Author name code: wheatland
ADS astronomy entries on 2022-09-14
author:"Wheatland, Michael S." 
------------------------------------------------------------------------  

Title: Editorial Appreciation
Authors: Arregui, Iñigo; Leibacher, John; Mandrini, Cristina H.;
   van Driel-Gesztelyi, Lidia; Wheatland, Michael S.
Bibcode: 2022SoPh..297...11A
Altcode:
  No abstract at ADS

Title: The ASKAP Variables and Slow Transients (VAST) Pilot Survey
Authors: Murphy, Tara; Kaplan, David L.; Stewart, Adam J.; O'Brien,
   Andrew; Lenc, Emil; Pintaldi, Sergio; Pritchard, Joshua; Dobie, Dougal;
   Fox, Archibald; Leung, James K.; An, Tao; Bell, Martin E.; Broderick,
   Jess W.; Chatterjee, Shami; Dai, Shi; d'Antonio, Daniele; Doyle,
   Gerry; Gaensler, B. M.; Heald, George; Horesh, Assaf; Jones, Megan L.;
   McConnell, David; Moss, Vanessa A.; Raja, Wasim; Ramsay, Gavin; Ryder,
   Stuart; Sadler, Elaine M.; Sivakoff, Gregory R.; Wang, Yuanming; Wang,
   Ziteng; Wheatland, Michael S.; Whiting, Matthew; Allison, James R.;
   Anderson, C. S.; Ball, Lewis; Bannister, K.; Bock, D. C. -J.; Bolton,
   R.; Bunton, J. D.; Chekkala, R.; Chippendale, A. P.; Cooray, F. R.;
   Gupta, N.; Hayman, D. B.; Jeganathan, K.; Koribalski, B.; Lee-Waddell,
   K.; Mahony, Elizabeth K.; Marvil, J.; McClure-Griffiths, N. M.;
   Mirtschin, P.; Ng, A.; Pearce, S.; Phillips, C.; Voronkov, M. A.
Bibcode: 2021PASA...38...54M
Altcode: 2021arXiv210806039M
  The Variables and Slow Transients Survey (VAST) on the Australian
  Square Kilometre Array Pathfinder (ASKAP) is designed to detect
  highly variable and transient radio sources on timescales from 5
  s to $∼ 5$ yr. In this paper, we present the survey description,
  observation strategy and initial results from the VAST Phase I Pilot
  Survey. This pilot survey consists of $∼ 162$ h of observations
  conducted at a central frequency of 888 MHz between 2019 August and
  2020 August, with a typical rms sensitivity of $0.24 mJy beam^{-1}$
  and angular resolution of $12-20$ arcseconds. There are 113 fields,
  each of which was observed for 12 min integration time, with between
  5 and 13 repeats, with cadences between 1 day and 8 months. The total
  area of the pilot survey footprint is 5 131 square degrees, covering
  six distinct regions of the sky. An initial search of two of these
  regions, totalling 1 646 square degrees, revealed 28 highly variable
  and/or transient sources. Seven of these are known pulsars, including
  the millisecond pulsar J2039-5617. Another seven are stars, four of
  which have no previously reported radio detection (SCR J0533-4257, LEHPM
  2-783, UCAC3 89-412162 and 2MASS J22414436-6119311). Of the remaining
  14 sources, two are active galactic nuclei, six are associated with
  galaxies and the other six have no multi-wavelength counterparts and
  are yet to be identified.

Title: Modelling magnetic flux ropes in solar, stellar, and laboratory
    contexts
Authors: Wheatland, Michael S.
Bibcode: 2021cosp...43E1754W
Altcode:
  Magnetic flux ropes are generally accepted to be critical to the
  processes of energy storage and release in solar activity, and by
  extension stellar activity, and are fundamental to the description
  of laboratory plasma devices. In this talk I will present a review
  of the understanding of the physics of magnetic flux ropes in
  solar, stellar, and laboratory contexts, with a focus on methods
  for modelling flux ropes, and the insight they provide into the
  mechanisms for solar/stellar activity, and magnetic energy release
  more generally. I will highlight the similarities and differences in
  the physical assumptions underlying the models, and identify possible
  future directions for work.

Title: Editorial Appreciation
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
   Lidia; Wheatland, Michael S.
Bibcode: 2021SoPh..296...14L
Altcode:
  No abstract at ADS

Title: Failed Eruption Caused by Interacting Multi-current System
    in the Solar Corona
Authors: Yang, Kai; Cao, Wenda; Wheatland, Michael S.
Bibcode: 2021cosp...43E1780Y
Altcode:
  Solar flares are one of the most energetic activities of the Sun,
  and are caused by current systems in the solar corona. Sometimes the
  eruption of a current system is confined in the solar corona and fails
  to trigger a coronal mass ejection or jet. A multi-current system
  (multi-flux rope system) makes the confined/failed eruption process
  more complex. To further investigate this phenomenon, we conduct a
  data-driven zero-beta magnetohydrodynamics (MHD) simulation using the
  Message Passing Interface Adaptive Mesh Refinement Versatile Advection
  Code (MPI-AMRVAC). The initial condition is obtained by applying the
  three-dimensional nonlinear force-free model to an observed vector
  magnetogram from HMI. From the force-free magnetic field, three
  flux ropes are identified in the active region, and the results are
  compared with H$\alpha$ observation by the Goode Solar Telescope at
  Big Bear Solar Observatory. The MHD simulation is driven by the time
  series of the observed magnetogram and the inferred photospheric plasma
  velocity. The simulation and observation confirm an interaction between
  the three flux ropes, which leads to the initial eruption. With the
  development of the interaction, magnetic reconnection mixes the flux
  ropes and leads the system to a new stable state.

Title: The CME Initiation Mechanism
Authors: Wheatland, Michael S.
Bibcode: 2021cosp...43E.995W
Altcode:
  The kink and torus instabilities in a magnetic flux rope are the
  most popular mechanisms used to explain coronal mass ejections
  (CMEs). However, these instabilities apply to idealised magnetic field
  configurations, which may not match conditions on the Sun, and they
  occur in ideal MHD, so they do not explain the dissipation in the
  flare associated with the CME. In the standard (CHSKP) flare model
  dissipation is attributed to secondary processes, but this presents
  additional problems. Finally, even if these mechanisms operate, it
  is necessary to explain how the system becomes unstable. This talk
  presents a review of our current understanding of CME initiation,
  based on recent observations, theory, simulation, and results from
  laboratory plasma experiments.

Title: Reconstructing Highly-twisted Magnetic Fields
Authors: Demcsak, Victor; Yang, Kai; Wheatland, Michael S.; Mastrano,
   Alpha
Bibcode: 2021cosp...43E1732D
Altcode:
  We investigate the ability of a nonlinear force-free code to
  calculate highly-twisted magnetic field configurations using the
  Titov and D\'{e}moulin (1999) equilibrium field as a test case. The
  code calculates a force-free field using boundary conditions on the
  normal component of the field in the lower boundary, and the normal
  component of the current density over one polarity of the field in
  the lower boundary. The code can also use the current density over
  both polarities of the field in the lower boundary as a boundary
  condition. We investigate the accuracy of the reconstructions with
  increasing flux-rope twist number $N_{\textrm{t}}$, achieved by
  decreasing the buried line current in the model. We find that the code
  can approximately reconstruct the Titov-D\'{e}moulin field for twist
  numbers $N_{\textrm{t}} \approx 8.8$. This includes configurations
  with bald patches, for which the magnetic skeleton is accurately
  reproduced. We identify the limitations of our method for highly-twisted
  fields. The results have implications for our ability to reconstruct
  coronal magnetic fields from observational data.

Title: Self-consistent Grad-Rubin nonlinear force-free field
    extrapolation from weighted boundary conditions
Authors: Mastrano, Alpha; Yang, Kai; Wheatland, Michael S.
Bibcode: 2021cosp...43E1801M
Altcode:
  Vector magnetogram data are often used as photospheric boundary
  condition in coronal force-free field extrapolations. One class of
  field extrapolation method, Grad-Rubin extrapolation, is attractive
  because it requires only the values of vertical field strength
  and the force-free parameter $\alpha$ over one magnetic polarity
  on the surface as boundary conditions. In general, however, vector
  magnetogram data are not flux-balanced and not consistent with the
  force-free assumption. This leads to an inconsistency between the
  solution generated from the $\alpha$ values in the positive magnetic
  polarity region and that generated from the values in the negative
  polarity region. In this talk, we present a method to arrive at a
  self-consistent field extrapolation from vector magnetogram data using
  the Grad-Rubin method and we show its application to active regions
  12017 and 12673. The method allows the use of a weighted average of
  the boundary conditions of $\alpha$ on the two polarities. Different
  choices of the weighting lead to different solutions, and this freedom
  can be used to achieve better agreement between the model and magnetic
  structures inferred from short wavelength observations of the corona.

Title: A Flare-type IV Burst Event from Proxima Centauri and
    Implications for Space Weather
Authors: Zic, Andrew; Murphy, Tara; Lynch, Christene; Heald,
   George; Lenc, Emil; Kaplan, David L.; Cairns, Iver H.; Coward, David;
   Gendre, Bruce; Johnston, Helen; MacGregor, Meredith; Price, Danny C.;
   Wheatland, Michael S.
Bibcode: 2020ApJ...905...23Z
Altcode: 2020arXiv201204642Z
  Studies of solar radio bursts play an important role in understanding
  the dynamics and acceleration processes behind solar space weather
  events, and the influence of solar magnetic activity on solar system
  planets. Similar low-frequency bursts detected from active M-dwarfs
  are expected to probe their space weather environments and therefore
  the habitability of their planetary companions. Active M-dwarfs
  produce frequent, powerful flares which, along with radio emission,
  reveal conditions within their atmospheres. However, to date, only
  one candidate solar-like coherent radio burst has been identified from
  these stars, preventing robust observational constraints on their space
  weather environment. During simultaneous optical and radio monitoring
  of the nearby dM5.5e star Proxima Centauri, we detected a bright,
  long-duration optical flare, accompanied by a series of intense,
  coherent radio bursts. These detections include the first example of an
  interferometrically detected coherent stellar radio burst temporally
  coincident with a flare, strongly indicating a causal relationship
  between these transient events. The polarization and temporal structure
  of the trailing long-duration burst enable us to identify it as a type
  IV burst. This represents the most compelling detection of a solar-like
  radio burst from another star to date. Solar type IV bursts are strongly
  associated with space weather events such as coronal mass ejections
  and solar energetic particle events, suggesting that stellar type IV
  bursts may be used as a tracer of stellar coronal mass ejections. We
  discuss the implications of this event for the occurrence of coronal
  mass ejections from Proxima Cen and other active M-dwarfs.

Title: On Measuring Divergence for Magnetic Field Modeling
Authors: Gilchrist, S. A.; Leka, K. D.; Barnes, G.; Wheatland, M. S.;
   DeRosa, M. L.
Bibcode: 2020ApJ...900..136G
Altcode: 2020arXiv200808863G
  A physical magnetic field has a divergence of zero. Numerical error
  in constructing a model field and computing the divergence, however,
  introduces a finite divergence into these calculations. A popular metric
  for measuring divergence is the average fractional flux $\left\langle
  | {f}_{i}| \right\rangle $ . We show that $\left\langle | {f}_{i}|
  \right\rangle $ scales with the size of the computational mesh, and
  may be a poor measure of divergence because it becomes arbitrarily
  small for increasing mesh resolution, without the divergence actually
  decreasing. We define a modified version of this metric that does
  not scale with mesh size. We apply the new metric to the results of
  DeRosa et al., who measured $\left\langle | {f}_{i}| \right\rangle
  $ for a series of nonlinear force-free field models of the coronal
  magnetic field based on solar boundary data binned at different spatial
  resolutions. We compute a number of divergence metrics for the DeRosa et
  al. data and analyze the effect of spatial resolution on these metrics
  using a nonparametric method. We find that some of the trends reported
  by DeRosa et al. are due to the intrinsic scaling of $\left\langle |
  {f}_{i}| \right\rangle $ . We also find that different metrics give
  different results for the same data set and therefore there is value
  in measuring divergence via several metrics.

Title: Reconstructing Highly-twisted Magnetic Fields
Authors: Demcsak, Victor M.; Wheatland, Michael S.; Mastrano, Alpha;
   Yang, Kai E.
Bibcode: 2020SoPh..295..116D
Altcode: 2020arXiv200802985D
  We investigate the ability of a nonlinear force-free code to calculate
  highly-twisted magnetic field configurations using the Titov and
  Démoulin (Astron. Astrophys. 351:707, 1999) equilibrium field as
  a test case. The code calculates a force-free field using boundary
  conditions on the normal component of the field in the lower boundary,
  and the normal component of the current density over one polarity of the
  field in the lower boundary. The code can also use the current density
  over both polarities of the field in the lower boundary as a boundary
  condition. We investigate the accuracy of the reconstructions with
  increasing flux-rope surface twist number N<SUB>t</SUB>, achieved by
  decreasing the sub-surface line current in the model. We find that
  the code can approximately reconstruct the Titov-Démoulin field
  for surface twist numbers up to N<SUB>t</SUB>≈8.8 . This includes
  configurations with bald patches. We investigate the ability to recover
  bald patches, and more generally identify the limitations of our
  method for highly-twisted fields. The results have implications for our
  ability to reconstruct coronal magnetic fields from observational data.

