics module of CO5BOLD has been steadily improved
  over the past decade and has been used for various solar and stellar
  physical applications. We give an overview of current work with it
  and of remaining and newly emerged shortcomings.

Title: Sub-photosphere to Solar Atmosphere Connection
Authors: Komm, Rudolf; De Moortel, Ineke; Fan, Yuhong; Ilonidis,
   Stathis; Steiner, Oskar
Bibcode: 2017hdsi.book..173K
Altcode:
  No abstract at ADS

Title: Non-magnetic photospheric bright points in 3D simulations of
    the solar atmosphere
Authors: Calvo, F.; Steiner, O.; Freytag, B.
Bibcode: 2016A&A...596A..43C
Altcode: 2016arXiv161204278C
  Context. Small-scale bright features in the photosphere of the Sun,
  such as faculae or G-band bright points, appear in connection with
  small-scale magnetic flux concentrations. <BR /> Aims: Here we report
  on a new class of photospheric bright points that are free of magnetic
  fields. So far, these are visible in numerical simulations only. We
  explore conditions required for their observational detection. <BR />
  Methods: Numerical radiation (magneto-)hydrodynamic simulations of the
  near-surface layers of the Sun were carried out. The magnetic field-free
  simulations show tiny bright points, reminiscent of magnetic bright
  points, only smaller. A simple toy model for these non-magnetic bright
  points (nMBPs) was established that serves as a base for the development
  of an algorithm for their automatic detection. Basic physical properties
  of 357 detected nMBPs were extracted and statistically evaluated. We
  produced synthetic intensity maps that mimic observations with various
  solar telescopes to obtain hints on their detectability. <BR /> Results:
  The nMBPs of the simulations show a mean bolometric intensity contrast
  with respect to their intergranular surroundings of approximately 20%, a
  size of 60-80 km, and the isosurface of optical depth unity is at their
  location depressed by 80-100 km. They are caused by swirling downdrafts
  that provide, by means of the centripetal force, the necessary pressure
  gradient for the formation of a funnel of reduced mass density that
  reaches from the subsurface layers into the photosphere. Similar,
  frequently occurring funnels that do not reach into the photosphere,
  do not produce bright points. <BR /> Conclusions: Non-magnetic bright
  points are the observable manifestation of vertically extending vortices
  (vortex tubes) in the photosphere. The resolving power of 4-m-class
  telescopes, such as the DKIST, is needed for an unambiguous detection
  of them. <P />The movie associated to Fig. 1 is available at <A
  href="http://www.aanda.org/10.1051/0004-6361/201628649/olm">http://www.aanda.org</A>

Title: Chromospheric and Coronal Wave Generation in a Magnetic
    Flux Sheath
Authors: Kato, Yoshiaki; Steiner, Oskar; Hansteen, Viggo; Gudiksen,
   Boris; Wedemeyer, Sven; Carlsson, Mats
Bibcode: 2016ApJ...827....7K
Altcode: 2016arXiv160608826K
  Using radiation magnetohydrodynamic simulations of the solar
  atmospheric layers from the upper convection zone to the lower corona,
  we investigate the self-consistent excitation of slow magneto-acoustic
  body waves (slow modes) in a magnetic flux concentration. We
  find that the convective downdrafts in the close surroundings of
  a two-dimensional flux slab “pump” the plasma inside it in
  the downward direction. This action produces a downflow inside the
  flux slab, which encompasses ever higher layers, causing an upwardly
  propagating rarefaction wave. The slow mode, excited by the adiabatic
  compression of the downflow near the optical surface, travels along the
  magnetic field in the upward direction at the tube speed. It develops
  into a shock wave at chromospheric heights, where it dissipates,
  lifts the transition region, and produces an offspring in the form
  of a compressive wave that propagates further into the corona. In the
  wake of downflows and propagating shock waves, the atmosphere inside
  the flux slab in the chromosphere and higher tends to oscillate with a
  period of ν ≈ 4 mHz. We conclude that this process of “magnetic
  pumping” is a most plausible mechanism for the direct generation
  of longitudinal chromospheric and coronal compressive waves within
  magnetic flux concentrations, and it may provide an important heat
  source in the chromosphere. It may also be responsible for certain
  types of dynamic fibrils.

Title: Polarized radiative transfer in discontinuous media
Authors: Steiner, O.; Züger, F.; Belluzzi, L.
Bibcode: 2016A&A...586A..42S
Altcode:
  Context. Observations of the solar atmosphere of ever increasing
  spatial resolution reveal steep gradients in the magnetic field
  and in thermal states. Likewise, numerical simulations of the solar
  atmosphere show contact discontinuities and shock fronts. This asks
  for the development of robust methods for computing the radiative
  transfer of polarized light in discontinuous media. <BR /> Aims:
  Here, we propose a new concept for dealing with discontinuities in
  the radiative transfer of polarized light and carry out a few basic
  test calculations. While in the past, the focus was on interpolating
  the source function with ever-increasing accuracy and smoothness,
  we propose to take the opposite approach by reconstructing it with
  piecewise continuous functions, taking discontinuities on purpose into
  account. This concept is known from computational fluid dynamics. <BR />
  Methods: Test calculations were carried out for (I) a Milne-Eddington
  atmosphere; (II) an atmosphere featuring a single discontinuity that
  is shifted across one grid cell; and (III) a two-layered atmosphere
  with discontinuities in the source function, the velocity, and the
  magnetic field. <BR /> Results: It is shown that the method of piecewise
  continuous reconstruction is a viable approach to solving the radiative
  transfer equation for polarized light. In the special case where a
  discontinuity coincides with a computational cell interface, the method
  is capable of producing the exact solution. Overall, the assessment
  of the piecewise continuous reconstruction method turns out to be
  cautiously positive, but it does not lead to an order-of-magnitude
  improvement in accuracy over conventional methods for the examples
  considered here. More realistic model atmospheres need to be considered
  for judging practical applicability.

Title: Sub-photosphere to Solar Atmosphere Connection
Authors: Komm, Rudolf; De Moortel, Ineke; Fan, Yuhong; Ilonidis,
   Stathis; Steiner, Oskar
Bibcode: 2015SSRv..196..167K
Altcode: 2013SSRv..tmp...93K
  Magnetic fields extend from the solar interior through the
  atmosphere. The formation and evolution of active regions can be studied
  by measuring subsurface flows with local helioseismology. The emergence
  of magnetic flux from the solar convection zone is associated with
  acoustic perturbation signatures. In near-surface layers, the average
  dynamics can be determined for emerging regions. MHD simulations
  of the emergence of a twisted flux tube show how magnetic twist
  and free energy are transported from the interior into the corona
  and the dynamic signatures associated with such transport in the
  photospheric and sub-photospheric layers. The subsurface twisted flux
  tube does not emerge into the corona as a whole in emerging active
  regions. Shear flows at the polarity inversion line and coherent
  vortical motions in the subsurface flux tubes are the major means by
  which twist is transported into the corona, leading to the formation
  of sigmoid-shaped coronal magnetic fields capable of driving solar
  eruptions. The transport of twist can be followed from the interior
  by using the kinetic helicity of subsurface flows as a proxy of
  magnetic helicity; this quantity holds great promise for improving
  the understanding of eruptive phenomena. Waves are not only vital for
  studying the link between the solar interior and the surface but for
  linking the photosphere with the corona as well. Acoustic waves that
  propagate from the surface into the magnetically structured, dynamic
  atmosphere undergo mode conversion and refraction. These effects
  enable atmospheric seismology to determine the topography of magnetic
  canopies in the solar atmosphere. Inclined magnetic fields lower
  the cut-off frequency so that low frequency waves can leak into the
  outer atmosphere. Recent high resolution, high cadence observations of
  waves and oscillations in the solar atmosphere, have lead to a renewed
  interest in the potential role of waves as a heating mechanism. In light
  of their potential contribution to the heating of the solar atmosphere,
  some of the recent observations of waves and oscillations and ongoing
  modelling efforts are reviewed.

Title: On the Evolution of Magnetic White Dwarfs
Authors: Tremblay, P. -E.; Fontaine, G.; Freytag, B.; Steiner, O.;
   Ludwig, H. -G.; Steffen, M.; Wedemeyer, S.; Brassard, P.
Bibcode: 2015ApJ...812...19T
Altcode: 2015arXiv150905398T
  We present the first radiation magnetohydrodynamic simulations of the
  atmosphere of white dwarf stars. We demonstrate that convective energy
  transfer is seriously impeded by magnetic fields when the plasma-β
  parameter, the thermal-to-magnetic-pressure ratio, becomes smaller
  than unity. The critical field strength that inhibits convection
  in the photosphere of white dwarfs is in the range B = 1-50 kG,
  which is much smaller than the typical 1-1000 MG field strengths
  observed in magnetic white dwarfs, implying that these objects have
  radiative atmospheres. We have employed evolutionary models to study the
  cooling process of high-field magnetic white dwarfs, where convection
  is entirely suppressed during the full evolution (B ≳ 10 MG). We
  find that the inhibition of convection has no effect on cooling rates
  until the effective temperature (T<SUB>eff</SUB>) reaches a value of
  around 5500 K. In this regime, the standard convective sequences start
  to deviate from the ones without convection due to the convective
  coupling between the outer layers and the degenerate reservoir of
  thermal energy. Since no magnetic white dwarfs are currently known
  at the low temperatures where this coupling significantly changes the
  evolution, the effects of magnetism on cooling rates are not expected
  to be observed. This result contrasts with a recent suggestion
  that magnetic white dwarfs with T<SUB>eff</SUB> ≲ 10,000 K cool
  significantly slower than non-magnetic degenerates.

Title: The statistical properties of vortex flows in the solar
    atmosphere
Authors: Wedemeyer, Sven; Kato, Yoshiaki; Steiner, Oskar
Bibcode: 2015IAUGA..2256852W
Altcode:
  Rotating magnetic field structures associated with vortex flows
  on the Sun, also known as “magnetic tornadoes”, may serve
  as waveguides for MHD waves and transport mass and energy upwards
  through the atmosphere. Magnetic tornadoes may therefore potentially
  contribute to the heating of the upper atmospheric layers in quiet
  Sun regions.Magnetic tornadoes are observed over a large range
  of spatial and temporal scales in different layers in quiet Sun
  regions. However, their statistical properties such as size, lifetime,
  and rotation speed are not well understood yet because observations
  of these small-scale events are technically challenging and limited
  by the spatial and temporal resolution of current instruments. Better
  statistics based on a combination of high-resolution observations and
  state-of-the-art numerical simulations is the key to a reliable estimate
  of the energy input in the lower layers and of the energy deposition
  in the upper layers. For this purpose, we have developed a fast and
  reliable tool for the determination and visualization of the flow
  field in (observed) image sequences. This technique, which combines
  local correlation tracking (LCT) and line integral convolution (LIC),
  facilitates the detection and study of dynamic events on small scales,
  such as propagating waves. Here, we present statistical properties
  of vortex flows in different layers of the solar atmosphere and try
  to give realistic estimates of the energy flux which is potentially
  available for heating of the upper solar atmosphere

Title: Properties of small-scale magnetism of stellar atmospheres
Authors: Steiner, Oskar; Salhab, René; Freytag, Bernd; Rajaguru,
   Paul; Schaffenberger, Werner; Steffen, Matthias
Bibcode: 2014PASJ...66S...5S
Altcode: 2014PASJ..tmp...95S
  The magnetic field outside of sunspots is concentrated in the
  intergranular space, where it forms a delicate filigree of bright
  ribbons and dots as seen on broad band images of the Sun. We expect this
  small-scale magnetic field to exhibit a similar behavior in stellar
  atmospheres. In order to find out more about it, we perform numerical
  simulations of the surface layers of stellar atmospheres. Here, we
  report on preliminary results from simulations in the range between
  4000 K and 6500 K effective temperature with an initial vertical,
  homogeneous magnetic field of 50 G strength. We find that the field
  strength of the strongest magnetic flux concentrations increases with
  decreasing effective temperature at the height level where the average
  Rosseland optical depth is one. On the other hand, at the same level,
  the field is less strong than the thermal equipartition value in the
  coolest model but assumes superequipartition in the models hotter
  than 5000 K. While the Wilson depression of the strongest field
  concentrations is about one pressure scale height in the coolest
  model, it is more than four times the pressure scale height in the
  hottest one. We also find that the relative contribution of the bright
  filigree to the bolometric, vertically directed radiative intensity is
  most significant for the T<SUB>eff</SUB> = 5000 K model (0.6%-0.79%)
  and least significant for the hottest and coolest models (0.1%-0.46%
  and 0.14%-0.32%, respectively). This behavior suggests that the effect
  of the small-scale magnetic field on the photometric variability is more
  significant for K dwarf stars than for F-type and also M-type stars.

Title: On the plasma flow inside magnetic tornadoes on the Sun
Authors: Wedemeyer, Sven; Steiner, Oskar
Bibcode: 2014PASJ...66S..10W
Altcode: 2014PASJ..tmp...98W; 2014arXiv1406.7270W
  High-resolution observations with the Swedish 1-m Solar Telescope (SST)
  and the Solar Dynamics Observatory (SDO) reveal rotating magnetic field
  structures that extend from the solar surface into the chromosphere
  and the corona. These so-called magnetic tornadoes are primarily
  detected as rings or spirals of rotating plasma in the Ca II 854.2 nm
  line core (also known as chromospheric swirls). Detailed numerical
  simulations show that the observed chromospheric plasma motion is
  caused by the rotation of magnetic field structures, which again
  are driven by photospheric vortex flows at their footpoints. Under
  the right conditions, two vortex flow systems are stacked on top of
  each other. We refer to the lower vortex, which extends from the low
  photosphere into the convection zone, as intergranular vortex flow
  (IVF). Once a magnetic field structure is co-located with an IVF,
  the rotation is mediated into the upper atmospheric layers and an
  atmospheric vortex flow (AVF, or magnetic tornado) is generated. In
  contrast to the recent work by Shelyag et al. (2013, ApJ, 776, L4),
  we demonstrate that particle trajectories in a simulated magnetic
  tornado indeed follow spirals and argue that the properties of the
  trajectories decisively depend on the location in the atmosphere and
  the strength of the magnetic field.

Title: Magnetic tornadoes and chromospheric swirls - Definition
    and classification
Authors: Wedemeyer, Sven; Scullion, Eamon; Steiner, Oskar; de la Cruz
   Rodriguez, Jaime; Rouppe van der Voort, L. H. M.
Bibcode: 2013JPhCS.440a2005W
Altcode: 2013arXiv1303.0179W
  Chromospheric swirls are the observational signatures of rotating
  magnetic field structures in the solar atmosphere, also known as
  magnetic tornadoes. Swirls appear as dark rotating features in the core
  of the spectral line of singly ionized calcium at a wavelength of 854.2
  nm. This signature can be very subtle and difficult to detect given
  the dynamic changes in the solar chromosphere. Important steps towards
  a systematic and objective detection method are the compilation and
  characterization of a statistically significant sample of observed
  and simulated chromospheric swirls. Here, we provide a more exact
  definition of the chromospheric swirl phenomenon and also present a
  first morphological classification of swirls with three types: (I) Ring,
  (II) Split, (III) Spiral. We also discuss the nature of the magnetic
  field structures connected to tornadoes and the influence of limited
  spatial resolution on the appearance of their photospheric footpoints.

Title: On the Effects of the SDO Orbital Motion on the HMI Vector
    Magnetic Field Measurements
Authors: Fleck, B.; Centeno, R.; Cheung, M.; Couvidat, S.; Hayashi,
   K.; Rezaei, R.; Steiner, O.; Straus, T.
Bibcode: 2013enss.confE.145F
Altcode:
  In a previous study we have investigated the magnetic field diagnostics
  potential of SDO/HMI. We have used the output of high-resolution
  3D, time-dependent, radiative magneto-hydrodynamics simulations to
  calculate Stokes profiles for the Fe I 6173 Å line. From these we
  constructed Stokes filtergrams using a representative set of HMI filter
  response functions. The magnetic field vector (x,y) and line-of-sight
  Doppler velocities V(x,y) were determined from these filtergrams using
  a simplified version of the HMI magnetic field processing pipeline,
  and the reconstructed magnetic field (x,y) and line-of-sight velocity
  V(x,y) were compared to the actual magnetic field (x,y,z) and vertical
  velocity V0(x,y,z) in the simulations. The present investigation expands
  this analysis to include the effects of the significant orbital motions
  of SDO, which, given the limited wavelength range of the HMI filter
  profiles, affects the outer wing measurements and therefore might impact
  the magnetic field measurements. We find that the effects of the orbital
  movement of SDO are noticeable, in particular for the strongest fields
  (B &gt; 3 kG) and the maximum wavelength shift of 5.5 km/s (3.5 km/s
  orbital movement + 2 km/s solar rotation). Saturation effects for strong
  fields (B &gt; 3 kG) are already visible for wavelength shifts of 3.2
  km/s (orbital movement, disk center). The measurements of inclination
  and vertical velocity are more robust. Compared to other factors of
  uncertainty in the inversion of HMI Stokes measurements the orbital
  movement is not a major concern or source of error.