Title: Self-consistent Nonlinear Force-Free Field Reconstruction
    from Weighted Boundary Conditions
Authors: Mastrano, A.; Yang, K. E.; Wheatland, M. S.
Bibcode: 2020SoPh..295...97M
Altcode: 2020arXiv200412510M
  Photospheric vector magnetogram data are often used as boundary
  conditions for force-free coronal magnetic field extrapolations. In
  general, however, vector magnetogram data are not consistent with the
  force-free assumption. In this article, we demonstrate a way to deal
  with inconsistent boundary data, by generalizing the "self-consistency
  procedure" of Wheatland and Régnier (Astrophys. J. Lett.700,
  L88, 2009). In that procedure, the inconsistency is resolved by an
  iterative process of constructing two solutions based on the values
  of the force-free parameter α on the two polarities of the field in
  the boundary (the P and N polarities), and taking uncertainty-weighted
  averages of the boundary α values in the P and N solutions. When the α
  values in the P and N regions are very different, the self-consistent
  solution may lose high α values from the boundary conditions. We
  show how, by altering the weighting of the uncertainties in the
  P or N boundary conditions, we can preserve high α values in the
  self-consistent solution. The weighted self-consistent extrapolation
  method is demonstrated on an analytic bipole field and applied to vector
  magnetogram data taken by the Helioseismic and Magnetic Imager (HMI)
  instrument on board the Solar Dynamics Observatory (SDO) spacecraft
  for NOAA active region AR 12017 on 2014 March 29.

Title: Relative Magnetic Helicity Based on a Periodic Potential Field
Authors: Yang, Kai E.; Wheatland, Michael S.; Gilchrist, Stuart A.
Bibcode: 2020ApJ...894..151Y
Altcode: 2020arXiv200408590Y
  Magnetic helicity is conserved under ideal magnetohydrodynamics and
  quasi-conserved even under a resistive process. The standard definition
  for magnetic helicity cannot be applied directly to an open magnetic
  field in a volume, because it is gauge-dependent. Instead, the relative
  magnetic helicity is widely used. We find that the energy of a potential
  magnetic field in a rectangular domain with periodic lateral boundary
  conditions is less than that of the field with a fixed normal component
  on all six boundaries. To make use of this lower energy potential
  field in the analysis of relative magnetic helicity, we introduce a
  new definition for magnetic helicity for the magnetic field, which
  involves the periodic potential field. We apply this definition to
  a sequence of analytic solutions and a numerical simulation. The
  results show that our new gauge-invariant helicity is very close
  to the current-carrying part of the relative magnetic helicity of
  the original magnetic field. We find also that the ratio between the
  current-carrying helicity and the relative magnetic helicity for the
  original and our defined relative helicity show different behavior. It
  seems that the new helicity is more sensitive to the component of the
  field due to the electric current in the volume, which is the source
  for instabilities and solar eruptive phenomena.

Title: Editorial Appreciation
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
   Lidia; Wheatland, Michael S.
Bibcode: 2020SoPh..295....9L
Altcode:
  No abstract at ADS

Title: Comparisons Between the Field Lines Using an Accelerating
    and a Constant Solar Wind model
Authors: Tasnim, S.; Cairns, Iver H.; Wheatland, M. S.; Li, B.; Zank,
   Gary P.
Bibcode: 2019JPhCS1332a2015T
Altcode:
  Magnetic field line mapping between the Sun and the Earth is important
  to trace the nonthermal particles. We generalize a recently developed
  mapping approach (B stepping) where this approach allows us to
  map the magnetic field lines by stepping along the local magnetic
  field direction. We employ an advanced solar wind model which
  includes acceleration, angular momentum conservation, and intrinsic
  non-radial velocities and magnetic fields at the inner boundary /
  source surface. We map the field lines using Wind spacecraft data
  for two solar rotation periods: one near a solar minimum between
  CR2118 and CR2119 and other CR1992 near a solar maximum. Maps using
  the accelerating solar wind model are compared with the maps using a
  constant solar wind model. On a broad scale, maps using two solar wind
  models for the same solar rotation periods are very similar. However,
  in a small scale, there are significant differences, e.g. differences
  are evident in connectivities, paths, and winding angles. In addition,
  field lines using the accelerating solar wind model are more azimuthally
  oriented for during the solar maximum. These differences demonstrate
  the significance of inclusion of the accelerating radial speed profile,
  intrinsic azimuthal velocity and magnetic field components.

Title: Mapping Magnetic Field Lines for an Accelerating Solar Wind
Authors: Tasnim, S.; Cairns, Iver H.; Li, B.; Wheatland, M. S.
Bibcode: 2019SoPh..294..155T
Altcode: 2019arXiv190708683T
  Mapping of magnetic field lines is important for studies of the
  solar wind and the sources and propagation of energetic particles
  between the Sun and observers. A recently developed mapping approach
  is generalized to use a more advanced solar wind model that includes
  the effects of solar wind acceleration, non-radial intrinsic magnetic
  fields and flows at the source surface/inner boundary, and conservation
  of angular momentum. The field lines are mapped by stepping along B
  and via a Runge-Kutta algorithm, leading to essentially identical
  maps. The new model's maps for Carrington rotation CR 1895 near
  solar minimum (19 April to 15 May 1995) and a solar rotation between
  CR 2145 and CR 2146 near solar maximum (14 January to 9 February
  2014) are compared with the published maps for a constant solar wind
  model. The two maps are very similar on a large scale near both solar
  minimum and solar maximum, meaning that the field-line orientations,
  winding angles, and connectivity generally agree very well. However,
  close inspection shows that the field lines have notable small-scale
  structural differences. An interpretation is that inclusion of the
  acceleration and intrinsic azimuthal velocity has significant effects
  on the local structure of the magnetic field lines. Interestingly,
  the field lines are more azimuthal for the accelerating solar wind
  model for both intervals. In addition, predictions for the pitch angle
  distributions (PADs) for suprathermal electrons agree at the 90 - 95%
  level with observations for both solar wind models for both intervals.

Title: Energy Balance in Avalanche Models for Solar Flares
Authors: Farhang, Nastaran; Wheatland, Michael S.; Safari, Hossein
Bibcode: 2019ApJ...883L..20F
Altcode: 2019arXiv190900195F
  The distributions of solar flare energies and waiting times have not
  been described simultaneously by a single physical model, yet. In this
  research, we investigate whether recent avalanche models can describe
  the distributions for both the released energies and waiting times
  of flares in an active region. Flaring events are simulated using the
  modified Lu and Hamilton model and also the optimized model. Applying
  a probability balance equation approach, we study the statistics of
  the simulated flaring events and investigate the origin of the observed
  power law in the flare frequency-size distribution. The results indicate
  that the power law originates in the distribution of transition rates
  (the distribution of the probabilities of transitions between different
  energies) rather than the distribution of the energy of the active
  region. It is also observed that the waiting-time distribution of
  simulated flaring events follows a q-exponential function, which
  approximates a simple Poisson distribution.

Title: Flare Reconnection-driven Magnetic Field and Lorentz Force
    Variations at the Sun’s Surface
Authors: Barczynski, Krzysztof; Aulanier, Guillaume; Masson, Sophie;
   Wheatland, Michael S.
Bibcode: 2019ApJ...877...67B
Altcode: 2019arXiv190405447B
  During eruptive flares, vector magnetograms show an increasing
  horizontal magnetic field and downward Lorentz force in the Sun’s
  photosphere around the polarity-inversion line (PIL). This behavior
  has often been associated with the implosion conjecture and has
  been interpreted as the result of either momentum conservation while
  the eruption moves upward or of the contraction of flare loops. We
  characterize the physical origin of these observed behaviors by
  analyzing a generic 3D magnetohydrodynamics simulation of an eruptive
  flare. Even though the simulation was not designed to recover the
  magnetic field and Lorentz force properties, it is fully consistent
  with them, and it provides key additional information for understanding
  them. The area where the magnetic field increases gradually develops
  between current ribbons, which spread away from each other and are
  connected to the coronal region. This area is merely the footprint of
  the coronal post-flare loops, whose contraction increases their shear
  field component and the magnetic energy density, in line with the ideal
  induction equation. For simulated data, we computed the Lorentz force
  density map by applying the method used in observations. We obtained an
  increase in the downward component of the Lorentz force density around
  the PIL, consistent with observations. However, this significantly
  differs from the Lorentz force density maps that are obtained directly
  from the 3D magnetic field and current. These results altogether
  question previous interpretations that were based on the implosion
  conjecture and momentum conservation with the coronal mass ejection,
  and rather imply that the observed increases in photospheric horizontal
  magnetic fields result from the reconnection-driven contraction of
  sheared flare loops.

Title: Editorial Appreciation
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
   Lidia; Wheatland, Michael S.
Bibcode: 2019SoPh..294....3L
Altcode:
  We are pleased to acknowledge, with sincere thanks, the following
  colleagues who supported the community by reviewing articles for Solar
  Physics during 2018.

Title: Very narrow coronal mass ejections producing solar energetic
    particles
Authors: Bronarska, K.; Wheatland, M. S.; Gopalswamy, N.; Michalek, G.
Bibcode: 2018A&A...619A..34B
Altcode:
  <BR /> Aims: Our main aim is to study the relationship between
  low-energy solar particles (energies below 1 MeV) and very narrow
  coronal mass ejections ("jets" with angular width ≤ 20°). <BR />
  Methods: For this purpose, we considered 125 very narrow coronal mass
  ejections (CMEs) from 1999 to 2003 that are potentially associated
  with low-energy solar particles (LESPs). These events were chosen on
  the basis of their source location. We studied only very narrow CMEs at
  the western limb, which are expected to have good magnetic connectivity
  with Earth. <BR /> Results: We found 24 very narrow CMEs associated
  with energetic particles such as ions (protons and <SUP>3</SUP>He),
  electrons, or both. We show that arrival times at Earth of energetic
  particles are consistent with onset times of the respective CMEs, and
  that in the same time intervals, there are no other potential sources
  of energetic particles. We also demonstrate statistical differences
  for the angular width distributions using the Kolmogorov-Smirnov
  test for angular widths for these 24 events. We consider a coherent
  sample of jets (mostly originating from boundaries of coronal holes)
  to identify properties of events that produce solar energetic particles
  (velocities, widths, and position angles). Our study presents a new
  approach and result: very narrow CMEs can generate low-energy particles
  in the vicinity of Earth without other activity on the Sun. The results
  could be very useful for space weather forecasting.

Title: Flare reconnection driven magnetic field and Lorentz force
    variations at the Sun's surface
Authors: Barczynski, Krzysztof; Aulanier, Guillaume; Masson, Sophie;
   Wheatland, Michael S.
Bibcode: 2018csc..confE..27B
Altcode:
  We show that the simulation is fully consistent with the observed
  increase of the photospheric horizontal magnetic field and electric
  currents around flaring PILs. The simulation also finds that the surface
  integral coming from the volume integral of the Maxwell stress tensor,
  as usually used in observational data analysis as the proxy of the
  Lorentz force, shows an increased downard component in the photosphere,
  as observed. But we also find that this proxy is significantly
  different from the true Lorentz force, which does not reveal this
  downward component. This result questions every previous interpretation
  based on the implosion conjecture and momentum conservation. However
  based on the analysis of the induction equation in the simulation,
  we unveil that the increase of the horizontal magnetic filed around
  active region PILs during eruptions is solely and exclusively result
  of the flare reconnection-driven contraction of flare loops.

Title: Nonlinear Force-free Modeling of Flare-related Magnetic Field
    Changes at the Photosphere and Chromosphere
Authors: Kleint, Lucia; Wheatland, Michael S.; Mastrano, Alpha;
   McCauley, Patrick I.
Bibcode: 2018ApJ...865..146K
Altcode: 2018arXiv180807079K
  Rapid and stepwise changes of the magnetic field are often observed
  during flares but cannot be explained by models yet. Using a 45 minute
  sequence of Solar Dynamics Observatory/Helioseismic and Magnetic
  Imager 135 s fast-cadence vector magnetograms of the X1 flare on 2014
  March 29 we construct, at each timestep, nonlinear force-free models
  for the coronal magnetic field. Observed flare-related changes in the
  line-of-sight magnetic field B <SUB>LOS</SUB> at the photosphere and
  chromosphere are compared with changes in the magnetic fields in the
  models. We find a moderate agreement at the photospheric layer (the
  basis for the models), but no agreement at chromospheric layers. The
  observed changes at the photosphere and chromosphere are surprisingly
  different, and are unlikely to be reproduced by a force-free model. The
  observed changes are likely to require a change in the magnitude of
  the field, not just in its direction.

Title: A Check on the Validity of Magnetic Field Reconstructions
Authors: Mastrano, A.; Wheatland, M. S.; Gilchrist, S. A.
Bibcode: 2018SoPh..293..130M
Altcode:
  We investigate a method to test whether a numerically computed model
  coronal magnetic field B departs from the divergence-free condition
  (also known as the solenoidality condition). The test requires a
  potential field B<SUB>0</SUB> to be calculated, subject to Neumann
  boundary conditions, given by the normal components of the model
  field B at the boundaries. The free energy of the model field may
  be calculated using 1/2 μ<SUB>0</SUB> ∫(B<SUP>−B<SUB>0</SUB>)
  2</SUP>d V , where the integral is over the computational volume of
  the model field. A second estimate of the free energy is provided
  by calculating 1/2 μ<SUB>0</SUB> ∫B<SUP>2</SUP>d V −1/2
  μ<SUB>0</SUB> ∫B<SUB>0</SUB><SUP>2</SUP>d V . If B is divergence
  free, the two estimates of the free energy should be the same. A
  difference between the two estimates indicates a departure from ∇
  ⋅B =0 in the volume. The test is an implementation of a procedure
  proposed by Moraitis et al. (Solar Phys.289, 4453, 2014) and is a
  simpler version of the Helmholtz decomposition procedure presented
  by Valori et al. (Astron. Astrophys.553, A38, 2013). We demonstrate
  the test in application to previously published nonlinear force-free
  model fields, and also investigate the influence on the results of
  the test of a departure from flux balance over the boundaries of the
  model field. Our results underline the fact that, to make meaningful
  statements about magnetic free energy in the corona, it is necessary to
  have model magnetic fields that satisfy the divergence-free condition
  to a good approximation.