Title: Three-dimensional magnetohydrodynamic simulations of M-dwarf
    chromospheres
Authors: Wedemeyer, S.; Ludwig, H. -G.; Steiner, O.
Bibcode: 2013AN....334..137W
Altcode: 2013csss...17..137W; 2012arXiv1207.2342W
  We present first results from three-dimensional radiation
  magnetohydrodynamic simulations of M-type dwarf stars with
  CO<SUP>5</SUP>BOLD. The local models include the top of the convection
  zone, the photosphere, and the chromosphere. The results are illustrated
  for models with an effective temperature of 3240 K and a gravitational
  acceleration of {log g = 4.5}, which represent analogues of AD Leo. The
  models have different initial magnetic field strengths and field
  topologies. This first generation of models demonstrates that the
  atmospheres of M dwarfs are highly dynamic and intermittent. Magnetic
  fields and propagating shock waves produce a complicated fine-structure,
  which is clearly visible in synthetic intensity maps in the core of the
  Ca II K spectral line and also at millimeter wavelengths. The dynamic
  small-scale pattern cannot be described by means of one-dimensional
  models, which has important implications for the construction of
  semi-empirical model atmospheres and thus for the interpretation
  of observations in general. Detailed three-dimensional numerical
  simulations are valuable in this respect. Furthermore, such models
  facilitate the analysis of small-scale processes, which cannot be
  observed on stars but nevertheless might be essential for understanding
  M-dwarf atmospheres and their activity. An example are so-called
  ``magnetic tornadoes'', which have recently been found on the Sun and
  are presented here in M-dwarf models for the first time.

Title: First steps with CO5BOLD using HLLMHD and PP reconstruction .
Authors: Steiner, O.; Rajaguru, S. P.; Vigeesh, G.; Steffen, M.;
   Schaffenberger, W.; Freytag, B.
Bibcode: 2013MSAIS..24..100S
Altcode:
  We report on first experiences with real-life applications using
  the MHD-module of CO5BOLD together with the piecewise parabolic
  reconstruction scheme and present preliminary results of stellar
  magnetic models with T<SUB>eff</SUB> = 4000 K to T<SUB>eff</SUB> =
  5770 K.

Title: The science challenges for large solar telescopes
Authors: Steiner, O.
Bibcode: 2012IAUSS...6E.101S
Altcode:
  Looking at numerical simulations of highest spatial resolution
  and highest resolution observations, we endeavor extrapolating
  what science questions can be tackled with future large solar
  telescopes. By means of selected examples we shall try to determine the
  instrumental requirements for answering these questions. For example,
  what polarimetric accuracy do we need to make progress regarding the
  topography of the internetwork magnetic field? What spatial and temporal
  resolution is needed to track the driving forces of dynamic fibrils,
  spicules and other jet-like features of the solar chromosphere, what to
  asses the role of vortical flows in the photosphere and its impact on
  the chromosphere and corona, or what to shed light on the turbulent
  dynamo supposedly working in the surface layers of the convection
  zone. Will large solar telescopes help us resolving the remaining
  puzzles of the sunspot penumbra and the still largely enigmatic
  formation process of sunspots? Besides such foreseeable science
  questions however, we should be aware that the best discoveries come
  unexpectedly and therefore, it may be worthwhile to wonder about what
  instrumental capabilities may be best conducive to the unexpected.

Title: Revealing the nature of magnetic shadows with numerical
    3D-MHD simulations
Authors: Nutto, C.; Steiner, O.; Roth, M.
Bibcode: 2012A&A...542L..30N
Altcode: 2012arXiv1205.5308N
  <BR /> Aims: We investigate the interaction of magneto-acoustic waves
  with magnetic network elements with the aim of finding possible
  signatures of the magnetic shadow phenomenon in the vicinity of
  network elements. <BR /> Methods: We carried out three-dimensional
  numerical simulations of magneto-acoustic wave propagation in a model
  solar atmosphere that is threaded by a complexly structured magnetic
  field, resembling that of a typical magnetic network element and of
  internetwork regions. High-frequency waves of 10 mHz are excited at
  the bottom of the simulation domain. On their way through the upper
  convection zone and through the photosphere and the chromosphere they
  become perturbed, refracted, and converted into different mode types. We
  applied a standard Fourier analysis to produce oscillatory power-maps
  of the line-of-sight velocity. <BR /> Results: In the power maps of
  the upper photosphere and the lower chromosphere, we clearly see the
  magnetic shadow: a seam of suppressed power surrounding the magnetic
  network elements. We demonstrate that this shadow is linked to the
  mode conversion process and that power maps at these height levels
  show the signature of three different magneto-acoustic wave modes.

Title: Magnetic tornadoes as energy channels into the solar corona
Authors: Wedemeyer-Böhm, Sven; Scullion, Eamon; Steiner, Oskar;
   Rouppe van der Voort, Luc; de La Cruz Rodriguez, Jaime; Fedun, Viktor;
   Erdélyi, Robert
Bibcode: 2012Natur.486..505W
Altcode:
  Heating the outer layers of the magnetically quiet solar atmosphere to
  more than one million kelvin and accelerating the solar wind requires
  an energy flux of approximately 100 to 300 watts per square metre,
  but how this energy is transferred and dissipated there is a puzzle and
  several alternative solutions have been proposed. Braiding and twisting
  of magnetic field structures, which is caused by the convective flows
  at the solar surface, was suggested as an efficient mechanism for
  atmospheric heating. Convectively driven vortex flows that harbour
  magnetic fields are observed to be abundant in the photosphere
  (the visible surface of the Sun). Recently, corresponding swirling
  motions have been discovered in the chromosphere, the atmospheric
  layer sandwiched between the photosphere and the corona. Here we
  report the imprints of these chromospheric swirls in the transition
  region and low corona, and identify them as observational signatures
  of rapidly rotating magnetic structures. These ubiquitous structures,
  which resemble super-tornadoes under solar conditions, reach from
  the convection zone into the upper solar atmosphere and provide an
  alternative mechanism for channelling energy from the lower into the
  upper solar atmosphere.

Title: First Results from the SUNRISE Mission
Authors: Solanki, S. K.; Barthol, P.; Danilovic, S.; Feller, A.;
   Gandorfer, A.; Hirzberger, J.; Jafarzadeh, S.; Lagg, A.; Riethmüller,
   T. L.; Schüssler, M.; Wiegelmann, T.; Bonet, J. A.; González,
   M. J. M.; Pillet, V. M.; Khomenko, E.; Yelles Chaouche, L.; Iniesta,
   J. C. d. T.; Domingo, V.; Palacios, J.; Knölker, M.; González,
   N. B.; Borrero, J. M.; Berkefeld, T.; Franz, M.; Roth, M.; Schmidt,
   W.; Steiner, O.; Title, A. M.
Bibcode: 2012ASPC..455..143S
Altcode:
  The SUNRISE balloon-borne solar observatory consists of a 1m aperture
  Gregory telescope, a UV filter imager, an imaging vector polarimeter,
  an image stabilization system, and further infrastructure. The first
  science flight of SUNRISE yielded high-quality data that reveal the
  structure, dynamics, and evolution of solar convection, oscillations,
  and magnetic fields at a resolution of around 100 km in the quiet
  Sun. Here we describe very briefly the mission and the first results
  obtained from the SUNRISE data, which include a number of discoveries.

Title: Excitation of Slow-Modes in Network Magnetic Elements
Authors: Kato, Y.; Steiner, O.; Steffen, M.; Suematsu, Y.
Bibcode: 2012ASPC..455..237K
Altcode:
  From radiation magnetohydrodynamic (RMHD) simulations of the solar
  atmosphere we have found a new mechanism for the excitation of
  longitudinal slow modes within magnetic flux concentrations. It is
  found that the convective downdrafts in the immediate surroundings of
  magnetic elements are responsible for the excitation of slow modes. The
  coupling between the external downdraft and the plasma motion internal
  to the flux concentration is mediated by the inertial forces of the
  downdraft that act on the magnetic flux concentration. These forces
  pump the internal atmosphere in the downward direction, which entails
  a fast downflow in the photospheric and chromospheric layers of the
  magnetic element. Subsequent to the transient pumping phase, the
  atmosphere rebounds, causing a slow mode traveling along the magnetic
  flux concentration in the upward direction and developing into a shock
  wave in chromospheric heights, possibly capable of producing some kind
  of dynamic fibril. This event occurs recurrently. We compare the power
  spectra of the temperature and velocity of the flux-sheet atmosphere
  to the corresponding spectra of the unmagnetized atmosphere.

Title: Recent Advances in the Exploration of the Small-Scale Structure
of the Quiet Solar Atmosphere: Vortex Flows, the Horizontal Magnetic
    Field, and the Stokes- V Line-Ratio Method
Authors: Steiner, O.; Rezaei, R.
Bibcode: 2012ASPC..456....3S
Altcode: 2012arXiv1202.4040S
  We review (i) observations and numerical simulations of vortical flows
  in the solar atmosphere and (ii) measurements of the horizontal magnetic
  field in quiet Sun regions. First, we discuss various manifestations of
  vortical flows and emphasize the role of magnetic fields in mediating
  swirling motion created near the solar surface to the higher layers
  of the photosphere and to the chromosphere. We reexamine existing
  simulation runs of solar surface magnetoconvection with regard to
  vortical flows and compare to previously obtained results. Second,
  we reviews contradictory results and problems associated with
  measuring the angular distribution of the magnetic field in quiet Sun
  regions. Furthermore, we review the Stokes-V-amplitude ratio method
  for the lines Fe i λλ 630.15 and 630.25 nm. We come to the conclusion
  that the recently discovered two distinct populations in scatter plots
  of this ratio must not bee interpreted in terms of “uncollapsed''
  and “collapsed'' fields but stem from weak granular magnetic fields
  and weak canopy fields located at the boundaries between granules and
  the intergranular space. Based on new simulation runs, we reaffirm
  earlier findings of a predominance of the horizontal field components
  over the vertical one, particularly in the upper photosphere and at
  the base of the chromosphere.

Title: On The Magnetic-Field Diagnostics Potential of SDO/HMI
Authors: Fleck, Bernard; Hayashi, K.; Rezaei, R.; Vitas, N.; Centeno,
   R.; Cheung, M.; Couvidat, S.; Fischer, C.; Steiner, O.; Straus, T.;
   Viticchie, B.
Bibcode: 2012AAS...22020701F
Altcode:
  The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics
  Observatory (SDO) is designed to study oscillations and the magnetic
  field in the solar photosphere. It observes the full solar disk
  in the Fe I absorption line at 6173 Å. We use the output of three
  high-resolution 3D, time-dependent, radiative magneto-hydrodynamics
  simulations (two based on the MURaM code, one on the CO<SUP>5</SUP>BOLD
  code) to calculate Stokes profiles for the Fe I 6173 Å line
  for snapshots of a sunspot, a plage area and an enhanced network
  region. Stokes filtergrams are constructed for the 6 nominal HMI
  wavelengths by multiplying the Stokes profiles with a representative
  set of HMI filter response functions. The magnetic field vector B(x,y)
  and line-of-sight Doppler velocities V(x,y) are determined from these
  filtergrams using a simplified version of the HMI magnetic field
  processing pipeline. Finally, the reconstructed magnetic field B(x,y)
  and line-of-sight velocity V(x,y) are compared to the actual magnetic
  field B<SUB>0</SUB>(x,y,z) and vertical velocity V<SUB>0</SUB>(x,y,z)
  in the simulations.

Title: Detection of Vortex Tubes in Solar Granulation from
    Observations SUNRISE
Authors: Steiner, O.; Franz, M.; González, N. B.; Nutto, C.; Rezaei,
   R.; Pillet, V. M.; Bonet, J. A.; Iniesta, J. C. d. T.; Domingo, V.;
   Solanki, S. K.; Knölker, M.; Schmidt, W.; Barthol, P.; Gandorfer, A.
Bibcode: 2012ASPC..455...35S
Altcode:
  We investigated a time series of continuum intensity maps and
  Dopplergrams of granulation in a very quiet solar region at the disk
  center, recorded with the Imaging Magnetograph eXperiment (IMaX)
  on board the balloon-borne solar observatory SUNRISE. We find that
  granules frequently show substructure in the form of lanes composed of
  a leading bright rim and a trailing dark edge, which move together
  from the boundary of a granule into the granule itself. We find
  strikingly similar events in synthesized intensity maps from an ab
  initio numerical simulation of solar surface convection. We conclude
  that these granular lanes are the visible signature of (horizontally
  oriented) vortex tubes. The characteristic optical appearance of vortex
  tubes at the solar surface is explained. This paper is a summary and
  update of the results previously presented in Steiner et al. (2010).

Title: Small-scale rotating magnetic flux structures as alternative
    energy channels into the low corona
Authors: Wedemeyer-Böhm; , Sven; Scullion; , Eamon; Steiner; , Oskar;
   Rouppe van der Voort, Luc; de la Cruz Rodriguez, Jaime; Erdelyi,
   Robertus; Fedun, Viktor
Bibcode: 2012decs.confE..67W
Altcode:
  Vortex flows are frequently observed in the downflow areas in the lanes
  between granules. The magnetic field is advected and trapped by these
  flows in the low photosphere. Consequently, the rotation of a vortex
  flow is transferred to the atmospheric layers above by means of the
  magnetic flux structure. This effect results in so-called swirls, which
  are observed in the chromosphere. New simultaneous observations with
  the Swedish Solar Telescope and the Solar Dynamics Observatory reveal
  that chromospheric swirls can have a coronal counterpart. This finding
  implies that the rotating flux structure couples the layers of the solar
  atmosphere from the photosphere to the (low) corona. Three-dimensional
  numerical simulations confirm this picture and reproduce the swirl
  signature. A combined analysis of the simulations and observations
  implies that such small-scale rotating flux structures could provide
  an alternative mechanism for channeling substantial energy from the
  photosphere into the upper solar atmosphere.

Title: On the Magnetic-Field Diagnostics Potential of SDO/HMI
Authors: Fleck, B.; Hayashi, K.; Rezaei, R.; Vitas, N.; Centeno,
   R.; Cheung, M.; Couvidat, S.; Fischer, C.; Steiner, O.; Straus, T.;
   Viticchie, B.
Bibcode: 2012decs.confE.104F
Altcode:
  The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics
  Observatory (SDO) is designed to study oscillations and the magnetic
  field in the solar photosphere. It observes the full solar disk
  in the Fe I absorption line at 6173 Å. We use the output of three
  high-resolution 3D, time-dependent, radiative magneto-hydrodynamics
  simulations (two based on the MURaM code, one on the CO5BOLD code)
  to calculate Stokes profiles Fi(λ,x,y; i=I, V, Q, U) for the Fe I
  6173 Å line for snapshots of a sunspot, a plage area and an enhanced
  network region. Stokes filtergrams are constructed for the 6 nominal
  HMI wavelengths by multiplying the Stokes profiles with a representative
  set of HMI filter response functions. The magnetic field vector B(x,y)
  and line-of-sight Doppler velocities V(x,y) are determined from these
  filtergrams using a simplified version of the HMI magnetic field
  processing pipeline. Finally, the reconstructed magnetic field B(x,y)
  and line-of-sight velocity V(x,y) are compared to the actual magnetic
  field B0(x,y,z) and vertical velocity V0(x,y,z) in the simulations.

Title: The generation of shock waves traveling from the photosphere
    to the transition region within network magnetic elements
Authors: Kato, Y.; Hansteen, V.; Steiner, O.; Carlsson, M.
Bibcode: 2012decs.confE..54K
Altcode:
  We investigate the generation of shock waves near the photosphere by
  convective downdrafts in the immediate surroundings of the magnetic
  flux concentration, using radiation magnetohydrodynamic (RMHD) 2D
  simulations of the solar atmosphere. The simulations comprise the layers
  from the upper convection zone to the lower corona. We call this the
  "magnetic pumping process". We find that the generated slow modes via
  magnetic pumping travel upward along the magnetic flux concentration,
  developing into a shock wave in chromospheric heights. The waves
  continue to propagate further up through the transition region and into
  the corona. In the course of propagation through the transition layer,
  a small fraction of the longitudinal slow mode is converted into a
  transverse wave mode. We report on how much energy is deposited by
  propagating shock waves through the transition region and we discuss
  the the dissipation process above the photosphere within the magnetic
  flux concentration..

Title: Simulations of stellar convection with CO5BOLD
Authors: Freytag, B.; Steffen, M.; Ludwig, H. -G.; Wedemeyer-Böhm,
   S.; Schaffenberger, W.; Steiner, O.
Bibcode: 2012JCoPh.231..919F
Altcode: 2011arXiv1110.6844F
  High-resolution images of the solar surface show a granulation
  pattern of hot rising and cooler downward-sinking material - the
  top of the deep-reaching solar convection zone. Convection plays a
  role for the thermal structure of the solar interior and the dynamo
  acting there, for the stratification of the photosphere, where most
  of the visible light is emitted, as well as for the energy budget of
  the spectacular processes in the chromosphere and corona. Convective
  stellar atmospheres can be modeled by numerically solving the coupled
  equations of (magneto)hydrodynamics and non-local radiation transport
  in the presence of a gravity field. The CO5BOLD code described in this
  article is designed for so-called "realistic" simulations that take
  into account the detailed microphysics under the conditions in solar
  or stellar surface layers (equation-of-state and optical properties of
  the matter). These simulations indeed deserve the label "realistic"
  because they reproduce the various observables very well - with only
  minor differences between different implementations. The agreement
  with observations has improved over time and the simulations are now
  well-established and have been performed for a number of stars. Still,
  severe challenges are encountered when it comes to extending these
  simulations to include ideally the entire star or substellar object:
  the strong stratification leads to completely different conditions in
  the interior, the photosphere, and the corona. Simulations have to cover
  spatial scales from the sub-granular level to the stellar diameter and
  time scales from photospheric wave travel times to stellar rotation
  or dynamo cycle periods. Various non-equilibrium processes have to be
  taken into account. Last but not least, realistic simulations are based
  on detailed microphysics and depend on the quality of the input data,
  which can be the actual accuracy limiter. This article provides an
  overview of the physical problem and the numerical solution and the
  capabilities of CO5BOLD, illustrated with a number of applications.

Title: Modification of wave propagation and wave travel-time by the
    presence of magnetic fields in the solar network atmosphere
Authors: Nutto, C.; Steiner, O.; Schaffenberger, W.; Roth, M.
Bibcode: 2012A&A...538A..79N
Altcode:
  Context. Observations of waves at frequencies above the acoustic cut-off
  frequency have revealed vanishing wave travel-times in the vicinity of
  strong magnetic fields. This detection of apparently evanescent waves,
  instead of the expected propagating waves, has remained a riddle. <BR />
  Aims: We investigate the influence of a strong magnetic field on the
  propagation of magneto-acoustic waves in the atmosphere of the solar
  network. We test whether mode conversion effects can account for the
  shortening in wave travel-times between different heights in the solar
  atmosphere. <BR /> Methods: We carry out numerical simulations of the
  complex magneto-atmosphere representing the solar magnetic network. In
  the simulation domain, we artificially excite high frequency waves
  whose wave travel-times between different height levels we then
  analyze. <BR /> Results: The simulations demonstrate that the wave
  travel-time in the solar magneto-atmosphere is strongly influenced by
  mode conversion. In a layer enclosing the surface sheet defined by the
  set of points where the Alfvén speed and the sound speed are equal,
  called the equipartition level, energy is partially transferred from the
  fast acoustic mode to the fast magnetic mode. Above the equipartition
  level, the fast magnetic mode is refracted due to the large gradient
  of the Alfvén speed. The refractive wave path and the increasing phase
  speed of the fast mode inside the magnetic canopy significantly reduce
  the wave travel-time, provided that both observing levels are above
  the equipartition level. <BR /> Conclusions: Mode conversion and the
  resulting excitation and propagation of fast magneto-acoustic waves is
  responsible for the observation of vanishing wave travel-times in the
  vicinity of strong magnetic fields. In particular, the wave propagation
  behavior of the fast mode above the equipartition level may mimic
  evanescent behavior. The present wave propagation experiments provide an
  explanation of vanishing wave travel-times as observed with multi-line
  high-cadence instruments. <P />Movies are available in electronic form
  at <A href="http://www.aanda.org">http://www.aanda.org</A>

Title: Stokes Diagnostics of Magneto-Acoustic Wave Propagation in
    the Magnetic Network on the Sun
Authors: Vigeesh, G.; Steiner, O.; Hasan, S. S.
Bibcode: 2011SoPh..273...15V
Altcode: 2011SoPh..tmp..349V; 2011arXiv1104.4069V
  The solar atmosphere is magnetically structured and highly
  dynamic. Owing to the dynamic nature of the regions in which the
  magnetic structures exist, waves can be excited in them. Numerical
  investigations of wave propagation in small-scale magnetic flux
  concentrations in the magnetic network on the Sun have shown that
  the nature of the excited modes depends on the value of plasma β
  (the ratio of gas to magnetic pressure) where the driving motion
  occurs. Considering that these waves should give rise to observable
  characteristic signatures, we have attempted a study of synthesised
  emergent spectra from numerical simulations of magneto-acoustic
  wave propagation. We find that the signatures of wave propagation
  in a magnetic element can be detected when the spatial resolution
  is sufficiently high to clearly resolve it, enabling observations in
  different regions within the flux concentration. The possibility to
  probe various lines of sight around the flux concentration bears the
  potential to reveal different modes of the magnetohydrodynamic waves
  and mode conversion. We highlight the feasibility of using the Stokes-V
  asymmetries as a diagnostic tool to study the wave propagation within
  magnetic flux concentrations. These quantities can possibly be compared
  with existing and new observations in order to place constraints on
  different wave excitation mechanisms.

Title: On the Magnetic-Field Diagnostics Potential of SDO/HMI
Authors: Fleck, B.; Hayashi, K.; Rezaei, R.; Vitas, N.; Centeno, R.;
   Couvidat, S.; Fischer, C.; Steiner, O.; Straus, T.; Viticchie, B.
Bibcode: 2011sdmi.confE..74F
Altcode:
  The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics
  Observatory (SDO) is designed to study oscillations and the magnetic
  field in the solar photosphere. It observes the full solar disk in the
  Fe I 6173 absorption line. We use the output of two high-resolution 3D,
  time-dependent, radiative magneto-hydrodynamics simulations (one based
  on the MURAM code, the other one on the COBOLD code) to calculate
  Stokes profiles for the Fe I 6173 line for a snapshot of a plage
  region and a snapshot of an enhanced network region. After spatially
  degrading the Stokes profiles to HMI resolution, they are multiplied
  by a representative set of HMI filter response functions and Stokes
  filtergrams are constructed for the 6 nominal HMI wavelengths. The
  magnetic field vector and line-of-sight Doppler velocities are
  determined from these filtergrams using a simplified version of the HMI
  magnetic field processing pipeline. Finally, the reconstructed magnetic
  field is compared to the actual magnetic field in the simulation.

Title: The Sun at high resolution: first results from the Sunrise
    mission
Authors: Solanki, S. K.; Barthol, P.; Danilovic, S.; Feller,
   A.; Gandorfer, A.; Hirzberger, J.; Lagg, A.; Riethmüller, T. L.;
   Schüssler, M.; Wiegelmann, T.; Bonet, J. A.; Pillet, V. Martínez;
   Khomenko, E.; del Toro Iniesta, J. C.; Domingo, V.; Palacios, J.;
   Knölker, M.; González, N. Bello; Borrero, J. M.; Berkefeld, T.;
   Franz, M.; Roth, M.; Schmidt, W.; Steiner, O.; Title, A. M.
Bibcode: 2011IAUS..273..226S
Altcode:
  The Sunrise balloon-borne solar observatory consists of a 1m aperture
  Gregory telescope, a UV filter imager, an imaging vector polarimeter,
  an image stabilization system and further infrastructure. The first
  science flight of Sunrise yielded high-quality data that reveal the
  structure, dynamics and evolution of solar convection, oscillations
  and magnetic fields at a resolution of around 100 km in the quiet
  Sun. Here we describe very briefly the mission and the first results
  obtained from the Sunrise data, which include a number of discoveries.

Title: On the Origin of Intergranular Jets
Authors: Yurchyshyn, V. B.; Goode, P. R.; Abramenko, V. I.; Steiner, O.
Bibcode: 2011ApJ...736L..35Y
Altcode: 2011arXiv1106.5535Y
  We observe that intergranular jets, originating in the intergranular
  space surrounding individual granules, tend to be associated with
  granular fragmentation, in particular, with the formation and evolution
  of a bright granular lane (BGL) within individual granules. The BGLs
  have recently been identified as vortex tubes by Steiner et al. We
  further discover the development of a well-defined bright grain
  located between the BGL and the dark intergranular lane to which it
  is connected. Signatures of a BGL may reach the lower chromosphere
  and can be detected in off-band Hα images. Simulations also indicate
  that vortex tubes are frequently associated with small-scale magnetic
  fields. We speculate that the intergranular jets detected in the New
  Solar Telescope (NST) data may result from the interaction between
  the turbulent small-scale fields associated with the vortex tube
  and the larger-scale fields existing in the intergranular lanes. The
  intergranular jets are much smaller and weaker than all previously known
  jet-like events. At the same time, they appear much more numerous than
  the larger events, leading us to the speculation that the total energy
  release and mass transport by these tiny events may not be negligible in
  the energy and mass-flux balance near the temperature minimum atop the
  photosphere. The study is based on the photospheric TiO broadband (1.0
  nm) filter data acquired with the 1.6 m NST operating at the Big Bear
  Solar Observatory. The data set also includes NST off-band Hα images
  collected through a Zeiss Lyot filter with a passband of 0.025 nm.

Title: Excitation of magneto-acoustic waves in network magnetic
    elements
Authors: Kato, Yoshiaki; Steiner, Oskar; Steffen, Matthias; Suematsu,
   Yoshinori
Bibcode: 2011IAUS..273..442K
Altcode:
  From radiation magnetohydrodynamic (RMHD) simulations we track the
  temporal evolution of a vertical magnetic flux sheet embedded in a
  two-dimensional non-stationary atmosphere that reaches all the way
  from the upper convection zone to the low chromosphere. Examining its
  temporal behavior near the interface between the convection zone and
  the photosphere, we describe the excitation of propagating longitudinal
  waves within the magnetic element as a result of convective motion in
  its surroundings.

Title: Flux Tube Model
Authors: Steiner, O.
Bibcode: 2011ascl.soft05008S
Altcode:
  This Fortran code computes magnetohydrostatic flux tubes and sheets
  according to the method of Steiner, Pneuman, &amp; Stenflo (1986)
  A&amp;A 170, 126-137. The code has many parameters contained in one
  input file that are easily modified. Extensive documentation is provided
  in README files.

Title: Excitation of Slow Modes in Network Magnetic Elements Through
    Magnetic Pumping
Authors: Kato, Yoshiaki; Steiner, Oskar; Steffen, Matthias; Suematsu,
   Yoshinori
Bibcode: 2011ApJ...730L..24K
Altcode: 2011arXiv1102.5164K
  From radiation magnetohydrodynamic simulations of the solar atmosphere,
  we find a new mechanism for the excitation of longitudinal slow modes
  within magnetic flux concentrations. We find that the convective
  downdrafts in the immediate surroundings of magnetic elements are
  responsible for the excitation of slow modes. The coupling between
  the external downdraft and the plasma motion internal to the flux
  concentration is mediated by the inertial forces of the downdraft that
  act on the magnetic flux concentration. These forces, in conjunction
  with the downward movement, pump the internal atmosphere in the
  downward direction, which entails a fast downdraft in the photospheric
  and chromospheric layers of the magnetic element. Subsequent to the
  transient pumping phase, the atmosphere rebounds, causing a slow
  mode traveling along the magnetic flux concentration in the upward
  direction. It develops into a shock wave in chromospheric heights,
  possibly capable of producing some kind of dynamic fibril. We propose
  an observational detection of this process.

Title: Magneto-acoustic wave propagation and mode conversion
in a magnetic solar atmosphere: Comparing results from the
    CO<SUP>5</SUP>BOLD code with ray theory
Authors: Nutto, C.; Steiner, O.; Roth, M.
Bibcode: 2010AN....331..915N
Altcode: 2010arXiv1009.5586N
  We present simulations of magneto-acoustic wave propagation in
  a magnetic, plane-parallel stratified solar model atmosphere,
  employing the CO<SUP>5</SUP>BOLD-code. The tests are carried out for
  two models of the solar atmosphere, which are similar to the ones used
  by \citet{nutto_cally07} and \citet{nutto_schunker06}. The two models
  differ only in the orientation of the magnetic field. A qualitative
  comparison shows good agreement between the numerical results and the
  results from ray theory. The tests are done in view of the application
  of the present numerical code for the computation of energy fluxes
  of propagating acoustic waves into a dynamically evolving magnetic
  solar atmosphere. For this, we consider waves with frequencies above
  the acoustic cut-off frequency.

Title: Detection of Vortex Tubes in Solar Granulation from
    Observations with SUNRISE
Authors: Steiner, O.; Franz, M.; Bello González, N.; Nutto, Ch.;
   Rezaei, R.; Martínez Pillet, V.; Bonet Navarro, J. A.; del Toro
   Iniesta, J. C.; Domingo, V.; Solanki, S. K.; Knölker, M.; Schmidt,
   W.; Barthol, P.; Gandorfer, A.
Bibcode: 2010ApJ...723L.180S
Altcode: 2010arXiv1009.4723S
  We have investigated a time series of continuum intensity maps and
  corresponding Dopplergrams of granulation in a very quiet solar region
  at the disk center, recorded with the Imaging Magnetograph eXperiment
  (IMaX) on board the balloon-borne solar observatory SUNRISE. We
  find that granules frequently show substructure in the form of lanes
  composed of a leading bright rim and a trailing dark edge, which move
  together from the boundary of a granule into the granule itself. We
  find strikingly similar events in synthesized intensity maps from an
  ab initio numerical simulation of solar surface convection. From cross
  sections through the computational domain of the simulation, we conclude
  that these granular lanes are the visible signature of (horizontally
  oriented) vortex tubes. The characteristic optical appearance of vortex
  tubes at the solar surface is explained. We propose that the observed
  vortex tubes may represent only the large-scale end of a hierarchy of
  vortex tubes existing near the solar surface.