Title: Photospheric Response to a Flare
Authors: Wheatland, Michael S.; Melrose, Donald B.; Mastrano, Alpha
Bibcode: 2018ApJ...864..159W
Altcode: 2018arXiv180803097W
  Flares produce sudden and permanent changes in the horizontal
  photospheric magnetic field. In particular, flares generally produce
  increased magnetic shear in the photospheric field along the neutral
  line. Recent observations also show that flares can produce sudden
  photospheric motion. We present a model for the observed changes as
  the response of the photosphere to a large-amplitude shear Alfvén
  wave propagating down from the corona on either side of the neutral
  line. The Alfvénic front is assumed to impact the photosphere close to
  the neutral line first and then successively further away with time,
  such that the line of impact coincides with the flare ribbon. The
  wave introduces magnetic shear and velocity shear. The magnetic shear
  introduced at the photosphere has the same sign on either side of
  the neutral line, while the velocity shear has the opposite sign. We
  discuss the possibility that this process is responsible for particle
  acceleration in flares.

Title: Mapping Magnetic Field Lines for an Accelerating Solar Wind
Authors: Tasnim, Samira; Wheatland, . M. S.; Cairns, Iver; Li, Bo
Bibcode: 2018cosp...42E3339T
Altcode:
  A new accelerating solar wind [Tasnim et al., 2018] is developed that
  includes conservation of angular momentum, deviations from corotation,
  and non-radial intrinsic velocity and magnetic field components from
  an inner boundary to beyond 1 AU. We fit the model to near-Earth
  observations of the Wind spacecraft for the solar rotation period
  between 19 April to 15 May 1995 (CR 1895). Later, we employ this
  accelerating solar wind to predict the magnetic field vectors and map
  the magnetic field lines. Note that magnetic field line mapping is
  important to trace the paths of solar energetic particles and electron
  beams in type III radio burst since superthermal beams move along the
  field lines from the Sun towards the Earth and even beyond. We map
  the magnetic field lines from the source surface towards 1 AU using
  the field line mapping algorithm developed by Li et al. [JGR,2016]. We
  compare these magnetic field lines with the field lines predicted by
  Li et al. [JGR,2016] using Schulte in den Baumen et al. [JGR,2012]'s
  model. The maps for accelerating and constant speed models are very
  similar. However, close comparisons show that the magnetic field lines
  for the radial speed model move further out than theaccelerating wind
  model. The obvious interpretation is that the accelerating solar wind
  is slower at small heliocentric distance (r) and so travels less far
  outward than the constant speed solar wind.

Title: Principle of Minimum Energy in Magnetic Reconnection in a
    Self-organized Critical Model for Solar Flares
Authors: Farhang, Nastaran; Safari, Hossein; Wheatland, Michael S.
Bibcode: 2018ApJ...859...41F
Altcode: 2018arXiv180410356F
  Solar flares are an abrupt release of magnetic energy in the Sun’s
  atmosphere due to reconnection of the coronal magnetic field. This
  occurs in response to turbulent flows at the photosphere that twist
  the coronal field. Similar to earthquakes, solar flares represent the
  behavior of a complex system, and expectedly their energy distribution
  follows a power law. We present a statistical model based on the
  principle of minimum energy in a coronal loop undergoing magnetic
  reconnection, which is described as an avalanche process. We show that
  the distribution of peaks for the flaring events in this self-organized
  critical system is scale-free. The obtained power-law index of 1.84 ±
  0.02 for the peaks is in good agreement with satellite observations
  of soft X-ray flares. The principle of minimum energy can be applied
  for general avalanche models to describe many other phenomena.

Title: Electric Currents in Geospace and Beyond.
Authors: Keiling, Andreas; Marghitu, Octav; Wheatland, Michael
Bibcode: 2018GMS...235.....K
Altcode:
  No abstract at ADS

Title: A Generalized Equatorial Model for the Accelerating Solar Wind
Authors: Tasnim, S.; Cairns, Iver H.; Wheatland, M. S.
Bibcode: 2018JGRA..123.1061T
Altcode:
  A new theoretical model for the solar wind is developed that includes
  the wind's acceleration, conservation of angular momentum, deviations
  from corotation, and nonradial velocity and magnetic field components
  from an inner boundary (corresponding to the onset of the solar
  wind) to beyond 1 AU. The model uses a solution of the time-steady
  isothermal equation of motion to describe the acceleration and
  analytically predicts the Alfvénic critical radius. We fit the
  model to near-Earth observations of the Wind spacecraft during the
  solar rotation period of 1-27 August 2010. The resulting data-driven
  model demonstrates the existence of noncorotating, nonradial flows
  and fields from the inner boundary (r = r<SUB>s</SUB>) outward and
  predicts the magnetic field B = (B<SUB>r</SUB>,B<SUB>ϕ</SUB>),
  velocity v = (v<SUB>r</SUB>,v<SUB>ϕ</SUB>), and density n(r,ϕ,t),
  which vary with heliocentric distance r, heliolatitude ϕ, and
  time t in a Sun-centered standard inertial plane. The description
  applies formally only in the equatorial plane. In a frame corotating
  with the Sun, the transformed velocity v' and a field B' are not
  parallel, resulting in an electric field with a component Ez'
  along the z axis. The resulting E'×B'=E'×B drift lies in the
  equatorial plane, while the ∇B and curvature drifts are out of
  the plane. Together these may lead to enhanced scattering/heating of
  sufficiently energetic particles. The model predicts that deviations
  δv<SUB>ϕ</SUB> from corotation at the inner boundary are common,
  with δv<SUB>ϕ</SUB>(r<SUB>s</SUB>,ϕ<SUB>s</SUB>,t<SUB>s</SUB>)
  comparable to the transverse velocities due to
  granulation and supergranulation motions. Abrupt changes in
  δv<SUB>ϕ</SUB>(r<SUB>s</SUB>,ϕ<SUB>s</SUB>,t<SUB>s</SUB>) are
  interpreted in terms of converging and diverging flows at the cell
  boundaries and centers, respectively. Large-scale variations in the
  predicted angular momentum demonstrate that the solar wind can drive
  vorticity and turbulence from near the Sun to 1 AU and beyond.

Title: Editorial Appreciation
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
   Lidia; Wheatland, Michael S.
Bibcode: 2018SoPh..293...14L
Altcode:
  No abstract at ADS

Title: A Study of External Magnetic Reconnection that Triggers a
    Solar Eruption
Authors: Zhou, G. P.; Zhang, J.; Wang, J. X.; Wheatland, M. S.
Bibcode: 2017ApJ...851L...1Z
Altcode:
  External magnetic reconnection (EMR) is suggested to play an
  essential role in triggering a solar eruption, but is rarely directly
  observed. Here, we report on a filament eruption on 2014 October 3
  that apparently involves the process of an early EMR. A total of 1.7 ×
  10<SUP>20</SUP> Mx flux was first canceled along the filament-related
  polarity inversion line over 12 hr, and then the filament axis started
  to brighten in extreme ultraviolet (EUV). An impulsive EUV brightening
  began 30 minutes later, and we attribute this to EMR, as it is located
  at the center of a bidirectional outflow with a velocity of 60-75 km
  s<SUP>-1</SUP> along large-scale magnetic loops from active regions
  NOAA 12178 and 12179, respectively, and over the filament mentioned
  above. Following the EMR, the filament was activated; then, partial
  eruption occurred 6 minutes later in the west, in which the decay
  index above the magnetic flux rope (MFR) reached the critical value of
  1.5. The observations are interpreted in terms of underlying magnetic
  flux cancelation leading to the buildup and eventual formation of the
  MFR with a filament embedded in it, and the MFR is elevated later. The
  activated MFR rises and pushes the overlying sheared field and forms a
  current sheet causing the EMR. The EMR in turn weakens the constraining
  effect of the overlying field, leading to the arising of the MFR,
  and subsequently erupting due to torus instability.

Title: Editorial: Last Print Issue of Solar Physics
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
   Lidia; Wheatland, Michael S.
Bibcode: 2017SoPh..292..196L
Altcode:
  No abstract at ADS

Title: Predicting the Where and the How Big of Solar Flares
Authors: Leka, K. D.; Barnes, G.; Gilchrist, S.; Wheatland, M.
Bibcode: 2017shin.confE..87L
Altcode:
  The approach to predicting solar flares generally characterizes global
  properties of a solar active region, for example the total magnetic flux
  or the total length of a sheared magnetic neutral line, and compares new
  data (from which to make a prediction) to similar observations of active
  regions and their associated propensity for flare production. We take
  here a different tack, examining solar active regions in the context
  of their energy storage capacity. Specifically, we characterize not
  the region as a whole, but summarize the energy-release prospects
  of different sub-regions within, using a sub-area analysis of the
  photospheric boundary, the CFIT non-linear force-free extrapolation
  code, and the Minimum Current Corona model. We present here early
  results from this approach whose objective is to understand the
  different pathways available for regions to release stored energy, thus
  eventually providing better estimates of the 'where' (what sub-areas
  are storing how much energy) and the 'how big' (how much energy is
  stored, and how much is available for release) of solar flares.

Title: Sunspot and Starspot Lifetimes in a Turbulent Erosion Model
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2017ApJ...834..108L
Altcode: 2016arXiv161103920L
  Quantitative models of sunspot and starspot decay predict the timescale
  of magnetic diffusion and may yield important constraints in stellar
  dynamo models. Motivated by recent measurements of starspot lifetimes,
  we investigate the disintegration of a magnetic flux tube by nonlinear
  diffusion. Previous theoretical studies are extended by considering
  two physically motivated functional forms for the nonlinear diffusion
  coefficient D: an inverse power-law dependence D ∝ B<SUP>-ν</SUP>
  and a step-function dependence of D on the magnetic field magnitude
  B. Analytical self-similar solutions are presented for the power-law
  case, including solutions exhibiting “superfast” diffusion. For the
  step-function case, the heat-balance integral method yields approximate
  solutions, valid for moderately suppressed diffusion in the spot. The
  accuracy of the resulting solutions is confirmed numerically, using a
  method which provides an accurate description of long-time evolution by
  imposing boundary conditions at infinite distance from the spot. The
  new models may allow insight into the differences and similarities
  between sunspots and starspots.

Title: Prediction of Solar Flares Using Unique Signatures of Magnetic
    Field Images
Authors: Raboonik, Abbas; Safari, Hossein; Alipour, Nasibe; Wheatland,
   Michael S.
Bibcode: 2017ApJ...834...11R
Altcode: 2016arXiv161003222R
  Prediction of solar flares is an important task in solar physics. The
  occurrence of solar flares is highly dependent on the structure and
  topology of solar magnetic fields. A new method for predicting large (M-
  and X-class) flares is presented, which uses machine learning methods
  applied to the Zernike moments (ZM) of magnetograms observed by the
  Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory
  for a period of six years from 2010 June 2 to 2016 August 1. Magnetic
  field images consisting of the radial component of the magnetic field
  are converted to finite sets of ZMs and fed to the support vector
  machine classifier. ZMs have the capability to elicit unique features
  from any 2D image, which may allow more accurate classification. The
  results indicate whether an arbitrary active region has the potential
  to produce at least one large flare. We show that the majority of large
  flares can be predicted within 48 hr before their occurrence, with only
  10 false negatives out of 385 flaring active region magnetograms and 21
  false positives out of 179 non-flaring active region magnetograms. Our
  method may provide a useful tool for the prediction of solar flares,
  which can be employed alongside other forecasting methods.

Title: Editorial Appreciation
Authors: Leibacher, John; Mandrini, Cristina H.; van Driel-Gesztelyi,
   Lidia; Wheatland, Michael S.
Bibcode: 2017SoPh..292...19L
Altcode:
  We are pleased to acknowledge, with sincere thanks, the following
  referees who supported the community by refereeing articles for Solar
  Physics during 2016.

Title: Is Cyclotron Maser Emission in Solar Flares Driven by a
    Horseshoe Distribution?
Authors: Melrose, D. B.; Wheatland, M. S.
Bibcode: 2016SoPh..291.3637M
Altcode: 2016SoPh..tmp..171M; 2016arXiv161004299M
  Since the early 1980s, decimetric spike bursts have been attributed
  to electron cyclotron maser emission (ECME) by the electrons that
  produce hard X-ray bursts as they precipitate into the chromosphere
  in the impulsive phase of a solar flare. Spike bursts are regarded
  as analogous to the auroral kilometric radiation (AKR), which is
  associated with the precipitation of auroral electrons in a geomagnetic
  substorm. Originally, a loss-cone-driven version of ECME, developed
  for AKR, was applied to spike bursts, but it is now widely accepted
  that the measured distribution function is horseshoe-like (an isotropic
  distribution with a one-sided loss cone), and that a horseshoe-driven
  version of ECME applies to AKR. We explore the implications of the
  assumption that horseshoe-driven ECME also applies to spike bursts. We
  develop a 1D model for the acceleration of the electrons by a parallel
  electric field, and show that under plausible assumptions it leads
  to a horseshoe distribution of electrons in a solar flare. A second
  requirement for horseshoe-driven ECME is an extremely low plasma
  density, referred to as a density cavity. We argue that a coronal
  density cavity should develop in association with a hard X-ray burst,
  and that such a density cavity can overcome a long-standing problem with
  the escape of ECME through the second-harmonic absorption layer. Both
  the horseshoe distribution and the associated coronal density cavity
  are highly localized, and could not be resolved in the statistically
  large number of local precipitation regions needed to explain a hard
  X-ray burst. The model highlights the "number problem" in the supply
  of the electrons needed to explain a hard X-ray burst.