Title: CO5BOLD: COnservative COde for the COmputation of COmpressible
    COnvection in a BOx of L Dimensions with l=2,3
Authors: Freytag, Bernd; Steffen, Matthias; Wedemeyer-Böhm, Sven;
   Ludwig, Hans-Günter; Leenaarts, Jorrit; Schaffenberger, Werner;
   Allard, France; Chiavassa, Andrea; Höfner, Susanne; Kamp, Inga;
   Steiner, Oskar
Bibcode: 2010ascl.soft11014F
Altcode:
  CO5BOLD - nickname COBOLD - is the short form of "COnservative
  COde for the COmputation of COmpressible COnvection in a BOx of L
  Dimensions with l=2,3". <P />It is used to model solar and stellar
  surface convection. For solar-type stars only a small fraction of the
  stellar surface layers are included in the computational domain. In
  the case of red supergiants the computational box contains the entire
  star. Recently, the model range has been extended to sub-stellar objects
  (brown dwarfs). <P />CO5BOLD solves the coupled non-linear equations
  of compressible hydrodynamics in an external gravity field together
  with non-local frequency-dependent radiation transport. Operator
  splitting is applied to solve the equations of hydrodynamics (including
  gravity), the radiative energy transfer (with a long-characteristics
  or a short-characteristics ray scheme), and possibly additional 3D
  (turbulent) diffusion in individual sub steps. The 3D hydrodynamics
  step is further simplified with directional splitting (usually). The 1D
  sub steps are performed with a Roe solver, accounting for an external
  gravity field and an arbitrary equation of state from a table. <P
  />The radiation transport is computed with either one of three
  modules: <P />MSrad module: It uses long characteristics. The lateral
  boundaries have to be periodic. Top and bottom can be closed or open
  ("solar module"). <P />LHDrad module: It uses long characteristics
  and is restricted to an equidistant grid and open boundaries at all
  surfaces (old "supergiant module"). <P />SHORTrad module: It uses
  short characteristics and is restricted to an equidistant grid and
  open boundaries at all surfaces (new "supergiant module"). <P />The
  code was supplemented with an (optional) MHD version [Schaffenberger
  et al. (2005)] that can treat magnetic fields. There are also modules
  for the formation and advection of dust available. The current version
  now contains the treatment of chemical reaction networks, mostly used
  for the formation of molecules [Wedemeyer-Böhm et al. (2005)], and
  hydrogen ionization [Leenaarts &amp; Wedemeyer-Böhm (2005)], too. <P
  />CO5BOLD is written in Fortran90. The parallelization is done with
  OpenMP directives.

Title: A Chromospheric Conundrum?
Authors: Judge, Philip; Knölker, Michael; Schmidt, Wolfgang;
   Steiner, Oskar
Bibcode: 2010ApJ...720..776J
Altcode: 2010arXiv1007.1203J
  We examine spectra of the Ca II H line, obtained under good seeing
  conditions with the VTT Echelle Spectrograph in 2007 June, and
  higher resolution data of the Ca II λ8542 line from Fabry-Pérot
  instruments. The VTT targets were areas near disk center which included
  quiet Sun and some dispersed plage. The infrared data included quiet
  Sun and plage associated with small pores. Bright chromospheric network
  emission patches expand little with wavelength from line wing to line
  center, i.e., with increasing line opacity and height. We argue that
  this simple observation has implications for the force and energy
  balance of the chromosphere, since bright chromospheric network
  emission is traditionally associated with enhanced local mechanical
  heating which increases temperatures and pressures. Simple physical
  considerations then suggest that the network chromosphere may not be
  able to reach horizontal force balance with its surroundings, yet the
  network is a long-lived structure. We speculate on possible reasons for
  the observed behavior. By drawing attention to a potential conundrum,
  we hope to contribute to a better understanding of a long-standing
  unsolved problem: the heating of the chromospheric network.

Title: Magnetic Coupling in the Quiet Solar Atmosphere
Authors: Steiner, O.
Bibcode: 2010ASSP...19..166S
Altcode: 2010mcia.conf..166S; 2009arXiv0904.2026S
  Three kinds of magnetic couplings in the quiet solar atmosphere are
  highlighted and discussed, all fundamentally connected to the Lorentz
  force: first, the coupling of the convecting and overshooting fluid
  in the surface layers of the Sun with the magnetic field. Here, the
  plasma motion provides the dominant force, which shapes the magnetic
  field and drives the surface dynamo. Progress in the understanding of
  the horizontal magnetic field is summarized and discussed. Second, the
  coupling between acoustic waves and the magnetic field, in particular
  the phenomenon of wave conversion and wave refraction. It is described
  how measurements of wave travel times in the atmosphere can provide
  information about the topography of the wave conversion zone, that
  is, the surface of equal Alfvéen and sound speed. In quiet regions,
  this surface separates a highly dynamic magnetic field with fast moving
  magnetosonic waves and shocks around and above it from the more slowly
  evolving field of high-beta plasma below it. Third, the magnetic
  field also couples to the radiation field, which leads to radiative
  flux channeling and increased anisotropy in the radiation field. It
  is shown how faculae can be understood in terms of this effect. The
  article starts with an introduction to the magnetic field of the quiet
  Sun in the light of new results from the Hinode space observatory and
  with a brief survey of measurements of the turbulent magnetic field
  with the help of the Hanle effect.

Title: Numerical simulations of wave propagation in the solar
    chromosphere .
Authors: Nutto, C.; Steiner, O.; Roth, M.
Bibcode: 2010MmSAI..81..744N
Altcode: 2010arXiv1009.5607N
  We present two-dimensional simulations of wave propagation in a
  realistic, non-stationary model of the solar atmosphere. This model
  shows a granular velocity field and magnetic flux concentrations in
  the intergranular lanes similar to observed velocity and magnetic
  structures on the Sun and takes radiative transfer into account. <P
  />We present three cases of magneto-acoustic wave propagation through
  the model atmosphere, where we focus on the interaction of different
  magneto-acoustic wave modes at the layer of similar sound and Alfvén
  speeds, which we call the equipartition layer. At this layer acoustic
  and magnetic mode can exchange energy depending on the angle between the
  wave vector and the magnetic field vector. <P />Our results show that
  above the equipartition layer and in all three cases the fast magnetic
  mode is refracted back into the solar atmosphere. Thus, the magnetic
  wave shows an evanescent behavior in the chromosphere. The acoustic
  mode, which travels along the magnetic field in the low plasma-beta
  regime, can be a direct consequence of an acoustic source within or
  outside the low-beta regime, or it can result from conversion of the
  magnetic mode, possibly from several such conversions when the wave
  travels across a series of equipartition layers.

Title: Wave propagation and energy transport in the magnetic network
    of the Sun
Authors: Vigeesh, G.; Hasan, S. S.; Steiner, O.
Bibcode: 2009A&A...508..951V
Altcode: 2009arXiv0909.2325V
  Aims. We investigate wave propagation and energy transport in
  magnetic elements, which are representatives of small scale magnetic
  flux concentrations in the magnetic network on the Sun. This is
  a continuation of earlier work by Hasan et al. (2005, ApJ, 631,
  1270). The new features in the present investigation include
  a quantitative evaluation of the energy transport in the various
  modes and for different field strengths, as well as the effect of the
  boundary-layer thickness on wave propagation.<BR /> Methods: We carry
  out 2D MHD numerical simulations of magnetic flux concentrations for
  strong and moderate magnetic fields for which β (the ratio of gas to
  magnetic pressure) on the tube axis at the photospheric base is 0.4 and
  1.7, respectively. Waves are excited in the tube and ambient medium by
  a transverse impulsive motion of the lower boundary.<BR /> Results: The
  nature of the modes excited depends on the value of β. Mode conversion
  occurs in the moderate field case when the fast mode crosses the β =
  1 contour. In the strong field case the fast mode undergoes conversion
  from predominantly magnetic to predominantly acoustic when waves are
  leaking from the interior of the flux concentration to the ambient
  medium. We also estimate the energy fluxes in the acoustic and magnetic
  modes and find that in the strong field case, the vertically directed
  acoustic wave fluxes reach spatially averaged, temporal maximum values
  of a few times 10<SUP>6</SUP> erg cm<SUP>-2</SUP> s<SUP>-1</SUP> at
  chromospheric height levels.<BR /> Conclusions: The main conclusions
  of our work are twofold: firstly, for transverse, impulsive excitation,
  flux tubes/sheets with strong fields are more efficient than those with
  weak fields in providing acoustic flux to the chromosphere. However,
  there is insufficient energy in the acoustic flux to balance the
  chromospheric radiative losses in the network, even for the strong
  field case. Secondly, the acoustic emission from the interface between
  the flux concentration and the ambient medium decreases with the width
  of the boundary layer.

Title: The Horizontal Magnetic Field of the Quiet Sun: Numerical
    Simulations in Comparison to Observations with Hinode
Authors: Steiner, O.; Rezaei, R.; Schlichenmaier, R.; Schaffenberger,
   W.; Wedemeyer-Böhm, S.
Bibcode: 2009ASPC..415...67S
Altcode: 2009arXiv0904.2030S
  Three-dimensional magnetohydrodynamic simulations of the surface layers
  of the Sun intrinsically produce a predominantly horizontal magnetic
  field in the photosphere. This is a robust result in the sense that it
  arises from simulations with largely different initial and boundary
  conditions for the magnetic field. While the disk-center synthetic
  circular and linear polarization signals agree with measurements from
  Hinode, their center-to-limb variation sensitively depends on the
  height variation of the horizontal and the vertical field component
  and they seem to be at variance with the observed behavior.

Title: Near-surface stellar magneto-convection: simulations for the
    Sun and a metal-poor solar analog
Authors: Steffen, Matthias; Ludwig, H. -G.; Steiner, O.
Bibcode: 2009IAUS..259..233S
Altcode: 2009arXiv0902.2753S
  We present 2D local box simulations of near-surface radiative
  magneto-convection with prescribed magnetic flux, carried out with the
  MHD version of the CO<SUP>5</SUP>BOLD code for the Sun and a solar-like
  star with a metal-poor chemical composition (metal abundances reduced by
  a factor 100, [M/H] = -2). The resulting magneto-hydrodynamical models
  can be used to study the influence of the metallicity on the properties
  of magnetized stellar atmospheres. A preliminary analysis indicates
  that the horizontal magnetic field component tends to be significantly
  stronger in the optically thin layers of metal-poor stellar atmospheres.

Title: Numerical simulation of wave propagation in magnetic network
Authors: Vigeesh, G.; Hasan, S. S.; Steiner, O.
Bibcode: 2009IAUS..257..185V
Altcode:
  We present 2-D numerical simulations of wave propagation in the magnetic
  network. The network is modelled as consisting of individual magnetic
  flux sheets located in intergranular lanes. They have a typical
  horizontal size of about 150 km at the base of the photosphere and
  expand upward and become uniform. We consider flux sheets of different
  field strengths. Waves are excited by means of transverse motions at
  the lower boundary, to simulate the effect of granular buffeting. We
  look at the magneto-acoustic waves generated within the flux sheet
  and the acoustic waves generated in the ambient medium due to the
  excitation. We calculate the wave energy fluxes separating them into
  contributions from the acoustic and the Poynting part and study the
  effect of the different field strengths.

Title: Observational Evidence for Shocks in the Solar Photosphere -
    New TESOS/VTT Results
Authors: Rybak, J.; Kucera, A.; Hanslmeier, A.; Woehl, H.;
   Wedemeyer-Boehm, S.; Steiner, O.
Bibcode: 2008ESPM...12.2.36R
Altcode:
  High-resolution spectroscopic observations recently acquired with the
  TESOS spectrometer at the Vacuum Tower Telescope (VTT, Observatorio
  del Teide, Tenerife) are used to test predictions regarding strongly
  dynamic events in the photosphere as obtained from three-dimensional
  numerical simulations with the CO5BOLD-code. <P />Time series of
  two-dimensional maps of the Fe I 543.4 nm spectral line profile at
  different centre-to-limb positions are investigated in a statistical
  sense by comparing the distributions of individual spectral parameters
  derived from observations with the corresponding distributions
  from synthesized spectra calculated with the LINFOR3D code from
  the simulations. Appropriate degradation of the synthesized spectra
  was applied in order to take the limited spatial resolution of the
  telescope, seeing effects, and the scattered instrumental light into
  account. <P />At the actual spatial resolution of 0.5 arc sec, the
  statistics show that signatures of the photospheric dynamics, including
  the most dynamical events like occasional supersonic flows of plasma in
  the nearly horizontal direction, are very similar in both observations
  and simulations. <P />Discrepancies are found only for those spectral
  parameters (residual line intensity, Doppler line core shifts), which
  are affected by non-LTE effects, since non-LTE effects are not taken
  into account in the synthesis of the Fe I 543.4nm spectral line.

Title: Numerical Experiments with Magnetoacoustic Waves in the
    Solar Atmosphere
Authors: Nutto, C.; Schaffenberger, W.; Steiner, O.
Bibcode: 2008ESPM...12.3.23N
Altcode:
  With numerical experiments we explore the feasibility of using high
  frequency waves for probing the magnetic field in the photosphere
  and the chromosphere of the Sun. We track monochromatic wave trains
  that propagates through a magnetically structured, realistic solar
  atmosphere. When entering the magnetically dominated chromosphere,
  the waves undergo partial mode conversion and get refracted and
  reflected. We explore the relationship between wave travel times and
  the topography of the surface of equal Alfven and sound speeds, viz.,
  the magnetic canopy.

Title: Numerical simulation of wave propagation in the presence of
    a magnetic flux sheet
Authors: Vigeesh, G.; Steiner, O.; Hasan, S. S.
Bibcode: 2008ESPM...12.3.24V
Altcode:
  We model network magnetic fields as consisting of individual magnetic
  flux sheets located in intergranular lanes. With a typical horizontal
  size of about 150 km at the base of the photosphere, they expand upward
  and merge with their neighbors at a height of about 600 km. Above
  a height of approximately 1000 km the magnetic field starts to
  become uniform. Granular buffeting is thought to excite waves in this
  medium, which is modeled by means of transversal motions at the lower
  boundary. The transverse driving, generates both fast and slow waves
  within the flux sheet and acoustic waves in the ambient medium. We
  consider flux sheets of different field strengths and different
  boundary-layer widths. Separating the energy flux of the waves into
  contributions due to the acoustic flux and the Poynting flux, we show
  the longitudinal and transversal components of both and study their
  temporal evolution.

Title: The Horizontal Internetwork Magnetic Field: Numerical
    Simulations in Comparison to Observations with Hinode
Authors: Steiner, O.; Rezaei, R.; Schaffenberger, W.; Wedemeyer-Böhm,
   S.
Bibcode: 2008ESPM...12.3.22S
Altcode:
  Observations with the Hinode space observatory led to the discovery
  of predominantly horizontal magnetic fields in the photosphere of the
  quiet internetwork region. Here we investigate realistic numerical
  simulations of the surface layers of the Sun with respect to horizontal
  magnetic fields and compute the corresponding polarimetric response
  in the Fe I 630 nm line pair. We find a local maximum in the mean
  strength of the horizontal field component at a height of around 500
  km in the photosphere, where, depending on the initial state or the
  boundary condition, it surpasses the vertical component by a factor
  of 2.0 or 5.6. From the synthesized Stokes profiles, we derive a mean
  horizontal field component that is 1.6 or 4.3 times stronger than
  the vertical component, depending on the initial state or the boundary
  condition. This is a consequence of both the intrinsically stronger flux
  density of and the larger area occupied by the horizontal fields. We
  find that convective overshooting expels horizontal fields to the upper
  photosphere, making the Poynting flux positive in the photosphere,
  whereas it is negative in the convectively unstable layer below it.

Title: The Horizontal Internetwork Magnetic Field: Numerical
    Simulations in Comparison to Observations with Hinode
Authors: Steiner, O.; Rezaei, R.; Schaffenberger, W.; Wedemeyer-Böhm,
   S.
Bibcode: 2008ApJ...680L..85S
Altcode: 2008arXiv0801.4915S
  Observations with the Hinode space observatory led to the discovery
  of predominantly horizontal magnetic fields in the photosphere of the
  quiet internetwork region. Here we investigate realistic numerical
  simulations of the surface layers of the Sun with respect to horizontal
  magnetic fields and compute the corresponding polarimetric response
  in the Fe I 630 nm line pair. We find a local maximum in the mean
  strength of the horizontal field component at a height of around 500
  km in the photosphere, where, depending on the initial state or the
  boundary condition, it surpasses the vertical component by a factor
  of 2.0 or 5.6. From the synthesized Stokes profiles, we derive a mean
  horizontal field component that is 1.6 or 4.3 times stronger than
  the vertical component, depending on the initial state or the boundary
  condition. This is a consequence of both the intrinsically stronger flux
  density of and the larger area occupied by the horizontal fields. We
  find that convective overshooting expels horizontal fields to the upper
  photosphere, making the Poynting flux positive in the photosphere,
  whereas the Poynting flux is negative in the convectively unstable
  layer below it.

Title: Wave propagation in multiple flux tubes and chromospheric
    heating
Authors: Hasan, S. S.; van Ballegooijen, A.; Steiner, O.
Bibcode: 2008IAUS..247...82H
Altcode: 2007IAUS..247...82H
  This investigation is a continuation of earlier work on the dynamics of
  the magnetic network. In a previous calculation (Hasan et al. 2005),
  we examined the response of a single flux tube to transverse motions
  of its footpoints. We now extend this analysis to a more realistic
  model of the network consisting of multiple flux tubes. We apply a
  transverse velocity perturbation uniformly along the lower boundary
  located at the base of the photosphere. Our 2-D MHD simulations enable
  us to study the complex wave pattern due to waves generated in the
  individual tubes as well as their interaction with those emanating
  from adjacent tubes. Our results show that the dominant heating of the
  chromosphere occurs due to slow magnetoacoustic waves in a region that
  is close to the central region of the flux tube.

Title: Inferring the chromospheric magnetic topology through waves
Authors: Hasan, S. S.; Steiner, O.; van Ballegooijen, A.
Bibcode: 2008IAUS..247...78H
Altcode: 2007IAUS..247...78H
  The aim of this work is to examine the hypothesis that the wave
  propagation time in the solar atmosphere can be used to infer the
  magnetic topography in the chromosphere as suggested by Finsterle et
  al. (2004). We do this by using an extension of our earlier 2-D MHD
  work on the interaction of acoustic waves with a flux sheet. It is well
  known that these waves undergo mode transformation due to the presence
  of a magnetic field which is particularly effective at the surface
  of equipartition between the magnetic and thermal energy density, the
  β = 1 surface. This transformation depends sensitively on the angle
  between the wave vector and the local field direction. At the β =
  1 interface, the wave that enters the flux sheet, (essentially the
  fast mode) has a higher phase speed than the incident acoustic wave. A
  time correlation between wave motions in the non-magnetic and magnetic
  regions could therefore provide a powerful diagnostic for mapping the
  magnetic field in the chromospheric network.

Title: Hinode observations reveal boundary layers of magnetic elements
    in the solar photosphere
Authors: Rezaei, R.; Steiner, O.; Wedemeyer-Böhm, S.; Schlichenmaier,
   R.; Schmidt, W.; Lites, B. W.
Bibcode: 2007A&A...476L..33R
Altcode: 2007arXiv0711.0408R
  Aims:We study the structure of the magnetic elements in network-cell
  interiors. <BR />Methods: A quiet Sun area close to the disc centre was
  observed with the spectro-polarimeter of the Solar Optical Telescope
  on board the Hinode space mission, which yielded the best spatial
  resolution ever achieved in polarimetric data of the Fe I 630 nm line
  pair. For comparison and interpretation, we synthesize a similar data
  set from a three-dimensional magneto-hydrodynamic simulation. <BR
  />Results: We find several examples of magnetic elements, either
  roundish (tube) or elongated (sheet), which show a central area of
  negative Stokes-V area asymmetry framed or surrounded by a peripheral
  area with larger positive asymmetry. This pattern was predicted
  some eight years ago on the basis of numerical simulations. Here,
  we observationally confirm its existence for the first time. <BR
  />Conclusions: We gather convincing evidence that this pattern of
  Stokes-V area asymmetry is caused by the funnel-shaped boundary of
  magnetic elements that separates the flux concentration from the
  weak-field environment. On this basis, we conclude that electric
  current sheets induced by such magnetic boundary layers are common in
  the photosphere.

Title: How to Reach Superequipartition Field Strengths in Solar
    Magnetic Flux Tubes
Authors: Ferriz-Mas, A.; Steiner, O.
Bibcode: 2007SoPh..246...31F
Altcode:
  A number of independent arguments indicate that the toroidal flux
  system responsible for the sunspot cycle is stored at the base of the
  convection zone in the form of flux tubes with field strength close
  to 10<SUP>5</SUP> G. Although the evidence for such strong fields is
  quite compelling, how such field strength can be reached is still a
  topic of debate. Flux expulsion by convection should lead to about
  the equipartition field strength, but the magnetic energy density of
  a 10<SUP>5</SUP>-G field is two orders of magnitude larger than the
  mean kinetic energy density of convective motions. Line stretching
  by differential rotation (i.e., the "Ω effect" in the classical
  mean-field dynamo approach) probably plays an important role, but
  arguments based on energy considerations show that it does not seem
  feasible that a 10<SUP>5</SUP>-G field can be produced in this way. An
  alternative scenario for the intensification of the toroidal flux
  system in the overshoot layer is related to the explosion of rising,
  buoyantly unstable magnetic flux tubes, which opens a complementary
  mechanism for magnetic-field intensification. A parallelism is pointed
  out with the mechanism of "convective collapse" for the intensification
  of photospheric magnetic flux tubes up to field strengths well above
  equipartition; both mechanisms, which are fundamentally thermal
  processes, are reviewed.

Title: Variation of the Stokes-V area asymmetry across magnetic
    elements
Authors: Rezaei, R.; Steiner, O.; Wedemeyer-Böhm, S.; Schlichenmaier,
   R.; Lites, B. W.
Bibcode: 2007AN....328..706R
Altcode:
  No abstract at ADS

Title: Opposite magnetic polarity of two photospheric lines in single
    spectrum of the quiet Sun
Authors: Rezaei, R.; Schlichenmaier, R.; Schmidt, W.; Steiner, O.
Bibcode: 2007A&A...469L...9R
Altcode: 2007arXiv0704.3135R
  Aims:We study the structure of the photospheric magnetic field of the
  quiet Sun by investigating weak spectro-polarimetric signals. <BR
  />Methods: We took a sequence of Stokes spectra of the Fe I 630.15
  nm and 630.25 nm lines in a region of quiet Sun near the disk
  center, using the POLIS spectro-polarimeter at the German VTT on
  Tenerife. The line cores of these two lines form at different heights
  in the atmosphere. The 3σ noise level of the data is about 1.8
  × 10<SUP>-3</SUP> I_c. <BR />Results: We present co-temporal and
  co-spatial Stokes-V profiles of the Fe I 630 nm line pair, where
  the two lines show opposite polarities in a single spectrum. We
  compute synthetic line profiles and reproduce these spectra with a
  two-component model atmosphere: a non-magnetic component and a magnetic
  component. The magnetic component consists of two magnetic layers with
  opposite polarity: the upper one moves upwards while the lower one moves
  downward. In-between, there is a region of enhanced temperature. <BR
  />Conclusions: The Stokes-V line pair of opposite polarity in a single
  spectrum can be understood as a magnetic reconnection event in the
  solar photosphere. We demonstrate that such a scenario is realistic,
  but the solution may not be unique.

Title: Photospheric processes and magnetic flux tubes
Authors: Steiner, Oskar
Bibcode: 2007AIPC..919...74S
Altcode: 2007arXiv0709.0081S
  New high-resolution observations reveal that small-scale magnetic
  flux concentrations have a delicate substructure on a spatial scale
  of 0.1''. Their basic structure can be interpreted in terms of a
  magnetic flux sheet or tube that vertically extends through the
  ambient weak-field or field-free atmosphere with which it is in
  mechanical equilibrium. A more refined interpretation comes from new
  three-dimensional magnetohydrodynamic simulations that are capable
  of reproducing the corrugated shape of magnetic flux concentrations
  and their signature in the visible continuum. Faculae are another
  manifestation of small-scale magnetic flux concentrations. It is shown
  that the characteristic asymmetric shape of the contrast profile
  of faculae is an effect of radiative transfer across the rarefied
  atmosphere of the magnetic flux concentration. Also discussed
  are three-dimensional radiation magnetohydrodynamic simulations
  of the integral layers from the top of the convection zone to the
  mid-chromosphere. They show a highly dynamic chromospheric magnetic
  field, marked by rapidly moving filaments of stronger than average
  magnetic field that form in the compression zone downstream and along
  propagating shock fronts. The simulations confirm the picture of flux
  concentrations that strongly expand through the photosphere into a
  more homogeneous, space filling chromospheric field. Future directions
  in the simulation of small-scale magnetic fields are indicated with a
  few examples from recent reports. <P />The second part of these lecture
  notes is devoted to a few basic properties of magnetic flux tubes that
  can be considered to be an abstraction of the more complicated flux
  concentrations known from observations and numerical simulations. By
  analytical means we will find that an electrical current flows in a
  sheet at the surface of a flux-tube for which location we also derive
  the mechanical equilibrium condition. The equations for constructing a
  magnetohydrostatic flux tube embedded in a gravitationally stratified
  atmosphere are derived. It is shown that the expansion of a flux
  tube with height sensibly depends on the difference in the thermal
  structure between the atmosphere of the flux tube and the surrounding
  atmosphere. Furthermore, we will find that radiative equilibrium
  produces a smaller temperature gradient within the flux tube compared
  to that in the surrounding atmosphere. The condition for interchange
  stability is derived and it is shown that small-scale magnetic flux
  concentrations are liable to the interchange instability.

Title: What is Heating the Quiet-Sun Chromosphere?
Authors: Wedemeyer-Böhm, S.; Steiner, O.; Bruls, J.; Rammacher, W.
Bibcode: 2007ASPC..368...93W
Altcode: 2006astro.ph.12627W
  It is widely believed that the heating of the chromosphere in quiet-Sun
  internetwork regions is provided by dissipation of acoustic waves
  that are excited by the convective motions close to the top of
  the convection zone and in the photospheric overshoot layer. This
  view lately became challenged by observations suggesting that the
  acoustic energy flux into the chromosphere is too low, by a factor
  of at least ten. Based on a comparison of TRACE data with synthetic
  image sequences for a three-dimensional simulation extending from
  the top layers of the convection zone to the middle chromosphere,
  we come to the contradicting conclusion that the acoustic flux in the
  model provides sufficient energy for heating the solar chromosphere of
  internetwork regions. The role of a weak magnetic field and associated
  electric current sheets is also discussed.

Title: First local helioseismic experiments with CO<SUP>5</SUP>BOLD
Authors: Steiner, O.; Vigeesh, G.; Krieger, L.; Wedemeyer-Böhm, S.;
   Schaffenberger, W.; Freytag, B.
Bibcode: 2007AN....328..323S
Altcode: 2007astro.ph..1029S
  With numerical experiments we explore the feasibility of using high
  frequency waves for probing the magnetic fields in the photosphere and
  the chromosphere of the Sun. We track a plane-parallel, monochromatic
  wave that propagates through a non-stationary, realistic atmosphere,
  from the convection-zone through the photosphere into the magnetically
  dominated chromosphere, where it gets refracted and reflected. We
  compare the wave travel time between two fixed geometrical height levels
  in the atmosphere (representing the formation height of two spectral
  lines) with the topography of the surface of equal magnetic and thermal
  energy density (the magnetic canopy or β=1 contour) and find good
  correspondence between the two. We conclude that high frequency waves
  indeed bear information on the topography of the `magnetic canopy'.

Title: Recent progresses in the simulation of small-scale magnetic
    fields
Authors: Steiner, O.
Bibcode: 2007msfa.conf..321S
Altcode: 2007arXiv0705.1848S
  New high-resolution observations reveal that small-scale magnetic
  flux concentrations have a delicate substructure on a spatial scale of
  0.1". Its basic structure can be interpreted in terms of a magnetic flux
  sheet or tube that vertically extends through the ambient weak-field or
  field-free atmosphere with which it is in mechanical equilibrium. A
  more refined interpretation comes from new three-dimensional
  magnetohydrodynamic simulations that are capable of reproducing the
  corrugated shape of magnetic flux concentrations and their signature in
  the visible continuum. Furthermore it is shown that the characteristic
  asymmetric shape of the contrast profile of facular granules is
  an effect of radiative transfer across the rarefied atmosphere of
  the magnetic flux concentration. I also discuss three-dimensional
  radiation magnetohydrodynamic simulations of the integral layers from
  the top of the convection zone to the mid-chromosphere. They show a
  highly dynamic chromospheric magnetic field, marked by rapidly moving
  filaments of stronger than average magnetic field that form in the
  compression zone downstream and along propagating shock fronts. The
  simulations confirm the picture of flux concentrations that strongly
  expand through the photosphere into a more homogeneous, space filling
  chromospheric field. Future directions in the simulation of small-scale
  magnetic fields are indicated by a few examples of very recent work.

Title: A New Method for Comparing Numerical Simulations with
    Spectroscopic Observations of the Solar Photosphere
Authors: Rybák, J.; Kučera, A.; Wöhl, H.; Wedemeyer-Böhm, S.;
   Steiner, O.
Bibcode: 2006ASPC..354...77R
Altcode:
  A method for comparing high-resolution spectroscopic observations of
  the solar photosphere with numerical simulations of convection in the
  solar photosphere is presented. <P />It is based on the comparison of
  the granular continuum contrast obtained from both the observations and
  the synthetic spectra, when the latter are calculated from numerical
  simulations using a particular type of data degradation. This method
  can be used post facto when a minimum of auxiliary information on
  characteristics of the telescope/spectrograph and on seeing conditions
  is available. <P />Here, the method is applied to results of numerical
  simulations computed with the CO5BOLD code and high-resolution
  spectroscopic observations obtained with the VTT on Tenerife.

Title: Holistic MHD-Simulation from the Convection Zone to the
    Chromosphere
Authors: Schaffenberger, W.; Wedemeyer-Böhm, S.; Steiner, O.;
   Freytag, B.
Bibcode: 2006ASPC..354..345S
Altcode:
  A three-dimensional magnetohydrodynamic simulation of the integral
  layers from the convection zone to the chromosphere has been
  carried out. The simulation represents magnetoconvection in a quiet
  network-cell interior. The following preliminary new results are
  obtained: The chromospheric magnetic field is very dynamic with a
  continuous rearrangement of magnetic flux on a time scale of less than
  one~minute. Rapidly moving magnetic filaments (rarely exceeding 40~G)
  form in the compression zone downstream and along propagating shock
  fronts that are present throughout the chromosphere. The magnetic
  filaments rapidly move, form, and dissolve with the shock waves. Flux
  concentrations strongly expand through the photosphere into a more
  homogeneous, space filling chromospheric field. ``Canopy fields''
  form on a granular scale above largely field-free granule centers
  leading to a mesh-work of current sheets in a height range between
  approximately 400 and 900~km.

Title: Recent Progresses in the Physics of Small-Scale Magnetic Fields
Authors: Steiner, O.
Bibcode: 2005ESASP.600E..10S
Altcode: 2005ESPM...11...10S; 2005dysu.confE..10S
  No abstract at ADS

Title: Simulations of Magnetohydrodynamics and CO Formation from
    the Convection Zone to the Chromosphere
Authors: Wedemeyer-Böhm, S.; Schaffenberger, W.; Steiner, O.; Steffen,
   M.; Freytag, B.; Kamp, I.
Bibcode: 2005ESASP.596E..16W
Altcode: 2005ccmf.confE..16W
  No abstract at ADS

Title: Magnetohydrodynamic Simulation from the Convection Zone to
    the Chromosphere
Authors: Schaffenberger, W.; Wedemeyer-Böhm, S.; Steiner, O.;
   Freytag, B.
Bibcode: 2005ESASP.596E..65S
Altcode: 2005ccmf.confE..65S
  No abstract at ADS

Title: Dynamics of the Solar Magnetic Network: Two-dimensional
    MHD Simulations
Authors: Hasan, S. S.; van Ballegooijen, A. A.; Kalkofen, W.;
   Steiner, O.
Bibcode: 2005ApJ...631.1270H
Altcode: 2005astro.ph..3525H
  The aim of this work is to identify the physical processes that occur
  in the network and contribute to its dynamics and heating. We model the
  network as consisting of individual flux tubes, each with a nonpotential
  field structure, that are located in intergranular lanes. With a typical
  horizontal size of about 150 km at the base of the photosphere, they
  expand upward and merge with their neighbors at a height of about 600
  km. Above a height of approximately 1000 km the magnetic field starts
  to become uniform. Waves are excited in this medium by means of motions
  at the lower boundary. We focus on transverse driving, which generates
  both fast and slow waves within a flux tube and acoustic waves at
  the interface of the tube and the ambient medium. The acoustic waves
  at the interface are due to compression of the gas on one side of
  the flux tube and expansion on the other. These longitudinal waves
  are guided upward along field lines at the two sides of the flux
  tube, and their amplitude increases with height due to the density
  stratification. Being acoustic in nature, they produce a compression
  and significant shock heating of the plasma in the chromospheric part of
  the flux tube. For impulsive excitation with a time constant of 120 s,
  we find that a dominant feature of our simulations is the creation of
  vortical motions that propagate upward. We have identified an efficient
  mechanism for the generation of acoustic waves at the tube edge, which
  is a consequence of the sharp interface of the flux concentration. We
  examine some broad implications of our results.