Title: Editorial: 50 Years of Solar Physics
Authors: Charbonneau, Paul; Leibacher, John; Mandrini, Cristina;
   van Driel-Gesztelyi, Lidia; Wheatland, Michael S.
Bibcode: 2016SoPh..291.3461C
Altcode: 2016SoPh..tmp..189C
  No abstract at ADS

Title: A Comparison of Flare Forecasting Methods. I. Results from
    the “All-Clear” Workshop
Authors: Barnes, G.; Leka, K. D.; Schrijver, C. J.; Colak, T.;
   Qahwaji, R.; Ashamari, O. W.; Yuan, Y.; Zhang, J.; McAteer, R. T. J.;
   Bloomfield, D. S.; Higgins, P. A.; Gallagher, P. T.; Falconer, D. A.;
   Georgoulis, M. K.; Wheatland, M. S.; Balch, C.; Dunn, T.; Wagner, E. L.
Bibcode: 2016ApJ...829...89B
Altcode: 2016arXiv160806319B
  Solar flares produce radiation that can have an almost immediate effect
  on the near-Earth environment, making it crucial to forecast flares
  in order to mitigate their negative effects. The number of published
  approaches to flare forecasting using photospheric magnetic field
  observations has proliferated, with varying claims about how well
  each works. Because of the different analysis techniques and data
  sets used, it is essentially impossible to compare the results from
  the literature. This problem is exacerbated by the low event rates of
  large solar flares. The challenges of forecasting rare events have long
  been recognized in the meteorology community, but have yet to be fully
  acknowledged by the space weather community. During the interagency
  workshop on “all clear” forecasts held in Boulder, CO in 2009,
  the performance of a number of existing algorithms was compared
  on common data sets, specifically line-of-sight magnetic field and
  continuum intensity images from the Michelson Doppler Imager, with
  consistent definitions of what constitutes an event. We demonstrate
  the importance of making such systematic comparisons, and of using
  standard verification statistics to determine what constitutes a good
  prediction scheme. When a comparison was made in this fashion, no one
  method clearly outperformed all others, which may in part be due to the
  strong correlations among the parameters used by different methods to
  characterize an active region. For M-class flares and above, the set
  of methods tends toward a weakly positive skill score (as measured
  with several distinct metrics), with no participating method proving
  substantially better than climatological forecasts.

Title: Nonlinear force-free modeling of magnetic fields in
    flare-productive active regions
Authors: Wheatland, M. S.; Gilchrist, S. A.
Bibcode: 2016IAUS..320..167W
Altcode:
  We review nonlinear force-free field (NLFFF) modeling of magnetic
  fields in active regions. The NLFFF model (in which the electric
  current density is parallel to the magnetic field) is often adopted
  to describe the coronal magnetic field, and numerical solutions to
  the model are constructed based on photospheric vector magnetogram
  boundary data. Comparative tests of NLFFF codes on sets of boundary
  data have revealed significant problems, in particular associated
  with the inconsistency of the model and the data. Nevertheless NLFFF
  modeling is often applied, in particular to flare-productive active
  regions. We examine the results, and discuss their reliability.

Title: The Influence of Spatial resolution on Nonlinear Force-free
    Modeling
Authors: DeRosa, M. L.; Wheatland, M. S.; Leka, K. D.; Barnes, G.;
   Amari, T.; Canou, A.; Gilchrist, S. A.; Thalmann, J. K.; Valori,
   G.; Wiegelmann, T.; Schrijver, C. J.; Malanushenko, A.; Sun, X.;
   Régnier, S.
Bibcode: 2015ApJ...811..107D
Altcode: 2015arXiv150805455D
  The nonlinear force-free field (NLFFF) model is often used to
  describe the solar coronal magnetic field, however a series of
  earlier studies revealed difficulties in the numerical solution of the
  model in application to photospheric boundary data. We investigate
  the sensitivity of the modeling to the spatial resolution of the
  boundary data, by applying multiple codes that numerically solve the
  NLFFF model to a sequence of vector magnetogram data at different
  resolutions, prepared from a single Hinode/Solar Optical Telescope
  Spectro-Polarimeter scan of NOAA Active Region 10978 on 2007 December
  13. We analyze the resulting energies and relative magnetic helicities,
  employ a Helmholtz decomposition to characterize divergence errors, and
  quantify changes made by the codes to the vector magnetogram boundary
  data in order to be compatible with the force-free model. This study
  shows that NLFFF modeling results depend quantitatively on the spatial
  resolution of the input boundary data, and that using more highly
  resolved boundary data yields more self-consistent results. The
  free energies of the resulting solutions generally trend higher
  with increasing resolution, while relative magnetic helicity values
  vary significantly between resolutions for all methods. All methods
  require changing the horizontal components, and for some methods also
  the vertical components, of the vector magnetogram boundary field in
  excess of nominal uncertainties in the data. The solutions produced
  by the various methods are significantly different at each resolution
  level. We continue to recommend verifying agreement between the modeled
  field lines and corresponding coronal loop images before any NLFFF
  model is used in a scientific setting.

Title: Nonlinear Force-Free Modelling of Magnetic Fields in Flare
    Productive Active Regions
Authors: Wheatland, M. S.
Bibcode: 2015IAUGA..2286135W
Altcode:
  This talk reviews nonlinear force-free field (NLFFF) modelling of
  magnetic fields in flare-productive active regions. The NLFFF model
  (in which the electric current density is parallel to the magnetic
  field) is often adopted to describe the coronal magnetic field, and
  numerical solutions to the model are constructed based on photospheric
  vector magnetogram boundary data. Comparative tests of NLFFF codes
  on sets of boundary data have revealed significant problems, in
  particular associated with the inconsistency of the model and the
  data. Nevertheless NLFFF modelling is often applied, in particular
  for flaring active regions, and is used to infer details of the flare
  process. We examine the results, and discuss their reliability.

Title: Estimating Electric Current Densities in Solar Active Regions
Authors: Wheatland, M. S.
Bibcode: 2015SoPh..290.1147W
Altcode: 2015arXiv150302741W; 2015SoPh..tmp...39W
  Electric currents in solar active regions are thought to provide the
  energy released via magnetic reconnection in solar flares. Vertical
  electric current densities J<SUB>z</SUB> at the photosphere may
  be estimated from vector magnetogram data, subject to substantial
  uncertainties. The values provide boundary conditions for nonlinear
  force-free modelling of active region magnetic fields. A method is
  presented for estimating values of J<SUB>z</SUB> taking into account
  uncertainties in vector magnetogram field values, and minimising
  J<SUB>z</SUB><SUP>2</SUP> across the active region. The method is
  demonstrated using the boundary values of the field for a force-free
  twisted bipole, with the addition of noise at randomly chosen locations.

Title: Modeling Sunspot and Starspot Decay by Turbulent Erosion
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2015ApJ...800..130L
Altcode: 2015arXiv150101699L
  Disintegration of sunspots (and starspots) by fluxtube erosion,
  originally proposed by Simon and Leighton, is considered. A moving
  boundary problem is formulated for a nonlinear diffusion equation that
  describes the sunspot magnetic field profile. Explicit expressions
  for the sunspot decay rate and lifetime by turbulent erosion are
  derived analytically and verified numerically. A parabolic decay law
  for the sunspot area is obtained. For moderate sunspot magnetic field
  strengths, the predicted decay rate agrees with the results obtained
  by Petrovay and Moreno-Insertis. The new analytical and numerical
  solutions significantly improve the quantitative description of sunspot
  and starspot decay by turbulent erosion.

Title: Active Region Magnetic Field Modeling Guided by Coronal Loops
    and Surface Fields
Authors: DeRosa, Marc L.; Malanushenko, Anna; Schrijver, Carolus J.;
   Wheatland, Michael S
Bibcode: 2014AAS...22432319D
Altcode:
  Dynamic events such as solar flares, filament eruptions, and mass
  ejections are powered by the evolving coronal magnetic field. However,
  the ways in which energy is stored in, and released from, the coronal
  magnetic field are poorly understood, in large part because the field
  configuration cannot be determined directly from observations and has
  eluded the successful application of routine modeling based on surface
  magnetograms. Recently, we have demonstrated that the Quasi-Grad-Rubin
  (QGR) method for modeling the current-carrying field associated with
  active regions shows promise. In Malanushenko et al. (2014, ApJ 783:102)
  we have used the QGR method to construct the magnetic field at several
  times during the evolution of AR11158 during February 2011. The QGR
  method does not require vector magnetograms, and instead uses the
  trajectories of observed coronal loops to constrain the locations
  of electric currents within the modeling domain. In this study,
  we continue to assess the utility of QGR by applying this method to
  additional active regions from the current activity cycle, making use
  of SDO/HMI line-of-sight magnetograms and imagery from the extreme
  ultraviolet channels of SDO/AIA.

Title: Nonlinear Force-Free Modeling of the Corona in Spherical
    Coordinates
Authors: Gilchrist, S. A.; Wheatland, M. S.
Bibcode: 2014SoPh..289.1153G
Altcode: 2013arXiv1308.5742G
  We present a code for solving the nonlinear force-free equations
  in spherical polar geometry, with the motivation of modeling the
  magnetic field in the corona. The code is an implementation of the
  Grad-Rubin method. Our method is applicable to a spherical domain of
  arbitrary angular size. The implementation is based on a global spectral
  representation for the magnetic field that makes no explicit assumptions
  about the form of the magnetic field at the transverse boundaries of
  the domain. We apply the code to a bipolar test case with analytic
  boundary conditions, and demonstrate the convergence of the Grad-Rubin
  method and the self-consistency of the resulting numerical solution.

Title: Bulk Energization of Electrons in Solar Flares by Alfvén Waves
Authors: Melrose, D. B.; Wheatland, M. S.
Bibcode: 2014SoPh..289..881M
Altcode: 2013arXiv1307.7772M
  Bulk energization of electrons to 10 - 20 keV in solar flares is
  attributed to dissipation of Alfvén waves that transport energy and
  potential downward to an acceleration region near the chromosphere. The
  acceleration involves the parallel electric field that develops in the
  limit of inertial Alfvén waves (IAWs). A two-potential model for IAWs
  is used to relate the parallel potential to the cross-field potential
  transported by the waves. We identify a maximum parallel potential in
  terms of a maximum current density that corresponds to the threshold
  for the onset of anomalous resistivity. This maximum is of order 10
  kV when the threshold is that for the Buneman instability. We argue
  that this restricts the cross-field potential in an Alfvén wave to
  about 10 kV. Effective dissipation requires a large number of up- and
  down-current paths associated with multiple Alfvén waves. The electron
  acceleration occurs in localized, transient, anomalously conducting
  regions (LTACRs) and is associated with the parallel electric field
  determined by Ohm's law with an anomalous resistivity. We introduce an
  idealized model in which the LTACRs are (upward-)current sheets, a few
  skin depths in thickness, separated by much larger regions of weaker
  return current. We show that this model can account semi-quantitatively
  for bulk energization.

Title: Using Coronal Loops to Reconstruct the Magnetic Field of an
    Active Region before and after a Major Flare
Authors: Malanushenko, A.; Schrijver, C. J.; DeRosa, M. L.; Wheatland,
   M. S.
Bibcode: 2014ApJ...783..102M
Altcode: 2013arXiv1312.5389M
  The shapes of solar coronal loops are sensitive to the presence
  of electrical currents that are the carriers of the non-potential
  energy available for impulsive activity. We use this information in
  a new method for modeling the coronal magnetic field of active region
  (AR) 11158 as a nonlinear force-free field (NLFFF). The observations
  used are coronal images around the time of major flare activity on
  2011 February 15, together with the surface line-of-sight magnetic
  field measurements. The data are from the Helioseismic and Magnetic
  Imager and Atmospheric Imaging Assembly on board the Solar Dynamics
  Observatory. The model fields are constrained to approximate the coronal
  loop configurations as closely as possible, while also being subject
  to the force-free constraints. The method does not use transverse
  photospheric magnetic field components as input and is thereby
  distinct from methods for modeling NLFFFs based on photospheric vector
  magnetograms. We validate the method using observations of AR 11158
  at a time well before major flaring and subsequently review the field
  evolution just prior to and following an X2.2 flare and associated
  eruption. The models indicate that the energy released during the
  instability is about 1 × 10<SUP>32</SUP> erg, consistent with what
  is needed to power such a large eruptive flare. Immediately prior to
  the eruption, the model field contains a compact sigmoid bundle of
  twisted flux that is not present in the post-eruption models, which
  is consistent with the observations. The core of that model structure
  is twisted by ≈0.9 full turns about its axis.

Title: Using coronal loops to model the coronal magnetic field before
    and after major eruptive events
Authors: Malanushenko, Anna; Schrijver, Carolus; Wheatland, M. S.;
   DeRosa, Marc
Bibcode: 2014cosp...40E1960M
Altcode:
  Solar flares are believed to be a manifestation of major release of
  magnetic energy stored in active region field. Modeling the coronal
  magnetic field may enable us to evaluate the energy available for
  release, as well as possible sites of the reconnection and other
  relevant properties of the field. We use a new method to aid this
  problem by including the observed structure of the field (manifested
  in coronal loops) as additional constraints. We verify that the method
  (previously shown to work on synthetic data in Malanushenko et. al.,
  ApJ, 756, 153, 2012) is generally acceptable for the solar data, as
  it gives self-consistent, slowly changing results for slowly evolving
  structures. We further develop the potential of this method to access
  changes in the coronal magnetic field triggered by major eruptive
  events, and compare the results with observations.