Title: Dynamics of the Magnetic Network on the Sun
Authors: Hasan, S.; van Ballegoiijen, A.; Kalkofen, W.; Steiner, O.
Bibcode: 2005AGUSMSH13C..08H
Altcode:
  Observations have revealed the presence of a rich spectrum of waves
  with different periods in regions of the solar atmosphere called the
  "magnetic network" that are dominated by strong magnetic fields. This
  network is believed to be heated by dissipation of magnetohydrodynamic
  (MHD) waves, but the MHD processes involved in wave generation,
  propagation and dissipation are poorly understood. In this work we
  attempt to identify some of the processes that occur in the network and
  which contribute to its dynamics and heating. We model the network as
  consisting of individual magnetic elements or flux tubes, rooted in
  intergranular lanes, with a typical horizontal size of 100 km. They
  expand upward and merge with their neighbors at a height of about 600
  km. Above this height the magnetic field becomes uniform. An equilibrium
  configuration based on the above model is constructed by solving the
  magnetostatic equations in 2-D. Waves are generated in this medium
  by means of motions at the lower boundary. We focus on transverse
  driving which generates fast waves within the flux tubes and acoustic
  waves at the interface of the tubes and the field-free medium, but not
  otherwise in the field-free gas. The acoustic waves at the interface
  are due to compression of the gas on one side of the flux tube and
  expansion on the other. These waves travel upward along the two sides
  of the (2D) flux tube and enter it, where they become longitudinal
  waves. For impulsive excitation with a time constant of 120 s, we
  find that a dominant feature is the creation of vortical motions that
  propagate upwards. We have identified a new and efficient mechanism
  for the generation of longitudinal waves and shock formation in the
  chromosphere. We examine the observational implications of our results
  and their broad applications to chromospheric heating and activity.

Title: Connecting solar radiance variability to the solar dynamo
    with the virial theorem
Authors: Steiner, O.; Ferriz-Mas, A.
Bibcode: 2005AN....326..190S
Altcode:
  The variability of solar radiance over a solar cycle is thought to
  result from a delicate balance between the radiative deficit of sunspots
  and the extra contribution of plage and network regions. Although the
  net effect is tiny, it must imply structural and thermal changes in
  the Sun or in partial layers of it as an unavoidable consequence of
  the virial theorem. Using the virial theorem for continua--including
  the magnetic field--it can be shown how solar radiance variability
  might be connected to a deeply seated flux-tube dynamo and how this
  connection is established on a hydrodynamical time scale.

Title: Radiative properties of magnetic elements. II. Center to limb
    variation of the appearance of photospheric faculae
Authors: Steiner, O.
Bibcode: 2005A&A...430..691S
Altcode:
  For the understanding of more complex numerical simulation results,
  a basic facular model is created consisting of a magnetic flux sheet
  embedded in a plane parallel atmosphere. The atmosphere within the
  flux sheet is similar to the external one but shifted in the downward
  direction to result in a Wilson depression of 150 km. It is shown that
  the horizontal spatial extension of the contrast enhancement produced
  by this model increases from center to limb from a few tenths to up
  to 1 arcsec as a consequence of enhanced radiation from the limbward
  surface outside (behind) the magnetic flux concentration. For a
  conceivable explanation of this radiative effect it is noted that
  a plasma parcel on the solar surface sideways of the flux sheet
  ``sees'' a more transparent sky in the direction towards the flux
  sheet compared to a direction away from it because of the rarefied
  atmosphere within the flux sheet. This facular model also produces a
  dark lane at the disk-center side (in front) of the flux sheet even
  though no flow is present. It it is due to the deep layers of the
  flux sheet that have a lower temperature gradient and are cooler
  than the surrounding atmosphere at equal geometrical depth. This
  implies that limb observations offer a glimpse of the ``cool bottom''
  of magnetic elements. The center-to-limb variation of the size and
  the dark-lane effect derived from this basic model is recovered in
  a self-consistent, two-dimensional non-stationary simulation of a
  magnetic flux concentration. These findings are in excellent agreement
  with and provide an interpretation of recent observations of faculae
  at very high resolution by Lites et al. (2004, \solphys, 221, 65).

Title: The deep roots of solar radiance variability .
Authors: Steiner, O.; Ferriz-Mas, A.
Bibcode: 2005MmSAI..76..789S
Altcode:
  The variability of solar radiance over a solar cycle is thought to
  result from a delicate balance between the radiative deficit of sunspots
  and the extra contribution of plage and network regions. Although the
  net effect is tiny, it implies structural and thermal changes in the
  Sun or in partial layers of it as an unavoidable consequence of the
  virial theorem. Using the virial theorem for continua--including the
  magnetic field--it can be shown how solar radiance variability might be
  connected to a deeply seated flux-tube dynamo and how this connection
  is established on a hydrodynamical time scale.

Title: Indications of shock waves in the solar photosphere
Authors: Rybák, J.; Wöhl, H.; Kučera, A.; Hanslmeier, A.;
   Steiner, O.
Bibcode: 2004A&A...420.1141R
Altcode:
  High resolution observations of solar granulation near the solar limb
  are used in a search for hydrodynamic shocks caused by an abrupt
  braking of the fast (probably supersonic) horizontal flow of the
  granular plasma towards the intergranular lane. Shock signatures in
  the spectral line of Fe II 6456.38 Åof one particular observed shock
  event are investigated in detail. Evolution, amplitude, and spatial
  relation of the spectral line characteristics of the shock event are in
  agreement with predictions from numerical simulations for such shock
  phenomena in the solar photosphere. The dimensions and amplitudes of
  the observed shock signatures are comparable to predicted values when
  seeing and instrumental effects as well as a possible obliqueness of
  the shock front with respect to the observer's line-of-sight are taken
  into account. The temporal evolution of such an event is observed for
  the first time. The stable and declining phase of the event were studied
  for a time period of almost 2 min. A particular relationship was found
  between the shock event and a nearby G-band bright point located 2''
  from the shock event. It is suggestive that the observed shock is a
  causal consequence of the magnetic flux concentration, traced by the
  G-band bright point. Such a type of shock can appear outside the flux
  concentrations as a consequence of a rapid flux-tube motion.

Title: Connecting solar radiance variability to the solar dynamo
    with the virial theorem
Authors: Steiner, Oskar
Bibcode: 2004IAUS..223...77S
Altcode: 2005IAUS..223...77S
  The variability of solar radiance over a solar cycle is thought to
  be a delicate balance between the radiative deficit of sunspots and
  the extra contribution of plage and network regions. Although the net
  effect is tiny, it must imply structural and thermal changes in the
  Sun or in partial layers of it as an unavoidable consequence of the
  virial theorem. Using the virial theorem for continua including the
  magnetic field it is shown, how solar radiance variability might be
  connected to a deeply seated flux-tube dynamo and how this connection
  is established on a hydrodynamical time-scale.

Title: Understanding facular granules and lanes
Authors: Steiner, Oskar
Bibcode: 2004IAUS..223..299S
Altcode: 2005IAUS..223..299S
  Recent high resolution observations by Lites et al. (2004) show
  details of facular granules at 0.12^{primeprime}, including dark
  facular lanes. For an interpretation of these data a basic facular
  model is constructed, consisting of a magnetic flux sheet embedded
  in a plane parallel atmosphere. While the maximum contrast originates
  from the "hot wall" of the flux-sheet depression, the model explains
  the wide brightening limbward of the facular magnetic field as due
  to a radiative transfer effect caused by the reduced opacity of the
  rarefied flux-sheet atmosphere. This model produces a dark, narrow
  lane centerward of the facular granule even in the absence of granular
  flow as a consequence of the cool deep layers of the magnetic flux
  sheet. These results carry over to a self-consistent simulation of
  a flux concentration in dynamic interaction with convective motion,
  where the dark lane deepens and broadens.

Title: Distribution of magnetic flux density at the solar
    surface. Formulation and results from simulations
Authors: Steiner, O.
Bibcode: 2003A&A...406.1083S
Altcode:
  A formal description of the distribution of magnetic flux density
  in a quiet Sun region supplemented by an example and an application
  is presented. We define a flux-based probability density, which
  is useful to reveal the presence of any strong-field component in
  the region. The corresponding flux-based probability distribution
  gives the fraction of the total absolute magnetic flux with a given
  field-strength limit. Application to the simulations of convective field
  intensification of Grossmann-Doerth et al. (1998) shows, that, depending
  on the strength of the initial homogeneous vertical field, 1-50% of the
  total magnetic flux within the computational domain of 3 arcsec width
  is concentrated into flux fibrils with a flux density exceeding 0.1
  T. It is shown that a low efficiency of the flux-concentration process
  is compatible with new observations that suggest a large fraction of
  the surface magnetic field to have a flux density below 0.1 T.

Title: Distribution of the Magnetic Flux Density at the Solar Surface
Authors: Steiner, Oskar
Bibcode: 2003ANS...324R..31S
Altcode: 2003ANS...324..D07S
  No abstract at ADS

Title: Solar Radiance Variability as a Direct Consequence of the
    Flux-tube Dynamo
Authors: Steiner, Oskar
Bibcode: 2003ANS...324..106S
Altcode: 2003ANS...324..P12S
  No abstract at ADS

Title: Convergence of a Solenoidal Discrete Rot-operator
Authors: Steiner, Oskar
Bibcode: 2003ANS...324...75S
Altcode: 2003ANS...324..I20S
  No abstract at ADS

Title: The contrast of magnetic elements across the solar spectrum
Authors: Steiner, O.; Hauschildt, P. H.; Bruls, J.
Bibcode: 2003AN....324..398S
Altcode:
  No abstract at ADS

Title: Multi-Grid Radiative Transfer Revisited
Authors: Steiner, O.
Bibcode: 2003ASPC..288...83S
Altcode: 2003sam..conf...83S
  Multi-grid radiation transfer is an efficient method for solving
  a variety of radiation transfer problems, in particular problems
  of multiple spatial dimensions on scalar computers. This advantage
  is lost on massively parallel machines in which the computational
  grid can be directly mapped onto the processor array. Contrary to
  operator splitting methods, the convergence rate of the multi-grid
  method does not deteriorate with increasing spatial resolution of the
  computational grid. It is therefore well suited for high resolution
  problems, while performance at low resolution is not better than the
  best operator splitting methods. <P />There exists a considerable
  variety of basic multi-grid algorithms, which leave ample room for
  improvements of the few multi-grid radiation-transfer calculations
  that have been carried out so far. This poster is available under <A
  href="http://www.kis.uni-freiburg.de/~steiner/"> Poster </A>

Title: Large-Scale Flow in Two-Dimensional Simulation of Solar
    Convection
Authors: Steiner, O.
Bibcode: 2003IAUS..210P.C11S
Altcode:
  No abstract at ADS

Title: Spectral signature of magnetic flux tubes in sunspot penumbrae
Authors: Müller, D. A. N.; Schlichenmaier, R.; Steiner, O.; Stix, M.
Bibcode: 2002A&A...393..305M
Altcode:
  We study the polarization of spectral lines in the penumbra by
  integrating the radiative transfer equation of polarized light for a
  three-dimensional model atmosphere of a sunspot. In this model, the
  Evershed flow is confined to magnetic flux tubes which are embedded
  in a static background atmosphere, in accordance with the moving tube
  model of Schlichenmaier et al. (\cite{Schlichenmaier1998apjl},b). The
  gradients and/or discontinuities in the fluid velocity and the
  magnetic field at the flux tube boundaries give rise to asymmetric
  Stokes profiles. We concentrate on the Stokes-V profiles and study the
  net circular polarization (NCP) of two photospheric spectral lines of
  neutral iron, Fe I 630.25 nm and Fe I 1564.8 nm. The different behavior
  of these two lines, which are exemplary for atomic spectral lines with
  a large Landé factor and significantly different wavelength, is based
  on the difference in excitation potential of the corresponding atomic
  transitions and the fact that the wavelength dependence of the Doppler
  shift is linear, while that of the Zeeman splitting is quadratic. We
  find that the azimuthal variation of the NCP, N(psi, is a predominantly
  antisymmetric function of psi with respect to the line connecting
  disk center and spot center (line-of-symmetry) for the infrared line
  of Fe I 1564.8 nm, while the variation is predominantly symmetric for
  Fe I 630.25 nm. We show that the antisymmetric variation is caused
  by anomalous dispersion (Faraday pulsation) and the discontinuity
  in the azimuthal angle of the magnetic field, which is due to the
  relative inclination between flux tube and background field. We
  then compute synthetic NCP maps of a sunspot and compare them with
  observational results. Finally, the center-to-limb variation of the
  NCP, N(theta ), of these spectral lines is investigated. We show
  that the location of the zero-crossing point of N(theta ) on the
  center side of the line-of-symmetry represents a diagnostic tool to
  determine the inclination angle of the Evershed flow: A vanishing NCP
  on the center-side of the line-of-symmetry is an indirect evidence of
  downflows in the penumbra.

Title: Net circular polarization of sunspot penumbrae - symmetry
    breaking by anomalous dispersion
Authors: Müller, D. A. N.; Schlichenmaier, R.; Steiner, O.; Stix, M.
Bibcode: 2002ESASP.508..141M
Altcode: 2002soho...11..141M
  We examine the polarization of spectral lines in the penumbra of
  sunspots by solving the radiative transfer equation of polarized
  light for a three-dimensional axially symmetric model atmosphere
  of a sunspot. The Evershed flow is confined to horizontal magnetic
  flux tubes obtained from MHD calculations. These are embedded in
  an inclined background magnetic field. In this work, we concentrate
  on the Stokes-V profiles and examine the net circular polarization
  (NCP), N = ∫V(λ)dλ, of two photospheric spectral lines of neutral
  iron, Fe I 630.25 nm and Fe I 1564.8 nm. Analyzing spectra at a fixed
  distance from the spot center, we find that the azimuthal variation
  of N, N(ψ), is an antisymmetric function of ψ w.r.t. to the line
  connecting disk center and spot center for Fe I 1564.8 nm, while
  the variation is predominantly symmetric for Fe I 630.25 nm. We show
  that the antisymmetric variation is caused by anomalous dispersion
  (rotation of the polarization vector in a magnetized plasma). The
  different inclination angles lead to a discontinuity in the azimuth
  of the magnetic field along the line-of-sight. We show that this
  discontinuity together with the effect of anomalous dispersion produced
  an antisymmetric component in N(ψ) which outweighs the symmetric
  component from the discontinuity for Fe I 1564.8 nm, while it is
  negligible for Fe I 630.25 nm. We finally compute synthetic NCP maps of
  a sunspot which offer an explanation for recent observational results.

Title: Net circular polarization of sunspot penumbrae. Symmetry
    breaking through anomalous dispersion
Authors: Schlichenmaier, R.; Müller, D. A. N.; Steiner, O.; Stix, M.
Bibcode: 2002A&A...381L..77S
Altcode:
  The net circular polarization, N, is used as a measure for the
  asymmetry of Stokes-V profiles: Nequiv int V(lambda ) d lambda ,
  integrated over an absorption line. Exemplary for Fe I 630.2 nm and
  Fe I 1564.8 nm, we synthesize penumbral V-profiles that stem from a
  model atmosphere in which the Evershed flow is confined to horizontal
  flux tubes which are embedded in a magnetic field that has the same
  magnetic field strength as the flow channel, but is less inclined
  w.r.t. the surface normal. At the two points where a line-of-sight
  enters and leaves the flow channel, discontinuities in the inclination,
  gamma , the velocity v, and the azimuth, phi , of the magnetic field
  vector w.r.t. the plane perpendicular to the line-of-sight produce
  V-asymmetries. Assuming an axially symmetric penumbra, we investigate
  the azimuthal dependence N(psi ) for a mid-penumbral radius. We find:
  (1) Without including anomalous dispersion, N(psi ) is symmetric
  w.r.t. the line that connects disk center to the center of the spot. (2)
  Including anomalous dispersion, this symmetry is broken. We demonstrate
  that this is due to the difference in azimuth, triangle phi (psi ),
  between the flow channel and the background that varies along the
  penumbral circle. For Fe I 630.2 nm this effect is found to be of
  minor relevance leading to essentially symmetric N-maps, whereas strong
  asymmetries are predicted for Fe I 1564.8 nm. Our results provide an
  explanation for recent observational findings.

Title: Time-slice diagrams of solar granulation
Authors: Müller, D. A. N.; Steiner, O.; Schlichenmaier, R.; Brandt,
   P. N.
Bibcode: 2001SoPh..203..211M
Altcode:
  From a series of 1400 white-light images of solar granulation spanning
  a time period of 8.2 hours, skeletal plots of time-slice diagrams are
  derived showing intergranular lane positions as a function of time. The
  diagrams permit to automatically track, classify, and relate 42 186
  granules. Recurrently fragmenting granules are found that survive
  by means of their descendants for more than 3 hours. Such long-lived
  active granules tend to have a mean spatial distance along the slice
  of about 10 Mm. This distance decreases with decreasing minimal
  required lifetime. Since active granules are expected to generate a
  steadily divergent flow over a long period of time, it is suggested
  to identify them as a source of the mesogranular flow. Deficiencies
  of the time-slice analysis are discussed. The relative frequency of
  different types of granules and the granule decay time as derived
  from the time-slice diagrams are compared with corresponding results
  of previous works.

Title: Radiative properties of magnetic elements. I. Why are vec
    G-band bright points bright?
Authors: Steiner, O.; Hauschildt, P. H.; Bruls, J.
Bibcode: 2001A&A...372L..13S
Altcode:
  Photospheric magnetic elements are most conspicuously visible in
  high-resolution G-band filtergrams. We show that their enhanced
  contrast in the G-band is due to a reduction of the CH abundance by
  dissociation in the deep photospheric layers of the flux tube, where
  it is hotter than in the surrounding atmosphere. As a consequence, the
  CH-lines weaken, allowing more of the continuum to ``shine'' through
  the forest of G-band CH-lines. We suggest that other molecular bands
  or atomic lines may exhibit a similar behaviour.

Title: Understanding Small Solar Magnetic Structures: Comparing
    Numerical Simulations to Observations
Authors: Leka, K. D.; Steiner, O.
Bibcode: 2001ApJ...552..354L
Altcode:
  We present direct comparisons of small magnetic structures observed
  in the solar photosphere with the results from numerical simulations
  of those structures. We compare diagnostic signatures derived
  from emergent Stokes polarization spectra from both the observed
  and model atmospheres, the former recorded with the National Solar
  Observatory/High Altitude Observatory Advanced Stokes Polarimeter,
  the latter from a fully dynamic MHD simulation of a magnetic flux
  sheet in a convective atmosphere. We focus on the asymmetries in the
  Stokes V spectra and find, first and foremost, that the asymmetries
  from the observed Stokes I and V in and around solar pores and azimuth
  centers (ACs) are quantitatively comparable to those derived from
  the simulation. We also find enhanced Stokes V asymmetry on the
  periphery of pores and ACs. We interpret this as a consequence of
  strong downdrafts in the surroundings of these magnetic structures,
  accompanied by the expansion of the magnetic field lines with height
  above these field-free downdrafts (the ``canopy effect''). The
  magnetic canopy can be present whether or not there is a continuum
  signature (i.e., a dark ``pore''). Not surprisingly, the patterns
  and magnitudes of asymmetries scale with the size of the magnetic
  element. In the interior of the pores and ACs, we find evidence for
  mixed up- and downflows, with little spatial correlation between the
  zero-crossing shift of the V profile and the V amplitude. Finally,
  we report on asymmetries observed in the linear polarization
  P<SUB>lin</SUB>(λ)=[Q(λ)<SUP>2</SUP>+U(λ)<SUP>2</SUP>]<SUP>1/2</SUP>,
  finding further support for the presence of the magnetic canopy
  from those diagnostics. We additionally present expectations for
  spectropolarimetric observations at significantly higher spatial
  resolution.

Title: Why are G-Band Bright Points Bright?
Authors: Steiner, O.; Bruls, J.; Hauschildt, P. H.
Bibcode: 2001ASPC..236..453S
Altcode: 2001aspt.conf..453S
  No abstract at ADS

Title: The Formation of Asymmetric Stokes V Profiles in the Presence
    of a Magnetopause
Authors: Steiner, O.
Bibcode: 2001ASPC..236..587S
Altcode: 2001aspt.conf..587S
  No abstract at ADS

Title: Chromosphere: Magnetic Canopy
Authors: Steiner, O.
Bibcode: 2000eaa..bookE2264S
Altcode:
  The magnetic canopy is a layer of magnetic field which is directed
  parallel to the solar surface and located in the low CHROMOSPHERE,
  overlying a field-free region of the SOLAR PHOTOSPHERE. It has a field
  strength of the order of 0.01 T and covers a large area fraction of
  the solar surface. The magnetic canopy can be compared with the canopy
  of the rain forest: the tree-trunks correspond to the ...

Title: The formation of asymmetric Stokes V profiles in the presence
    of a magnetopause
Authors: Steiner, Oskar
Bibcode: 2000SoPh..196..245S
Altcode:
  A magnetopause that separates two regimes of different flow, additional
  to the separation of a magnetic field from a field-free plasma, gives
  rise to the formation of asymmetric Stokes profiles. Using a simple
  two-layer model atmosphere, where one layer comprises a magnetic field,
  the other being field-free, it is shown by analytical derivation that
  a wide variety of Stokes V profiles can be produced, having amplitude
  asymmetries δa in the range −∞≤δa≤∞. These include
  two-humped V profiles, which have two lobes of equal sign. For the
  most simple models, the asymmetry depends on the ratio of continuum
  intensity to the Planck radiation intensity of the magnetic layer
  at the wavelength of the spectral line under consideration, and
  on the line depth. Two-humped profiles (|δa|&gt;1) require the
  temperature of the magnetic layer to surpass the temperature of the
  line-core forming region, implying a temperature inversion, so that
  the V profile is partially in emission. The confrontation of this
  formation scenario with properties of observed one-lobe profiles of
  quiet-Sun network regions is inconclusive due to insufficient spatial
  resolution and lack of a sufficient sample of simultaneously recorded
  Stokes spectral lines of varying line depths. It seems, however, to be
  in good agreement with the observed frequent occurrence of abnormal
  V profiles of the very strong Na i D<SUB>2</SUB> and D<SUB>2</SUB>
  spectral line. A possible observational verification for the present
  formation scenario of abnormal Stokes V profiles and a novel method
  of Stokes inversion are discussed.

Title: Strong Stokes V asymmetries of photospheric spectral lines:
    What can they tell us about the magnetic field structure?
Authors: Grossmann-Doerth, U.; Schüssler, M.; Sigwarth, M.;
   Steiner, O.
Bibcode: 2000A&A...357..351G
Altcode:
  In an attempt to identify the mechanism responsible for the extremely
  asymmetric Stokes V profiles which were recently observed we analyzed
  several simple atmospheric configurations with separated layers of mass
  flow and magnetic field. We found that under appropriate conditions
  the models are capable of producing the observed one-lobe profiles.

Title: Flux Tube Dynamics
Authors: Steiner, O.
Bibcode: 1999ASPC..184...38S
Altcode:
  We propose that the observed fragmentation of magnetic elements is
  due to their inherent liability to the interchange instability. The
  convective collapse and numerical simulations of the formation of
  intense magnetic flux sheets including spectral signatures of the
  formation process are discussed. We suggest that the mean downflow
  measured in magnetic elements is due to a fraction of an ensemble of
  magnetic elements being in the formation phase at any given time. It is
  shown that observed Stokes V profiles of magnetic elements are actua
  lly an average of spatially strongly varying profiles with a delicate
  balance of positive and negative contributions to the area asymmetry.

Title: Understanding Small Solar Magnetic Elements: Comparing Models
    and Observations
Authors: Leka, K. D.; Steiner, O.; Grossmann-Doerth, U.
Bibcode: 1999AAS...194.5507L
Altcode: 1999BAAS...31R.911L
  We perform direct comparisons of high-resolution spectropolarimetric
  observations with a full MHD model of the magnetized solar
  atmosphere. In this manner we investigate the evolution and dynamics of
  small magnetic elements by fully utilizing the diagnostics available
  with Stokes spectropolarimetry, both computed and observed. The model
  is a 2-D time-dependent numerical simulation of a small (~ 600 km
  diameter) magnetic feature embedded in a non-magnetized atmosphere
  (Steiner et al., 1998). At select time-steps, synthetic emergent
  Stokes I and V profiles are computed using a polarized radiation
  transfer code. The data consist of Stokes I and V spectra from the
  Advanced Stokes Polarimeter for seventeen small magnetic elements
  located near disk-center. For both the observed and computed Stokes
  spectra, diagnostics are computed including the emergent continuum
  intensity, V-crossing shift, and amplitude and area asymmetries of
  the V-profile. We find that it is possible to differentiate between
  salient processes occurring in the magnetic atmosphere (strong flows,
  gradients, etc.) by their spectropolarimetric signature; from this,
  we determine the dominant processes present in the observed magnetic
  structures. The results are extremely encouraging. We find good
  qualitative agreement between the amplitude and area asymmetries
  and their spatial variation. Quantitatively, the agreement is
  surprisingly good in many cases. While limitations exist for both
  the model and observations, this stringent test allows us to comment
  on the dynamics and possible evolutionary differences present in the
  observed magnetic features. This work is funded in part by NSF grant
  ATM-9710782. Reference: - Steiner, O., Grossmann-Doerth, U., Knolker,
  M., Schussler, M.: 1998, ApJ 495, 468

Title: Small Scale Magnetic Flux Tubes in the Photosphere: A
    Simulation Perspective
Authors: Steiner, O.
Bibcode: 1999ASPC..183...17S
Altcode: 1999hrsp.conf...17S
  No abstract at ADS

Title: 2D radiative equilibrium models of magnetic flux tubes
Authors: Hasan, S. S.; Kalkofen, W.; Steiner, O.
Bibcode: 1999ASSL..243..409H
Altcode: 1999sopo.conf..409H
  No abstract at ADS

Title: The formation of extremely asymmetric Stokes V profiles
Authors: Steiner, O.; Grossmann-Doerth, U.; Schüssler, M.; Sigwarth,
   M.
Bibcode: 1999AGAb...15R..10S
Altcode: 1999AGM....15..A11S
  Recent polarimetric observations at high spatial resolution (&lt;
  1 arcsec) and with high polarimetric accuracy (noise of Stokes V/I_c
  &lt; 3 cdot 10^{-4}) have revealed that about 10% of all Stokes V
  profiles of a quiet Sun region have an abnormal shape that strongly
  deviates from the more common, nearly antisymmetric profiles. 35% of the
  abnormal Stokes V profiles are of one-wing type, where the profile shows
  essentially one lobe only. We show, that a strongly asymmetric Stokes
  V profile can be obtained when the atmosphere, in which the profile
  is formed, is divided into two or more layers of different magnetic,
  flow, and thermal properties. A simple configuration of that kind
  (sometimes referred to as magnetic canopy) consists of a layer of
  plasma at rest with a magnetic field component parallel to the line
  of sight, located on top of a field-free layer with downdraft. The
  Stokes V asymmetry in this case sensitively depends on the position
  of the layers interface and may assume values up to about 80%. An
  asymmetry of nearly 100% (corresponding to a one-wing profile) is
  obtained when the plasma below the magnetic canopy is relatively cool,
  giving rise to the formation of a strong, redshifted spectral line in
  the field-free plasma beneath the canopy. If the core of this line is
  formed at lower temperature than the temperature of the canopy layer,
  the red wing of the resulting Stokes V profile is driven into emission,
  leading to a ``pathological'' V profile.

Title: Meso and supergranulation in two-dimensional simulation of
    solar convection
Authors: Steiner, O.
Bibcode: 1999AGAb...15...92S
Altcode: 1999AGM....15..P10S
  A two-dimensional hydrodynamic simulation of a thin surface layer
  of the solar convection zone, encompassing a horizontal span of 150
  Mm and a depth of 1 Mm, is carried out. An additional 0.5 Mm height
  includes the photospheric layer. Radiation transfer using the OPAL
  Rosseland mean opacity is taken into account as well as Hydrogen
  ionization. The simulation shows granule evolution of the well known
  dichotomous character: granules either dissolve by shrinking or they
  fragment into smaller granules. The maximum horizontal granule size
  in the simulation is about 3.5 Mm. The Fourier decomposition of
  the horizontal velocity near the solar surface (tau_c = 1) shows
  a local maximum in amplitude at around 5-7 Mm, which we identify
  with mesogranular flow. The maximum amplitude is found at 50 Mm,
  corresponding to supergranular flow. Cork tracks visualize these
  findings. The occurrence of supergranules in this shallow simulation
  domain supports recent results from local helioseismology, suggesting
  that supergranulation pertains to a thin surface layer only. We discuss
  possible interpretation of the simulation results.

Title: Convective intensification of solar surface magnetic fields:
    results of numerical experiments
Authors: Grossmann-Doerth, U.; Schuessler, M.; Steiner, O.
Bibcode: 1998A&A...337..928G
Altcode:
  The concentration of magnetic flux by convective flows in the solar
  surface layers is studied by means of two-dimensional numerical
  simulations with radiative transfer. We follow the evolution of an
  initially homogeneous, vertical magnetic field, starting from an
  evolved state of simulated solar granulation. The results of three
  simulation runs with initial field strengths, B_0, of 100 G, 200 G,
  and 400 G, respectively, are shown. In all cases, horizontal convective
  flows rapidly sweep magnetic flux into the intergranular downflow
  channels. The field is further amplified up to kilogauss values by
  partial evacuation due to a strongly accelerated downflow within
  the magnetic structure. The value of the field strength reached at
  a given depth and the size of the flux concentrations grows with the
  initial field strength (i.e., the amount of magnetic flux within the
  computional box). In the case of B_0 = 400 G, the downflow within the
  flux concentration becomes so strong that it `bounces' off the high
  density plasma in the deeper layers; the resulting upflow leads to a
  strong, upward moving shock and to the dispersal of the flux sheet after
  a lifetime of about 200 s. In the cases with less magnetic flux (B_0 100
  G, 200 G), the downflow is less vigorous and the flux concentrations
  persist to the end of the simulation (about 5 minutes). Radiation
  diagnostics in the continuum and in spectral lines predicts observable
  signatures of the intensification process. The accelerated downflow
  leads to a conspicuous Doppler shift and a negative area asymmetry of
  Stokes V-profiles of spectral lines, while the intensification of the
  magnetic field may be detectable through the `magnetic line ratio'
  method in the visible and by direct Zeeman splitting of magnetically
  sensitive lines in the infrared wavelength ranges.

Title: On the reliability of Stokes diagnostics of magnetic elements
    away from solar disc centre
Authors: Solanki, S. K.; Steiner, O.; Buente, M.; Murphy, G.; Ploner,
   S. R. O.
Bibcode: 1998A&A...333..721S
Altcode:
  {The spectropolarimetric signature of models of small-scale magnetic
  features is well understood at the centre of the solar disc, but
  has been little studied near the solar limb, mainly because the
  detailed geometry of the flux tubes must then be taken into account
  in a realistic analysis. We present multi-ray calculations of Stokes
  profiles through arrays of 2-D magnetohydrostatic models of small flux
  tubes. We compare the Stokes profile shapes and Stokes based diagnostics
  (Q to V ratio, V amplitude, magnetic line ratio, centre of gravity
  wavelengths, etc.) resulting from plane-parallel and 2-D flux-tube
  models at different limb distances for two lines in the visible and
  an infrared H-band line. For the visible lines around 5250 Angstroms
  all the diagnostics we have studied, with the exception of the Q and U
  to V ratio, are significantly affected by the finite size of the flux
  tubes and the passage of the rays through non-magnetic material near
  the limb. We show that magnetic filling factors and the global magnetic
  flux may be underestimated using the usual calibration techniques. In
  addition, near the solar limb the magnetic line ratio can move into
  a regime that is forbidden according to simpler models. The spatially
  averaged longitudinal field derived from the centre-of-gravity method
  also becomes strongly model dependent. The thermal structure of the
  non-magnetic atmosphere appears to play a particularly important role
  in determining the values of these diagnostic parameters. The infrared
  line at 1.5648 mu m, on the one hand, reacts little to the external
  atmosphere and provides superior diagnostics of both the magnetic field
  strength and filling factor. On the other hand, for a flux tube with
  a sharp boundary this line shows little dependence on the flux-tube
  diameter, in contrast to the earlier findings of Zayer et al. (1989). }

Title: Dynamical Interaction of Solar Magnetic Elements and Granular
Convection: Results of a Numerical Simulation
Authors: Steiner, O.; Grossmann-Doerth, U.; Knölker, M.; Schüssler,
   M.
Bibcode: 1998ApJ...495..468S
Altcode:
  Nonstationary convection in the solar photosphere and its
  interaction with photospheric magnetic structures (flux sheets in
  intergranular lanes) have been simulated using a numerical code
  for two-dimensional MHD with radiative energy transfer. Dynamical
  phenomena are identified in the simulations, which may contribute to
  chromospheric and coronal heating. Among these are the bending and
  horizontal displacement of a flux sheet by convective flows and the
  excitation and propagation of shock waves both within and outside the
  magnetic structure. Observational signatures of these phenomena are
  derived from calculated Stokes profiles of Zeeman-sensitive spectral
  lines. We suggest that the extended red wings of the observed Stokes
  V profiles are due to downward coacceleration of magnetized material
  in a turbulent boundary layer between the flux sheet and the strong
  external downflow. Upward-propagating shocks in magnetic structures
  should be detectable if a time resolution of about 10 s is achieved,
  together with a spatial resolution that allows one to isolate individual
  magnetic structures. Determination of the complicated internal dynamics
  of magnetic elements requires observations with a spatial resolution
  better than 100 km in the solar photosphere.