Title: Transfer of Energy, Potential, and Current by Alfvén Waves
    in Solar Flares
Authors: Melrose, D. B.; Wheatland, M. S.
Bibcode: 2013SoPh..288..223M
Altcode: 2013arXiv1304.1938M
  Alfvén waves play three related roles in the impulsive phase of
  a solar flare: they transport energy from a generator region to an
  acceleration region; they map the cross-field potential (associated
  with the driven energy release) from the generator region onto the
  acceleration region; and within the acceleration region they damp
  by setting up a parallel electric field that accelerates electrons
  and transfers the wave energy to them. The Alfvén waves may also be
  regarded as setting up new closed-current loops, with field-aligned
  currents that close across field lines at boundaries. A model is
  developed for large-amplitude Alfvén waves that shows how Alfvén
  waves play these roles in solar flares. A picket-fence structure for
  the current flow is incorporated into the model to account for the
  "number problem" and the energy of the accelerated electrons.

Title: The state of nonlinear force-free magnetic field extrapolation
Authors: Wheatland, M. S.; Gilchrist, S. A.
Bibcode: 2013JPhCS.440a2037W
Altcode:
  Magnetic field extrapolation is the construction of a model solution for
  the coronal magnetic field in active regions from magnetic boundary data
  originating close to the Sun's surface. The nonlinear force-free model
  (in which the electric current density is parallel to the magnetic
  field) is often adopted to describe the coronal field. The solution
  of the nonlinear force-free equations is a challenging computational
  task, and the application of codes to available boundary data has
  revealed a number of significant problems with nonlinear force-free
  extrapolation. This paper summarises the present status of coronal
  field extrapolation, and describes some recent developments.

Title: Origin and Use of the Laplace Distribution in Daily Sunspot
    Numbers
Authors: Noble, P. L.; Wheatland, M. S.
Bibcode: 2013SoPh..282..565N
Altcode: 2012arXiv1210.3119N
  Recently Pop (Solar Phys.276, 351, 2012) identified a Laplace (or double
  exponential) distribution in the number of days with a given absolute
  value in the change over a day, in sunspot number, for days on which
  the sunspot number does change. We show this phenomenological rule has a
  physical origin attributable to sunspot formation, evolution, and decay,
  rather than being due to the changes in sunspot number caused by groups
  rotating onto and off the visible disc. We also demonstrate a simple
  method to simulate daily sunspot numbers over a solar cycle using the
  Pop (Solar Phys.276, 351, 2012) result, together with a model for the
  cycle variation in the mean sunspot number. The procedure is applied to
  three recent solar cycles. We check that the simulated sunspot numbers
  reproduce the observed distribution of daily changes over those cycles.

Title: A Magnetostatic Grad-Rubin Code for Coronal Magnetic Field
    Extrapolations
Authors: Gilchrist, S. A.; Wheatland, M. S.
Bibcode: 2013SoPh..282..283G
Altcode: 2012SoPh..tmp..246G; 2012arXiv1209.5843G
  The coronal magnetic field cannot be directly observed, but, in
  principle, it can be reconstructed from the comparatively well
  observed photospheric magnetic field. A popular approach uses a
  nonlinear force-free model. Non-magnetic forces at the photosphere
  are significant, meaning the photospheric data are inconsistent with
  the force-free model, and this causes problems with the modeling (De
  Rosa et al., Astrophys. J.696, 1780, 2009). In this paper we present a
  numerical implementation of the Grad-Rubin method for reconstructing the
  coronal magnetic field using a magnetostatic model. This model includes
  a pressure force and a non-zero magnetic Lorentz force. We demonstrate
  our implementation on a simple analytic test case and obtain the speed
  and numerical error scaling as a function of the grid size.

Title: Guiding Nonlinear Force-free Modeling Using Coronal
Observations: First Results Using a Quasi-Grad-Rubin Scheme
Authors: Malanushenko, A.; Schrijver, C. J.; DeRosa, M. L.; Wheatland,
   M. S.; Gilchrist, S. A.
Bibcode: 2012ApJ...756..153M
Altcode: 2012arXiv1202.5420M
  At present, many models of the coronal magnetic field rely on
  photospheric vector magnetograms, but these data have been shown
  to be problematic as the sole boundary information for nonlinear
  force-free field extrapolations. Magnetic fields in the corona
  manifest themselves in high-energy images (X-rays and EUV) in the
  shapes of coronal loops, providing an additional constraint that
  is not at present used as constraints in the computational domain,
  directly influencing the evolution of the model. This is in part due
  to the mathematical complications of incorporating such input into
  numerical models. Projection effects, confusion due to overlapping
  loops (the coronal plasma is optically thin), and the limited number
  of usable loops further complicate the use of information from
  coronal images. We develop and test a new algorithm to use images of
  coronal loops in the modeling of the solar coronal magnetic field. We
  first fit projected field lines with those of constant-α force-free
  fields to approximate the three-dimensional distribution of currents
  in the corona along a sparse set of trajectories. We then apply a
  Grad-Rubin-like iterative technique, which uses these trajectories as
  volume constraints on the values of α, to obtain a volume-filling
  nonlinear force-free model of the magnetic field, modifying a code
  and method presented by Wheatland. We thoroughly test the technique
  on known analytical and solar-like model magnetic fields previously
  used for comparing different extrapolation techniques and compare the
  results with those obtained by currently available methods relying
  only on the photospheric data. We conclude that we have developed a
  functioning method of modeling the coronal magnetic field by combining
  the line-of-sight component of the photospheric magnetic field with
  information from coronal images. Whereas we focus on the use of coronal
  loop information in combination with line-of-sight magnetograms, the
  method is readily extended to incorporate vector-magnetic data over
  any part of the photospheric boundary.

Title: A current sheet traced from the Sun to interplanetary space
Authors: Zhou, Guiping; Xiao, C. J.; Wang, Jingxu; Wheatland, . M. S.;
   Zhao, . Hui
Bibcode: 2012cosp...39.2273Z
Altcode: 2012cosp.meet.2273Z
  Magnetic reconnection is a central concept for understanding solar
  activity, including filament eruptions, flares, and coronal mass
  ejections (CMEs). The existence of transverse and vertical current
  sheets, sites where reconnection takes place in the solar atmosphere,
  is frequently proposed as a precondition for flare/CME models, but is
  rarely identified in observations. We aim at identifying a transverse
  current sheet that existed in the pre-CME structure and persisted from
  the CME solar source to interplanetary space. STEREO A/B provide us
  a unique opportunity to calculate the interplanetary current sheets
  for the magnetic cloud. We analyze such a structure related to the
  fast halo CME of 2006 December 13 with assembled observations. A
  current sheet at the front of the magnetic cloud is analyzed to its
  origin in a transverse current sheet in the CME solar source, which
  can be revealed in the magnetic field extrapolations, XRT, and LASCO
  observations. Results. An interplanetary current sheet is identified
  as coming from the CME solar source by carefully mapping and examining
  multiple observations from the Sun to interplanetary space, along with
  nonlinear force-free magnetic field extrapolations of the active region
  NOAA 10930. The structure identified in the pre-flare state is a global
  transverse current sheet, which plays a role in the CME initiation,
  and propagates from the corona to interplanetary space.

Title: Non-Linear Force-Free Modeling of Solar Corona With The Aid
    of Coronal Loops
Authors: Malanushenko, A.; DeRosa, M.; Schrijver, C.; Wheatland,
   M. S.; Gilchrist, S.
Bibcode: 2012decs.confE.113M
Altcode:
  Accurate models of the coronal magnetic field are vital for
  understanding and predicting solar activity and are therefore of the
  greatest interest for solar physics. As no reliable measurements of the
  coronal magnetic field exists at present, the problem of constructing
  field models is typically viewed as a boundary value problem. The
  construction of realistic field models requires knowledge of the full
  vector of magnetic field at the boundaries of the model domain; vector
  magnetograms are, however, measured in the non force-free photosphere
  and their horizontal components are subject to large uncertainties. Even
  if an uncertainty-free vector magnetogram at the top layer of the
  chromosphere was known, the problem remains an extremely challenging
  non-linear problem. There are various methods for pre-processing
  vector magnetograms and using them to construct models of the coronal
  field. The success of these models is often judged based on how close
  its field lines correspond to the observed coronal loops, which are
  believed to follow lines of the coronal magnetic field. At present,
  the correspondence between coronal loops and magnetic field lines
  of many models based on the vector magnetograms is far from perfect
  (DeRosa et. al., 2009). The estimates of free energy in the field as
  well as distribution of the magnetic currents through the volume could
  be dramatically different for different models used (Schrijver et. al.,
  2008). This testifies to the need of a completely new approach to this
  problem. We present such an approach and demonstrate its results based
  on AIA and HMI data. We have developed a way to use coronal loops as a
  constraint for magnetic modelling; the field is therefore constructed to
  match coronal loops. We found that when tested on known magnetic fields
  the new method is able to reproduce overall shape of the field lines,
  large-scale spatial distribution of the electric currents and measure
  up to 60% of the free energy stored in the field. This was achieved
  with as little as line-of-sight magnetogram and less than hundred of
  synthetic "loops", that is, lines of magnetic fields projected onto
  a plane of the sky. We found that line-of-sight HMI magnetograms and
  spatial resolution of the AIA instrument combined with the amount of
  filters available are more than sufficient for obtaining such data. We
  briefly describe this new method and demonstrate reconstructions of the
  coronal magnetic field obtained using AIA and HMI data. We evaluate how
  well it reproduces coronal features and how much energy and helicity
  estimates fluctuate with time for a stable non-flaring active region,
  thus establishing the reliability of the new method.

Title: The Free Energy of NOAA Solar Active Region AR 11029
Authors: Gilchrist, S. A.; Wheatland, M. S.; Leka, K. D.
Bibcode: 2012SoPh..276..133G
Altcode: 2011arXiv1110.4418G
  The NOAA active region (AR) 11029 was a small but highly active
  sunspot region which produced 73 GOES soft X-ray flares during
  its transit of the disk in late October 2009. The flares appear
  to show a departure from the well-known power law frequency-size
  distribution. Specifically, too few GOES C-class and no M-class flares
  were observed by comparison with a power law distribution (Wheatland,
  Astrophys. J.710, 1324, 2010). This was conjectured to be due to
  the region having insufficient magnetic energy to power the missing
  large events. We construct nonlinear force-free extrapolations of the
  coronal magnetic field of AR 11029 using data taken on 24 October by
  the SOLIS Vector SpectroMagnetograph (SOLIS/VSM) and data taken on
  27 October by the Hinode Solar Optical Telescope SpectroPolarimeter
  (Hinode/SP). Force-free modeling with photospheric magnetogram data
  encounters problems, because the magnetogram data are inconsistent with
  a force-free model. We employ a recently developed "self-consistency"
  procedure which addresses this problem and accommodates uncertainties
  in the boundary data (Wheatland and Régnier, Astrophys. J.700,
  L88, 2009). We calculate the total energy and free energy of
  the self-consistent solution, which provides a model for the
  coronal magnetic field of the active region. The free energy of
  the region was found to be ≈ 4×10<SUP>29</SUP> erg on 24 October
  and ≈ 7×10<SUP>31</SUP> erg on 27 October. An order of magnitude
  scaling between RHESSI non-thermal energy and GOES peak X-ray flux is
  established from a sample of flares from the literature and is used to
  estimate flare energies from the observed GOES peak X-ray flux. Based
  on the scaling, we conclude that the estimated free energy of AR
  11029 on 27 October when the flaring rate peaked was sufficient to
  power M-class or X-class flares; hence, the modeling does not appear
  to support the hypothesis that the absence of large flares is due to
  the region having limited energy.

Title: A Bayesian Approach to Forecasting Solar Cycles Using a
    Fokker-Planck Equation
Authors: Noble, P. L.; Wheatland, M. S.
Bibcode: 2012SoPh..276..363N
Altcode: 2011arXiv1111.3084N
  A Bayesian method for forecasting solar cycles is presented. The
  approach combines a Fokker-Planck description of short-timescale (daily)
  fluctuations in sunspot number (Noble and Wheatland, Astrophys. J.732,
  5, 2011) with information from other sources, such as precursor and/or
  dynamo models. The forecasting is illustrated in application to two
  historical cycles (cycles 19 and 20), and then to the current solar
  cycle (cycle 24). The new method allows the prediction of quantiles,
  i.e. the probability that the sunspot number falls outside large or
  small bounds at a given future time. It also permits Monte Carlo
  simulations to identify the expected size and timing of the peak
  daily sunspot number, as well as the smoothed sunspot number for a
  cycle. These simulations show how the large variance in daily sunspot
  number determines the actual reliability of any forecast of the smoothed
  maximum of a cycle. For cycle 24 we forecast a maximum daily sunspot
  number of 166±24, to occur in March 2013, and a maximum value of the
  smoothed sunspot number of 66±5, indicating a very small solar cycle.

Title: Non-Linear Force-Free Modeling With The Aid of Coronal
    Observations
Authors: Malanushenko, A. V.; DeRosa, M. L.; Schrijver, C. J.;
   Gilchrist, S. A.; Wheatland, M. S.
Bibcode: 2011AGUFMSH43B1956M
Altcode:
  Currently many models of coronal magnetic field rely on vector
  magnetograms and other kinds of information drawn from the
  photosphere. Magnetic fields in the corona, however, manifest themselves
  in the shapes of coronal loops, providing a constraint that at the
  present stage receives little use due to mathematical complications of
  incorporating such input into the numeric models. Projection effects
  and the limited number of usable loops further complicate their
  use. We present a possible way to account for coronal loops in the
  models of magnetic field. We first fit the observed loops with lines
  of constant-alpha fields and thus approximate three-dimensional
  distribution of currents in the corona along a sparse set of
  trajectories. We then apply a Grad-Rubin-like averaging technique
  to obtain a volume-filling non-linear force-free model of magnetic
  field, modified from the method presented in Wheatland &amp; Regnier
  (2009). We present thorough tests of this technique on several known
  magnetic fields that were previously used for comparing different
  extrapolation techniques (Schrijver et. al., 2006; Metcalf et. al.,
  2008; Schrijver et. al., 2008; DeRosa et. al., 2009), as well as on
  solar data and compare the results with those obtained by the currently
  developed methods that rely completely on the photospheric data.

Title: Modeling the Sunspot Number Distribution with a Fokker-Planck
    Equation
Authors: Noble, P. L.; Wheatland, M. S.
Bibcode: 2011ApJ...732....5N
Altcode: 2011arXiv1102.5158N
  Sunspot numbers exhibit large short-timescale (daily-monthly)
  variation in addition to longer-timescale variation due to solar
  cycles. A formal statistical framework is presented for estimating
  and forecasting randomness in sunspot numbers on top of deterministic
  (including chaotic) models for solar cycles. The Fokker-Planck approach
  formulated assumes a specified long-term or secular variation in sunspot
  number over an underlying solar cycle via a driver function. The model
  then describes the observed randomness in sunspot number on top of this
  driver function. We consider a simple harmonic choice for the driver
  function, but the approach is general and can easily be extended to
  include other drivers which account for underlying physical processes
  and/or empirical features of the sunspot numbers. The framework is
  consistent during both solar maximum and minimum, and requires no
  parameter restrictions to ensure non-negative sunspot numbers. Model
  parameters are estimated using statistically optimal techniques. The
  model agrees both qualitatively and quantitatively with monthly sunspot
  data even with the simplistic representation of the periodic solar
  cycle. This framework should be particularly useful for solar cycle
  forecasters and is complementary to existing modeling techniques. An
  analytic approximation for the Fokker-Planck equation is presented,
  which is analogous to the Euler approximation, which allows for
  efficient maximum likelihood estimation of large data sets and/or when
  using difficult to evaluate driver functions.

Title: Simulating Coronal Emission in Six AIA Channels Using
    Quasi-Static Atmosphere Models and Non-Linear Magnetic Field Models
Authors: Malanushenko, Anna; Schrijver, C.; DeRosa, M.; Aschwanden,
   M.; Wheatland, M. S.; van Ballegooijen, A. A.
Bibcode: 2011SPD....42.2116M
Altcode: 2011BAAS..43S.2116M
  We present the results of simulations of the EUV coronal emission in
  AIA channels. We use a non-linear force-free model of magnetic field
  constructed in such a way that its field lines resemble the observed
  coronal loops in EUV. We then solve one-dimensional quasi-steady
  atmosphere model along the magnetic field lines (Schrijver &amp;
  Ballegooijen, 2005). Using coronal abundances from CHIANTI and AIA
  response functions we then simulate the emission that would be observed
  in AIA EUV channels. The resulting intensities are compared against the
  real observations in a manner similar to that in Aschwanden et. al.,
  2011. The study is similar to those by Lindquist et. al., 2008, with a
  few important differences. We use a model of the coronal magnetic field
  that resembles the topology observed in EUV, we study EUV emission of
  cool loops (rather than SXR) and we make use of high resolution and
  cadence AIA and HMI data.

Title: Achieving Self-consistent Nonlinear Force-free Modeling of
    Solar Active Regions
Authors: Wheatland, M. S.; Leka, K. D.
Bibcode: 2011ApJ...728..112W
Altcode: 2010arXiv1012.3503W
  A nonlinear force-free solution is constructed for the coronal magnetic
  field in NOAA solar active region (AR) 10953 based on a photospheric
  vector magnetogram derived from Hinode satellite observations on
  2007 April 30, taking into account uncertainties in the boundary data
  and using improved methods for merging multiple-instrument data. The
  solution demonstrates the "self-consistency" procedure of Wheatland
  &amp; Régnier, for the first time including uncertainties. The
  self-consistency procedure addresses the problem that photospheric
  vector magnetogram data are inconsistent with the force-free model,
  and in particular that the boundary conditions on vertical electric
  current density are overspecified and permit the construction of two
  different nonlinear force-free solutions. The procedure modifies the
  boundary conditions on current density during a sequence of cycles until
  the two nonlinear force-free solutions agree. It hence constructs an
  accurate single solution to the force-free model, with boundary values
  close, but not matched exactly, to the vector magnetogram data. The
  inclusion of uncertainties preserves the boundary conditions more
  closely at points with smaller uncertainties. The self-consistent
  solution obtained for AR 10953 is significantly non-potential, with
  magnetic energy E/E <SUB>0</SUB> ≈ 1.08, where E <SUB>0</SUB> is the
  energy of the reference potential (current-free) magnetic field. The
  self-consistent solution is shown to be robust against changes in
  the details of the construction of the two force-free models at each
  cycle. This suggests that reliable nonlinear force-free modeling of
  ARs is possible if uncertainties in vector magnetogram boundary data
  are included.

Title: A current sheet traced from the Sun to interplanetary space
Authors: Zhou, G. P.; Xiao, C. J.; Wang, J. X.; Wheatland, M. S.;
   Zhao, H.
Bibcode: 2011A&A...525A.156Z
Altcode:
  Context. Magnetic reconnection is a central concept for understanding
  solar activity, including filament eruptions, flares, and coronal mass
  ejections (CMEs). The existence of transverse and vertical current
  sheets, sites where reconnection takes place in the solar atmosphere,
  is frequently proposed as a precondition for flare/CME models, but is
  rarely identified in observations. <BR /> Aims: We aim at identifying
  a transverse current sheet that existed in the pre-CME structure and
  persisted from the CME solar source to interplanetary space. <BR />
  Methods: STEREO A/B provide us a unique opportunity to calculate the
  interplanetary current sheets for the magnetic cloud. We analyze
  such a structure related to the fast halo CME of 2006 December 13
  with assembled observations. A current sheet at the front of the
  magnetic cloud is analyzed to its origin in a transverse current
  sheet in the CME solar source, which can be revealed in the magnetic
  field extrapolations, XRT, and LASCO observations. <BR /> Results:
  An interplanetary current sheet is identified as coming from the CME
  solar source by carefully mapping and examining multiple observations
  from the Sun to interplanetary space, along with nonlinear force-free
  magnetic field extrapolations of the active region NOAA 10930. <BR />
  Conclusions: The structure identified in the pre-flare state is a global
  transverse current sheet, which plays a role in the CME initiation,
  and propagates from the corona to interplanetary space.

Title: Solar physics research in Australia
Authors: Cally, P. S.; Wheatland, M. S.; Cairns, I. H.; Melrose, D. B.
Bibcode: 2011ASInC...2..397C
Altcode:
  Australia has a small but world-class solar physics research community,
  with strong international ties, working in areas of particular
  strength defined by the research interests of individuals and small
  groups. Most research occurs at the major universities, and a small
  number of Ph.D. students are trained in the field each year. This paper
  surveys Australia's current contribution to solar physics research,
  and the prospects for future development of the field.

Title: Modelling magnetic fields in the corona using nonlinear
    force-free fields
Authors: Wheatland, M. S.; Leka, K. D.
Bibcode: 2011ASInC...2..203W
Altcode:
  Force-free magnetic fields, in which the magnetic or Lorentz force is
  self-balancing and hence zero, provide a simple model for fields in
  the Sun's corona. In principle the model may be solved using boundary
  values of the field derived from observations, e.g. data from the Hinode
  spectro-polarimeter. In practise the boundary data is inconsistent
  with the model, because fields at the photospheric level are subject
  to non-magnetic forces, and because of substantial uncertainties in the
  boundary data. The `self-consistency' procedure tep{2009ApJ...700L..88W}
  provides an approach to resolving the problem. This talk reports
  on results achieved with the procedure, in particular new results
  obtained for active region AR 10953 using Hinode data incorporating
  uncertainties in the boundary conditions tep{2011ApJ...728..112W}.

Title: The free energy of NOAA active region AR 11029
Authors: Gilchrist, S. A.; Wheatland, M. S.
Bibcode: 2010AGUFMSH53B..02G
Altcode:
  Active region AR 11029 was a small but highly active sunspot region
  that produced over 70 GOES soft X-ray flares during its transit
  of the disk in late October 2009, during a period of deep solar
  minimum. The flares appear to show a departure from the well known
  flare power-law frequency-size distribution. Specifically, too few
  GOES C class and no M class flares were observed by comparison with a
  simple power-law distribution (Wheatland 2010). This was conjectured
  to be due to the region having insufficient magnetic energy to
  power large events (Wheatland 2010). We perform nonlinear force-free
  modeling of the coronal magnetic field of the region on 24, 25 and 26
  October using three photospheric magnetograms provided by the SOLIS
  vector spectromagnetograph. We find the free magnetic energy of the
  region is ≤ 1030 ergs which is consistent with the region having
  insufficient energy to produce large flares. A recently developed
  self-consistency procedure (Wheatland and Régnier 2009) is applied
  to overcome the incompatibility between the force-free model and the
  forced photospheric data. Force-free model of the coronal magnetic field
  (black field lines) of AR 11029 on 24 October superimposed on SOLIS
  magnetogram data. The magnetogram shows the line-of-sight magnetic
  field on the photosphere. Positive polarity regions are colored blue
  and negative polarity regions are colored red.

Title: Time-Dependent Stochastic Modeling of Solar Active Region
    Energy
Authors: Kanazir, M.; Wheatland, M. S.
Bibcode: 2010SoPh..266..301K
Altcode: 2010arXiv1008.0459K; 2010SoPh..tmp..162K
  A time-dependent model for the energy of a flaring solar active region
  is presented based on an existing stochastic jump-transition model
  (Wheatland and Glukhov in Astrophys. J.494, 858, 1998; Wheatland
  in Astrophys. J.679, 1621, 2008 and Solar Phys.255, 211, 2009). The
  magnetic free energy of an active region is assumed to vary in time due
  to a prescribed (deterministic) rate of energy input and prescribed
  (random) jumps downwards in energy due to flares. The existing model
  reproduces observed flare statistics, in particular flare frequency -
  size and waiting-time distributions, but modeling presented to date has
  considered only the time-independent choices of constant energy input
  and constant flare-transition rates with a power-law distribution
  in energy. These choices may be appropriate for a solar active
  region producing a constant mean rate of flares. However, many solar
  active regions exhibit time variation in their flare productivity, as
  exemplified by NOAA active region (AR) 11029, observed during October
  - November 2009 (Wheatland in Astrophys. J.710, 1324, 2010). Time
  variation is incorporated into the jump-transition model for two
  cases: (1) a step change in the rates of flare transitions, and (2)
  a step change in the rate of energy supply to the system. Analytic
  arguments are presented describing the qualitative behavior of the
  system in the two cases. In each case the system adjusts by shifting
  to a new stationary state over a relaxation time which is estimated
  analytically. The model exhibits flare-like event statistics. In
  each case the frequency - energy distribution is a power law for
  flare energies less than a time-dependent rollover set by the largest
  energy the system is likely to attain at a given time. The rollover
  is not observed if the mean free energy of the system is sufficiently
  large. For Case 1, the model exhibits a double exponential waiting-time
  distribution, corresponding to flaring at a constant mean rate during
  two intervals (before and after the step change), if the average energy
  of the system is large. For Case 2 the waiting-time distribution is a
  simple exponential, again provided the average energy of the system is
  large. Monte Carlo simulations of Case 1 are presented which confirm the
  estimate for the relaxation time and the expected forms of the frequency
  - energy and waiting-time distributions. The simulation results provide
  a qualitative model for observed flare statistics in AR 11029.

Title: Modelling the Coronal Magnetic Field Using Hinode (and
    Future) Data
Authors: Wheatland, M. S.; Gilchrist, S. A.; Régnier, S.
Bibcode: 2010aogs...21..327W
Altcode:
  There is considerable interest in accurate modelling of the solar
  coronal magnetic field using photospheric vector magnetograms
  as boundary data, and the nonlinear force-free model is often
  used. However, recent studies using Hinode data have demonstrated that
  this modelling fails in basic ways, with the failure attributable to the
  departure of the inferred photospheric magnetic field from a force-free
  state. The solar boundary data are inconsistent with the model, which
  leads to inconsistencies in calculated force-free solutions. A method
  for constructing a self-consistent nonlinear force-free solution is
  described, which identifies a force-free solution that is close to the
  observed boundary data. Steps towards developing more sophisticated
  magnetohydrostatic modelling — taking into account pressure and
  gravitational forces at the level of the solar boundary data — are
  also outlined.