Title: Computational methods for astrophysical fluid flow
Authors: Steiner, O.; Gautschy, A.
Bibcode: 1998cmaf.conf.....S
Altcode:
  No abstract at ADS

Title: Numerical simulations of magnetic flux sheets.
Authors: Steiner, O.; Knölker, M.; Schüssler, M.
Bibcode: 1997smf..conf...31S
Altcode:
  Non-stationary convection in the solar photosphere and its interaction
  with photospheric magnetic structures (flux sheets in intergranular
  lanes) has been simulated using a numerical code for two-dimensional
  MHD with radiative transfer. Dynamical phenomena, which may contribute
  to chromospheric and coronal heating, like bending and horizontal
  displacement of a flux sheet by convective flows as well as the
  excitation and propagation of shock waves within and outside the
  magnetic structure are found. Observational signature of transversal
  displacement and shocks are derived. It is shown that upward propagating
  shocks in magnetic structures should be detectable. The evolution of
  an initially homogeneous vertical magnetic field is followed, starting
  from an evolved state of a two-dimensional numerical simulation of
  solar granulation.

Title: Convective intensification of magnetic fields at the solar
    surface.
Authors: Steiner, O.
Bibcode: 1996NAWG.1996..185S
Altcode:
  The evolution of an initially homogeneous vertical magnetic field is
  followed, starting from an evolved state of a 2D numerical simulation of
  solar granulation. The field is concentrated in the intergranular lane
  by the combined action of flux expulsion and field intensification by
  the downflow. A flux sheet forms with a maximum field strength of 1600
  G at the solar surface, a value well above the equipartition field
  strength of about 700 G. The rapid downflow within the flux sheet
  bounces off the high density plasma in the deeper layers of the flux
  sheet; the resulting upflow leads to a strong, upward moving shock and
  to the destruction of the flux sheet after a lifetime of about 200 s.

Title: Polarized Radiation Diagnostics of Magnetohydrodynamic Models
    of the Solar Atmosphere
Authors: Steiner, O.; Grossmann-Doerth, U.; Schüssler, M.; Knölker,
   M.
Bibcode: 1996SoPh..164..223S
Altcode:
  Solar magnetic elements and their dynamical interaction with
  the convective surface layers of the Sun are numerically
  simulated. Radiation transfer in the photosphere is taken into
  account. A simulation run over 18.5 minutes real time shows that the
  granular flow is capable of moving and bending a magnetic flux sheet
  (the magnetic element). At times it becomes inclined by up to 30°
  with respect to the vertical around the level τ<SUB>5000</SUB> =
  1 and it moves horizontally with a maximal velocity of 4 km/s. Shock
  waves form outside and within the magnetic flux sheet. The latter
  cause a distinctive signature in a time series of synthetic Stokes
  V-profiles. Such shock events occur with a mean frequency of about
  2.5 minutes. A time resolution of at least 10 seconds in Stokes V
  recordings is needed to reveal an individual shock event by observation.

Title: Convective intensification of photospheric magnetic fields.
Authors: Schüssler, M.; Grossmann-Doerth, U.; Steiner, O.; Knölker,
   M.
Bibcode: 1996AGAb...12...89S
Altcode:
  No abstract at ADS

Title: Simulation of the Interaction of Convective Flow with Magnetic
    Elements in the Solar Atmosphere.
Authors: Steiner, O.; Grossmann-Doerth, U.; Knoelker, M.; Schuessler,
   M.
Bibcode: 1995RvMA....8...81S
Altcode:
  No abstract at ADS

Title: Dynamic interaction of convection with magnetic flux sheets:
    first results of a new MHD code
Authors: Steiner, O.; Knölker, M.; Schüssler, M.
Bibcode: 1994ASIC..433..441S
Altcode:
  No abstract at ADS

Title: Flux Tube Shredding Its Infrared Signature
Authors: Bunte, M.; Steiner, O.; Solanki, S. K.; Pizzo, V. J.
Bibcode: 1994IAUS..154..459B
Altcode:
  No abstract at ADS

Title: Theoretical Models of Magnetic Flux Tubes: Structure and
    Dynamics
Authors: Steiner, O.
Bibcode: 1994IAUS..154..407S
Altcode:
  No abstract at ADS

Title: The upper photosphere and lower chromosphere of small-scale
    magnetic features
Authors: Solanki, S. K.; Bruls, J. H. M. J.; Steiner, O.; Ayres, T.;
   Livingston, W.; Uitenbroek, H.
Bibcode: 1994ASIC..433...91S
Altcode:
  No abstract at ADS

Title: MHD simulations with adaptive mesh refinement
Authors: Steiner, O.; Grossmann-Doerth, U.; Knölker, M.; Schüssler,
   M.
Bibcode: 1994smf..conf..282S
Altcode:
  No abstract at ADS

Title: Simulation of magneto-convection with radiative transfer
Authors: Steiner, O.; Grossmann-Doerth, U.; Knölker, M.; Schüssler,
   M.
Bibcode: 1994smf..conf..286S
Altcode:
  No abstract at ADS

Title: Centre-to-limb variation of the Stokes V asymmetry in solar
    magnetic flux tubes
Authors: Buente, M.; Solanki, S. K.; Steiner, O.
Bibcode: 1993A&A...268..736B
Altcode:
  The center-to-limb variation (CLV) of synthetic Stokes V line
  profiles of the spectral lines Fe 15250.22 A and Fe I 5083.35 A is
  computed and compared with observations. The basic elements of the
  hydromagnetic model used to calculate the Stokes V profiles consist
  of a vertical cylindrical flux tube surrounded by a field-free plasma
  in stationary motion with a downflow along the tube boundary and
  an upflow further away from it. It is shown that an array of such
  magnetic flux tubes reproduces the peculiar observed CLV of the Stokes
  V asymmetry, in particular the sign reversal of the asymmetry near the
  limb. We determine a minimum number of model components needed for the
  reproduction of the Stokes V area asymmetry and study the influence of
  various free model parameters on it. Satisfactory agreement between
  synthetic and observed Stokes V profiles can only be achieved by
  including a considerable amount of realism into the model such as
  a granular temperature-velocity correlation. This suggests that the
  basic picture of magnetic structures in the quiet solar network and
  active region plages is correct.

Title: On the interchange instability of solar magnetic flux tubes. I
    - The influence of magnetic tension and internal gas pressure
Authors: Buente, M.; Steiner, O.; Pizzo, V. J.
Bibcode: 1993A&A...268..299B
Altcode:
  Small magnetic flux tubes at the solar surface are known to be
  interchange-unstable. Previous studies of this instability have focused
  on evacuated tubes in the thin tube approximation, thereby neglecting
  magnetic tension forces and internal atmospheres. We have extended the
  analysis to study the influence of these two missing components. An
  internal atmosphere can either have a stabilizing or destabilizing
  effect, depending upon the details of the prescribed gas pressure
  stratification. Magnetic tension forces in general stabilize the tubes
  by reducing the curvature of the boundary. For evacuated numerical
  models we find that the instability can be suppressed by a critical
  whirl flow of 2.2 km/s surrounding the tubes. This is considerably
  lower than previously found for evacuated thin tube structures. For
  tubes in temperature equilibrium with their surroundings this critical
  whirl velocity is even lower, while temperature differences at equal
  geometric height increase its value. The sharp interface between
  the magnetic field and the whirl flow is due to the Kelvin-Helmholtz
  instability (KHI). However, the boundary layer of finite width at the
  tube surface might suppress the KHI, and hence make the whirl flow
  mechanism feasible, if the tube is highly evacuated at the relevant
  height of the atmosphere.

Title: CA II K Line Diagnostics of Two Dimensional Models of the
    Solar Chromosphere
Authors: Solanki, S. K.; Buente, M.; Steiner, O.; Uitenbroek, H.
Bibcode: 1992ASPC...26..294S
Altcode: 1992csss....7..294S
  No abstract at ADS

Title: MHD simulations with adaptive mesh refinement.
Authors: Steiner, O.; Grossmann-Doerth, U.; Knölker, M.; Schüssler,
   M.
Bibcode: 1992AGAb....7..213S
Altcode:
  No abstract at ADS

Title: Two-dimensional models of the solar chromosphere. I - The CA
II K line as a diagnostic: 1.5-D radiative transfer
Authors: Solanki, S. K.; Steiner, O.; Uitenbroeck, H.
Bibcode: 1991A&A...250..220S
Altcode:
  Ca II K line calculations for a 5-level atom and partial frequency
  redistribution along multiple rays passing through 2D MHD models of
  magnetic flux tubes in the solar atmosphere are presented. Temperature
  stratifications corresponding to various empirical chromospheric
  models are incorporated into the models. The influence of a number
  of model parameters on individual and spatially averaged line
  profiles is considered in detail. The profiles are also compared
  with observations. It is found that the present models can, at
  least qualitatively, reproduce a wide variety of observations if the
  temperature within the magnetic component lies between that of model
  F of Vernazza et al. (1981) and of model VALP of Ayres et al. (1986)
  and if the temperature in the nonmagnetic part of the atmosphere
  corresponds to that of the COOLC model of Ayres et al. Observations
  that are consistent with this model are presented.

Title: Fast solution of radiative transfer problems using a method
    of multiple grids
Authors: Steiner, O.
Bibcode: 1991A&A...242..290S
Altcode:
  A method of multiple grids of the second kind is used to solve two
  basic radiative transfer problems: the spectral line transfer in a
  homogeneous slab of two-level atoms and a two-dimensional LTE model
  atmosphere in radiative equilibrium. The employed multigrid method
  (W-cycle) alternately performs coarse-grid corrections and smoothing
  steps, the latter in the form of an accelerated Lambda-iteration. The
  new iterative method preserves all the advantages of approximate
  operator techniques, but convergence is considerably improved. In all
  the relevant examples of line transfer calculations made, the multigrid
  method is faster by a factor that varies from 4 to more than 20 with
  respect to the CPU time needed by an accelerated Lambda-iteration based
  on a nonlocal approximate operator. The two-dimensional slab problem
  even shows speedup factors as high as 40. Grid refinement generally
  improves the convergence rate.

Title: Center-to-limb variation of the Stokes V asymmetry in solar
    magnetic flux tubes.
Authors: Bünte, M.; Steiner, O.; Solanki, S. K.
Bibcode: 1991sopo.work..468B
Altcode:
  The center-to-limb-variation of synthetic Stokes V line profiles
  of the spectral line Fe I 5250.22 Å is presented and compared with
  observations. These synthetic profiles are calculated using models
  that contain the main features of the current basic pictures of small
  scale magnetic fields on the Sun.

Title: Fast Solution of Radiative Transfer Problems with a Multi-Grid
    Method
Authors: Steiner, O.
Bibcode: 1991ASIC..341...19S
Altcode: 1991sabc.conf...19S
  No abstract at ADS

Title: How magnetic is the solar chromosphere?
Authors: Solanki, S. K.; Steiner, O.
Bibcode: 1990A&A...234..519S
Altcode:
  The lower solar chromosphere is thought to have a very inhomogeneous
  temperature structure, with hot magnetic flux tubes surrounded by cool
  (T less than 4000 K) nonmagnetic gas (Ayres et al., 1986). The effect
  of such a thermally bifurcated atmosphere on the structure of the
  magnetic field in the chromosphere is considered. It is shown that
  magnetic flux tubes expand much more rapidly if the atmosphere is
  thermally bifurcated than if it is homogeneous. They merge and form a
  magnetic canopy with an almost horizontal base which does not exceed
  approximately 800-1000 km above tau = 1, irrespective of the magnetic
  filling factor. Hence the middle and upper chromosphere is filled with
  a magnetic field almost everywhere on the sun. The consequences of this
  result both for the sun and for other late type stars are discussed.

Title: Structure of solar magnetic fluxtubes from the inversion of
    Stokes spectra at disk center
Authors: Keller, C. U.; Steiner, O.; Stenflo, J. O.; Solanki, S. K.
Bibcode: 1990A&A...233..583K
Altcode:
  The paper presents an inversion procedure that derives the temperature
  stratification, the turbulent velocity, and the magnetic field strength
  of the photospheric layers of small-scale magnetic fields from observed
  Stokes V spectra and the continuum intensity. The inversion is based
  on the determination of a small number of model flux parameters by a
  nonlinear least squares fitting algorithm. The minimization of the sum
  of the squared differences between observed and synthetic observables
  makes it possible to determine the temperature stratification and the
  magnetic field strength.

Title: A rapidly converging temperature correction procedure using
    operator perturbation
Authors: Steiner, O.
Bibcode: 1990A&A...231..278S
Altcode:
  The Lambda-operator perturbation technique, known in NLTE line transfer
  calculations, is used for improving the temperature correction
  procedure. The approach presented here makes use of the formal
  solution to the radiative transfer equation and is capable of treating
  line blanketing effects by considering line opacity distribution
  functions. The method is shown to overcome all the problems related
  to the classical Lambda-iteration.

Title: Model calculations of solar magnetic fluxtubes and radiative
    transfer
Authors: Steiner, Oskar Urs
Bibcode: 1990PhDT.......358S
Altcode:
  No abstract at ADS

Title: Model Calculations of the Photospheric Layers of Solar
    Magnetic Fluxtubes
Authors: Steiner, O.; Stenflo, J. O.
Bibcode: 1990IAUS..138..181S
Altcode:
  No abstract at ADS

Title: A parametric survey of model solar fluxtubes
Authors: Steiner, O.; Pizzo, V. J.
Bibcode: 1989A&A...211..447S
Altcode:
  A parametric survey of numerically-generated, axially-symmetric
  two-dimensional magnetostatic fluxtubes is conducted to quantify the
  sensitivity of the properties of fluxtube models. It is found that
  heating of a static fluxtube atmosphere leads to an increase in the
  gas pressure above the level where the heating occurs, causing the
  fluxtube to fan out more rapidly with height. The heating also leads
  an increase in the opacity, causing to an upward shift in the surfaces
  of constant optical depth in the tube. The magnitude of these effects
  depends upon the temperature excess in the tube relative to that in
  the surrounding photosphere and upon the level in the tube atmosphere
  where heating is introduced. The consequences of these results for
  fluxtube models are discussed.

Title: Numerical models for solar magnetic fluxtubes
Authors: Steiner, O.; Pneuman, G. W.; Stenflo, J. O.
Bibcode: 1986A&A...170..126S
Altcode:
  A fully self-consistent method for constructing magnetostatic solutions
  for magnetic fluxtubes is presented, and the method is applied to three
  untwisted fluxtube configurations, two in which a sheet current exists
  at the surface of the tube, and one in which the the internal magnetic
  field varies continuously as a Gaussian. Convergence was obtained in
  all three cases, though the rate of convergence and accuracy of the
  solution were superior for the continuous field distribution case. For
  twisted fluxtubes, a maximum twist compatible with equilibrium is
  found for a given configuration, and the merging height is shown to
  decrease slightly with increased twist and to increase if the twist
  is concentrated more toward the surface of the tube.