Title: Evidence for Departure from a Power-Law Flare Size Distribution
    for a Small Solar Active Region
Authors: Wheatland, M. S.
Bibcode: 2010ApJ...710.1324W
Altcode: 2010arXiv1001.1464W
  Active region 11029 was a small, highly flare-productive solar active
  region observed at a time of extremely low solar activity. The region
  produced only small flares: the largest of the &gt;70 Geostationary
  Observational Environmental Satellite (GOES) events for the region
  has a peak 1-8 Å flux of 2.2 × 10<SUP>-6</SUP> W m<SUP>-2</SUP>
  (GOES C2.2). The background-subtracted GOES peak-flux distribution
  suggests departure from power-law behavior above 10<SUP>-6</SUP>
  W m<SUP>-2</SUP>, and a Bayesian model comparison strongly favors
  a power-law plus rollover model for the distribution over a simple
  power-law model. The departure from the power law is attributed to
  this small active region having a finite amount of energy. The rate
  of flaring in the region varies with time, becoming very high for 2
  days coinciding with the onset of an increase in complexity of the
  photospheric magnetic field. The observed waiting-time distribution
  for events is consistent with a piecewise-constant Poisson model. These
  results present challenges for models of flare statistics and of energy
  balance in solar active regions.

Title: On The Brightness and Waiting-Time Distributions of a Type
    III Radio Storm Observed By Stereo/Waves
Authors: Eastwood, J. P.; Wheatland, M. S.; Hudson, H. S.; Krucker,
   S.; Bale, S. D.; Maksimovic, M.; Goetz, K.; Bougeret, J. -L.
Bibcode: 2010ApJ...708L..95E
Altcode: 2009arXiv0911.4131E
  Type III solar radio storms, observed at frequencies below ~16 MHz
  by space-borne radio experiments, correspond to the quasi-continuous,
  bursty emission of electron beams onto open field lines above active
  regions. The mechanisms by which a storm can persist in some cases
  for more than a solar rotation whilst exhibiting considerable radio
  activity are poorly understood. To address this issue, the statistical
  properties of a type III storm observed by the STEREO/WAVES radio
  experiment are presented, examining both the brightness distribution
  and (for the first time) the waiting-time distribution (WTD). Single
  power-law behavior is observed in the number distribution as a function
  of brightness; the power-law index is ~2.1 and is largely independent of
  frequency. The WTD is found to be consistent with a piecewise-constant
  Poisson process. This indicates that during the storm individual type
  III bursts occur independently and suggests that the storm dynamics are
  consistent with avalanche-type behavior in the underlying active region.

Title: A Self-Consistent Nonlinear Force-Free Solution for a Solar
    Active Region Magnetic Field
Authors: Wheatland, M. S.; Régnier, S.
Bibcode: 2009ApJ...700L..88W
Altcode: 2009arXiv0906.4414W
  Nonlinear force-free solutions for the magnetic field in the solar
  corona constructed using photospheric vector magnetic field boundary
  data suffer from a basic problem: the observed boundary data are
  inconsistent with the nonlinear force-free model. Specifically, there
  are two possible choices of boundary conditions on vertical current
  provided by the data, and the two choices lead to different force-free
  solutions. A novel solution to this problem is described. Bayesian
  probability is used to modify the boundary values on current density,
  using field-line connectivity information from the two force-free
  solutions and taking into account uncertainties, so that the
  boundary data are more consistent with the two nonlinear force-free
  solutions. This procedure may be iterated until a set of self-consistent
  boundary data (the solutions for the two choices of boundary conditions
  are the same) is achieved. The approach is demonstrated to work in
  application to Hinode/Solar Optical Telescope observations of NOAA
  active region 10953.

Title: Nonlinear Force-Free Magnetic Field Modeling of AR 10953:
    A Critical Assessment
Authors: De Rosa, Marc L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.;
   Lites, B. W.; Aschwanden, M. J.; Amari, T.; Canou, A.; McTiernan,
   J. M.; Régnier, S.; Thalmann, J. K.; Valori, G.; Wheatland, M. S.;
   Wiegelmann, T.; Cheung, M. C. M.; Conlon, P. A.; Fuhrmann, M.;
   Inhester, B.; Tadesse, T.
Bibcode: 2009SPD....40.3102D
Altcode:
  Nonlinear force-free field (NLFFF) modeling seeks to provide accurate
  representations of the structure of the magnetic field above solar
  active regions, from which estimates of physical quantities of interest
  (e.g., free energy and helicity) can be made. However, the suite of
  NLFFF algorithms have failed to arrive at consistent solutions when
  applied to (thus far, two) cases using the highest-available-resolution
  vector magnetogram data from Hinode/SOT-SP (in the region of the
  modeling area of interest) and line-of-sight magnetograms from
  SOHO/MDI (where vector data were not available). One issue is that
  NLFFF models require consistent, force-free vector magnetic boundary
  data, and vector magnetogram data sampling the photosphere do not
  satisfy this requirement. Consequently, several problems have arisen
  that are believed to affect such modeling efforts. We use AR 10953
  to illustrate these problems, namely: (1) some of the far-reaching,
  current-carrying connections are exterior to the observational field
  of view, (2) the solution algorithms do not (yet) incorporate the
  measurement uncertainties in the vector magnetogram data, and/or (3)
  a better way is needed to account for the Lorentz forces within the
  layer between the photosphere and coronal base. In light of these
  issues, we conclude that it remains difficult to derive useful and
  significant estimates of physical quantities from NLFFF models.

Title: A Critical Assessment of Nonlinear Force-Free Field Modeling
    of the Solar Corona for Active Region 10953
Authors: De Rosa, Marc L.; Schrijver, Carolus J.; Barnes, Graham;
   Leka, K. D.; Lites, Bruce W.; Aschwanden, Markus J.; Amari, Tahar;
   Canou, Aurélien; McTiernan, James M.; Régnier, Stéphane; Thalmann,
   Julia K.; Valori, Gherardo; Wheatland, Michael S.; Wiegelmann, Thomas;
   Cheung, Mark C. M.; Conlon, Paul A.; Fuhrmann, Marcel; Inhester,
   Bernd; Tadesse, Tilaye
Bibcode: 2009ApJ...696.1780D
Altcode: 2009arXiv0902.1007D
  Nonlinear force-free field (NLFFF) models are thought to be viable
  tools for investigating the structure, dynamics, and evolution of
  the coronae of solar active regions. In a series of NLFFF modeling
  studies, we have found that NLFFF models are successful in application
  to analytic test cases, and relatively successful when applied
  to numerically constructed Sun-like test cases, but they are less
  successful in application to real solar data. Different NLFFF models
  have been found to have markedly different field line configurations
  and to provide widely varying estimates of the magnetic free energy in
  the coronal volume, when applied to solar data. NLFFF models require
  consistent, force-free vector magnetic boundary data. However,
  vector magnetogram observations sampling the photosphere, which is
  dynamic and contains significant Lorentz and buoyancy forces, do not
  satisfy this requirement, thus creating several major problems for
  force-free coronal modeling efforts. In this paper, we discuss NLFFF
  modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT,
  STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process
  illustrate three such issues we judge to be critical to the success of
  NLFFF modeling: (1) vector magnetic field data covering larger areas
  are needed so that more electric currents associated with the full
  active regions of interest are measured, (2) the modeling algorithms
  need a way to accommodate the various uncertainties in the boundary
  data, and (3) a more realistic physical model is needed to approximate
  the photosphere-to-corona interface in order to better transform the
  forced photospheric magnetograms into adequate approximations of nearly
  force-free fields at the base of the corona. We make recommendations
  for future modeling efforts to overcome these as yet unsolved problems.

Title: Monte Carlo Simulation of Solar Active-Region Energy
Authors: Wheatland, M. S.
Bibcode: 2009SoPh..255..211W
Altcode: 2009arXiv0902.0424W
  A Monte Carlo approach to solving a stochastic-jump transition model
  for active-region energy (Wheatland and Glukhov: Astrophys. J.494,
  858, 1998; Wheatland: Astrophys. J.679, 1621, 2008) is described. The
  new method numerically solves the stochastic differential equation
  describing the model, rather than the equivalent master equation. This
  has the advantages of allowing more efficient numerical solution, the
  modeling of time-dependent situations, and investigation of details of
  event statistics. The Monte Carlo approach is illustrated by application
  to a Gaussian test case and to the class of flare-like models presented
  in Wheatland (Astrophys. J.679, 1621, 2008), which are steady-state
  models with constant rates of energy supply, and power-law distributed
  jump transition rates. These models have two free parameters: an index
  (δ), which defines the dependence of the jump transition rates on
  active-region energy, and a nondimensional ratio ( \overline{r} )
  of total flaring rate to rate of energy supply. For \overline{r}≪
  1 the nondimensional mean energy \langle \overline{E}\rangle of the
  active-region satisfies \langle \overline{E}\rangle ≫ 1 , resulting
  in a power-law distribution of flare events over many decades of
  energy. The Monte Carlo method is used to explore the behavior of
  the waiting-time distributions for the flare-like models. The models
  with δ≠0 are found to have waiting times that depart significantly
  from simple Poisson behavior when \langle \overline{E}\rangle ≫ 1
  . The original model from Wheatland and Glukhov (Astrophys. J.494,
  858, 1998), with δ=0 (i.e., no dependence of transition rates on
  active-region energy), is identified as being most consistent with
  observed flare statistics.

Title: Nonlinear Force-Free Magnetic Field Modeling of the Solar
Corona: A Critical Assessment
Authors: De Rosa, M. L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.;
   Lites, B. W.; Aschwanden, M. J.; McTiernan, J. M.; Régnier, S.;
   Thalmann, J.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung,
   M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T.
Bibcode: 2008AGUFMSH41A1604D
Altcode:
  Nonlinear force-free field (NLFFF) modeling promises to provide accurate
  representations of the structure of the magnetic field above solar
  active regions, from which estimates of physical quantities of interest
  (e.g., free energy and helicity) can be made. However, the suite of
  NLFFF algorithms have so far failed to arrive at consistent solutions
  when applied to cases using the highest-available-resolution vector
  magnetogram data from Hinode/SOT-SP (in the region of the modeling
  area of interest) and line-of-sight magnetograms from SOHO/MDI (where
  vector data were not been available). It is our view that the lack of
  robust results indicates an endemic problem with the NLFFF modeling
  process, and that this process will likely continue to fail until (1)
  more of the far-reaching, current-carrying connections are within the
  observational field of view, (2) the solution algorithms incorporate
  the measurement uncertainties in the vector magnetogram data, and/or
  (3) a better way is found to account for the Lorentz forces within
  the layer between the photosphere and coronal base. In light of these
  issues, we conclude that it remains difficult to derive useful and
  significant estimates of physical quantities from NLFFF models.

Title: The Energetics of a Flaring Solar Active Region and Observed
    Flare Statistics
Authors: Wheatland, M. S.
Bibcode: 2008ApJ...679.1621W
Altcode: 2008arXiv0802.3931W
  A stochastic model for the energy of a flaring solar active region is
  presented, generalizing and extending the approach of Wheatland and
  Glukhov. The probability distribution for the free energy of an active
  region is described by the solution to a master equation involving
  deterministic energy input and random jump transitions downward in
  energy (solar flares). It is shown how two observable distributions,
  the flare frequency-energy distribution and the flare waiting-time
  distribution, may be derived from the steady state solution to the
  master equation, for given choices for the energy input and for the
  rates of flare transitions. An efficient method of numerical solution
  of the steady state master equation is presented. Solutions appropriate
  for flaring, involving a constant rate of energy input and power-law
  distributed jump transition rates, are numerically investigated. The
  flarelike solutions exhibit power-law flare frequency-energy
  distributions below a high-energy rollover, set by the largest energy
  the active region is likely to have. The solutions also exhibit
  approximately exponential (i.e., Poisson) waiting-time distributions,
  despite the rate of flaring depending on the free energy of the system.

Title: Non-Linear Force-Free Field Modeling of a Solar Active Region
    Around the Time of a Major Flare and Coronal Mass Ejection
Authors: De Rosa, M. L.; Schrijver, C. J.; Metcalf, T. R.; Barnes,
   G.; Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann,
   T.; Wheatland, M.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann,
   M.; Kusano, K.; Régnier, S.; Thalmann, J.
Bibcode: 2008AGUSMSP31A..06D
Altcode:
  Solar flares and coronal mass ejections are associated with rapid
  changes in coronal magnetic field connectivity and are powered by
  the partial dissipation of electrical currents that run through
  the solar corona. A critical unanswered question is whether the
  currents involved are induced by the advection along the photosphere
  of pre-existing atmospheric magnetic flux, or whether these currents
  are associated with newly emergent flux. We address this problem by
  applying nonlinear force-free field (NLFFF) modeling to the highest
  resolution and quality vector-magnetographic data observed by the
  recently launched Hinode satellite on NOAA Active Region 10930 around
  the time of a powerful X3.4 flare in December 2006. We compute 14
  NLFFF models using 4 different codes having a variety of boundary
  conditions. We find that the model fields differ markedly in geometry,
  energy content, and force-freeness. We do find agreement of the best-fit
  model field with the observed coronal configuration, and argue (1)
  that strong electrical currents emerge together with magnetic flux
  preceding the flare, (2) that these currents are carried in an ensemble
  of thin strands, (3) that the global pattern of these currents and
  of field lines are compatible with a large-scale twisted flux rope
  topology, and (4) that the ~1032~erg change in energy associated with
  the coronal electrical currents suffices to power the flare and its
  associated coronal mass ejection. We discuss the relative merits of
  these models in a general critique of our present abilities to model
  the coronal magnetic field based on surface vector field measurements.

Title: Nonlinear Force-free Field Modeling of a Solar Active Region
    around the Time of a Major Flare and Coronal Mass Ejection
Authors: Schrijver, C. J.; DeRosa, M. L.; Metcalf, T.; Barnes, G.;
   Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann, T.;
   Wheatland, M. S.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann,
   M.; Kusano, K.; Régnier, S.; Thalmann, J. K.
Bibcode: 2008ApJ...675.1637S
Altcode: 2007arXiv0712.0023S
  Solar flares and coronal mass ejections are associated with rapid
  changes in field connectivity and are powered by the partial dissipation
  of electrical currents in the solar atmosphere. A critical unanswered
  question is whether the currents involved are induced by the motion of
  preexisting atmospheric magnetic flux subject to surface plasma flows or
  whether these currents are associated with the emergence of flux from
  within the solar convective zone. We address this problem by applying
  state-of-the-art nonlinear force-free field (NLFFF) modeling to the
  highest resolution and quality vector-magnetographic data observed
  by the recently launched Hinode satellite on NOAA AR 10930 around
  the time of a powerful X3.4 flare. We compute 14 NLFFF models with
  four different codes and a variety of boundary conditions. We find
  that the model fields differ markedly in geometry, energy content,
  and force-freeness. We discuss the relative merits of these models in
  a general critique of present abilities to model the coronal magnetic
  field based on surface vector field measurements. For our application
  in particular, we find a fair agreement of the best-fit model field
  with the observed coronal configuration, and argue (1) that strong
  electrical currents emerge together with magnetic flux preceding the
  flare, (2) that these currents are carried in an ensemble of thin
  strands, (3) that the global pattern of these currents and of field
  lines are compatible with a large-scale twisted flux rope topology,
  and (4) that the ~10<SUP>32</SUP> erg change in energy associated with
  the coronal electrical currents suffices to power the flare and its
  associated coronal mass ejection.

Title: Analysis and Packaging of Radiochemical Solar Neutrino Data:
    A Bayesian Approach
Authors: Sturrock, P. A.; Wheatland, M. S.
Bibcode: 2008SoPh..247..217S
Altcode: 2007arXiv0706.2192S; 2008SoPh..tmp....4S
  According to current practice, the results of each run of a
  radiochemical solar neutrino experiment comprise an estimate of the
  flux and upper and lower error estimates. These estimates are derived
  by a maximum-likelihood procedure from the times of decay events in
  the analysis chamber. This procedure has the following shortcomings:
  (a) published results sometimes include negative flux estimates; (b)
  even if the flux estimate is non-negative, the probability distribution
  function implied by the flux and error estimates will extend into
  negative territory; and (c) the overall flux estimate derived from
  the results of a sequence of runs may differ substantially from an
  estimate made by a "global" analysis of all of the timing data taken
  together. These defects indicate that the usual "packaging" of data
  in radiochemical solar neutrino experiments provides an inadequate
  summary of the data, which implies a loss of information. This article
  reviews this problem from a Bayesian perspective, and we suggest an
  alternative scheme for the packaging of radiochemical solar neutrino
  data, which we believe is free from these shortcomings.

Title: Nonlinear Force-Free Modeling of Coronal Magnetic
    Fields. II. Modeling a Filament Arcade and Simulated Chromospheric
    and Photospheric Vector Fields
Authors: Metcalf, Thomas R.; De Rosa, Marc L.; Schrijver, Carolus J.;
   Barnes, Graham; van Ballegooijen, Adriaan A.; Wiegelmann, Thomas;
   Wheatland, Michael S.; Valori, Gherardo; McTtiernan, James M.
Bibcode: 2008SoPh..247..269M
Altcode: 2008SoPh..tmp...17M
  We compare a variety of nonlinear force-free field (NLFFF) extrapolation
  algorithms, including optimization, magneto-frictional, and Grad -
  Rubin-like codes, applied to a solar-like reference model. The model
  used to test the algorithms includes realistic photospheric Lorentz
  forces and a complex field including a weakly twisted, right helical
  flux bundle. The codes were applied to both forced "photospheric" and
  more force-free "chromospheric" vector magnetic field boundary data
  derived from the model. When applied to the chromospheric boundary data,
  the codes are able to recover the presence of the flux bundle and the
  field's free energy, though some details of the field connectivity are
  lost. When the codes are applied to the forced photospheric boundary
  data, the reference model field is not well recovered, indicating
  that the combination of Lorentz forces and small spatial scale
  structure at the photosphere severely impact the extrapolation of the
  field. Preprocessing of the forced photospheric boundary does improve
  the extrapolations considerably for the layers above the chromosphere,
  but the extrapolations are sensitive to the details of the numerical
  codes and neither the field connectivity nor the free magnetic energy in
  the full volume are well recovered. The magnetic virial theorem gives
  a rapid measure of the total magnetic energy without extrapolation
  though, like the NLFFF codes, it is sensitive to the Lorentz forces in
  the coronal volume. Both the magnetic virial theorem and the Wiegelmann
  extrapolation, when applied to the preprocessed photospheric boundary,
  give a magnetic energy which is nearly equivalent to the value derived
  from the chromospheric boundary, but both underestimate the free
  energy above the photosphere by at least a factor of two. We discuss
  the interpretation of the preprocessed field in this context. When
  applying the NLFFF codes to solar data, the problems associated with
  Lorentz forces present in the low solar atmosphere must be recognized:
  the various codes will not necessarily converge to the correct, or
  even the same, solution.

Title: Calculating and Testing Nonlinear Force-Free Fields
Authors: Wheatland, M. S.
Bibcode: 2007SoPh..245..251W
Altcode:
  Improvements to an existing method for calculating nonlinear force-free
  magnetic fields (Wheatland, Solar Phys. 238, 29, 2006) are described. In
  particular a solution of the 3-D Poisson equation using 2-D Fourier
  transforms is presented. The improved nonlinear force-free method
  is demonstrated in application to linear force-free test cases with
  localized nonzero values of the normal component of the field in the
  boundary. These fields provide suitable test cases for nonlinear
  force-free calculations because the boundary conditions involve
  localized nonzero values of the normal components of the field and
  of the current density, and because (being linear force-free fields)
  they have more direct numerical solutions. Despite their simplicity,
  fields of this kind have not been recognized as test cases for
  nonlinear methods before. The examples illustrate the treatment of
  the boundary conditions on current in the nonlinear force-free method,
  and in particular the limitations imposed by field lines that connect
  outside of the boundary region.

Title: Non-linear Force-free Modeling Of Coronal Magnetic Fields
Authors: Metcalf, Thomas R.; De Rosa, M. L.; Schrijver, C. J.; Barnes,
   G.; van Ballegooijen, A.; Wiegelmann, T.; Wheatland, M. S.; Valori,
   G.; McTiernan, J. M.
Bibcode: 2007AAS...210.9102M
Altcode: 2007BAAS...39..204M
  We compare a variety of nonlinear force-free field (NLFFF)
  extrapolation algorithms, including optimization, magneto-frictional,
  and Grad-Rubin-like codes, applied to a solar-like reference
  model. The model used to test the algorithms includes realistic
  photospheric Lorentz forces and a complex field including a weakly
  twisted, right helical flux bundle. The codes were applied to both
  forced "photospheric'' and more force-free "chromospheric'' vector
  magnetic field boundary data derived from the model. When applied to
  the <P />chromospheric boundary data, the codes are able to recover
  the presence of the flux bundle and the field's free energy, though
  some details of the field connectivity are lost. When the codes are
  applied to the forced photospheric boundary data, the reference
  model field is not well recovered, indicating that the Lorentz
  forces on the photosphere severely impact the extrapolation of the
  field. Preprocessing of the photospheric boundary does improve the
  extrapolations considerably, although the results depend sensitively
  on the details of the numerical codes. When applying the NLFFF codes
  to solar data, the problems associated with Lorentz forces present in
  the low solar atmosphere must be recognized: the various codes will
  not necessarily converge to the correct, or even the same, solution.

Title: Reconstruction of Nonlinear Force-Free Fields and Solar
    Flare Prediction
Authors: Wheatland, M. S.
Bibcode: 2007aogs....8..123W
Altcode:
  A brief review is presented of methods for calculating nonlinear
  force-free fields, with emphasis on a new, fast current-field iteration
  procedure. The motivation is to reconstruct coronal magnetic fields
  using high-resolution vector magnetic field boundary data from a new
  generation of spectro-polarimetric instruments. Methods of solar flare
  prediction are also reviewed, with focus on the need to reproduce
  observed solar flare statistics. The event statistics method is
  described, as well as an extension of the method to incorporate
  additional information, based on Bayesian predictive discrimination.

Title: A Fast Current-Field Iteration Method for Calculating Nonlinear
    Force-Free Fields
Authors: Wheatland, M. S.
Bibcode: 2006SoPh..238...29W
Altcode: 2006SoPh..tmp...55W
  Existing methods for calculating nonlinear force-free magnetic fields
  are slow, and are likely to be inadequate for reconstructing coronal
  magnetic fields based on high-resolution vector magnetic field data
  from a new generation of spectro-polarimetric instruments. In this
  paper a new implementation of the current-field iteration method is
  presented, which is simple, fast, and accurate. The time taken by the
  method scales as N<SUP>4</SUP>, for a three-dimensional grid with
  N<SUP>3</SUP> points. The method solves the field-updating part of
  the iteration by exploiting a three-dimensional Fast Fourier Transform
  solution of Ampere's law with a current density field constructed to
  satisfy the required boundary conditions, and uses field line tracing
  to solve the current-updating part of the iteration. The method is
  demonstrated in application to a known nonlinear force-free field and
  to a bipolar test case.

Title: Including Flare Sympathy in a Model for Solar Flare Statistics
Authors: Wheatland, M. S.; Craig, I. J. D.
Bibcode: 2006SoPh..238...73W
Altcode: 2006SoPh..tmp...34W
  There is a variety of observational evidence for solar flare sympathy,
  i.e., the triggering of a flare in one active region by a flare in
  another region. Models for solar flare statistics, however, usually
  ignore sympathy by assuming that flares occur as independent events. In
  this paper, we argue that statistical flare models should be robust
  to the effects of sympathetic flaring. Further, we investigate the
  consequences of flare sympathy for a specific model of flare statistics,
  the M. S. Wheatland and I. J. D. Craig (Astrophys. J.595, 458, 2003)
  model. The original treatment describes an assembly of reconnecting
  structures (labelled separators) that flare independently according
  to simple rules consistent with magnetohydrodynamic flare models. This
  description is modified by allowing a flare at one separator to increase
  the probability of flaring at all other separators for a period of
  time following the flare, by an amount proportional to the energy of
  the flare. Simulations illustrate the transition of the model from weak
  to strong sympathy. In the limit of weak sympathy, the model reproduces
  observed flare frequency-energy and waiting-time distributions.

Title: A Rate-Independent Test for Solar Flare Sympathy
Authors: Wheatland, M. S.
Bibcode: 2006SoPh..236..313W
Altcode:
  Solar flare sympathy is the triggering of a flare in one active
  region by a flare in another. Statistical tests for flare sympathy
  have returned varying results. However, existing tests have relied on
  flaring rates in active regions being constant in time, or else have
  attempted to model the rate variation, which is a difficult task. A
  simple test is described which is independent of flaring rates. The test
  generalizes the approach of L. Fritzová-Švestkova, R.C. Chase, and
  Z. Švestka [Solar Phys.48, 275, 1976], and examines the distribution
  of flare coincidences in pairs of active regions as a function of
  coincidence interval τ. The test is applied to available soft X-ray
  and Hα flare event listings. The soft X-ray events exhibit a deficit
  of flare coincidences for τ≤;20 min, which is most likely due to an
  event-selection effect whereby the increased soft X-ray emission due
  to one flare prevents a second flare being identified. The Hα events
  show an excess of flare coincidences for τ≤; 10 min, suggesting
  flare sympathy. The number of Hα event pairs occurring within 10 min
  of one another is higher than that expected on the basis of random
  coincidence by a fraction 0.12± 0.02. Nearby active regions (spatial
  separation &lt;50˚) show a greater excess of coincidences for τ≤;
  10 min than do active regions which are far apart (spatial separation
  ≥50˚). However, the active regions which are far apart still show
  some evidence for an excess of coincidences at very short coincidence
  intervals (τ≤; 2 min), which appears to exclude the possibility of
  a coronal disturbance propagating from one region to another.

Title: Nonlinear Force-Free Modeling of Coronal Magnetic Fields Part
I: A Quantitative Comparison of Methods
Authors: Schrijver, Carolus J.; De Rosa, Marc L.; Metcalf, Thomas R.;
   Liu, Yang; McTiernan, Jim; Régnier, Stéphane; Valori, Gherardo;
   Wheatland, Michael S.; Wiegelmann, Thomas
Bibcode: 2006SoPh..235..161S
Altcode:
  We compare six algorithms for the computation of nonlinear force-free
  (NLFF) magnetic fields (including optimization, magnetofrictional,
  Grad-Rubin based, and Green's function-based methods) by evaluating
  their performance in blind tests on analytical force-free-field models
  for which boundary conditions are specified either for the entire
  surface area of a cubic volume or for an extended lower boundary
  only. Figures of merit are used to compare the input vector field to
  the resulting model fields. Based on these merit functions, we argue
  that all algorithms yield NLFF fields that agree best with the input
  field in the lower central region of the volume, where the field and
  electrical currents are strongest and the effects of boundary conditions
  weakest. The NLFF vector fields in the outer domains of the volume
  depend sensitively on the details of the specified boundary conditions;
  best agreement is found if the field outside of the model volume is
  incorporated as part of the model boundary, either as potential field
  boundaries on the side and top surfaces, or as a potential field in
  a skirt around the main volume of interest. For input field (B) and
  modeled field (b), the best method included in our study yields an
  average relative vector error E<SUB>n</SUB> = « |B−b|»/« |B|» of
  only 0.02 when all sides are specified and 0.14 for the case where only
  the lower boundary is specified, while the total energy in the magnetic
  field is approximated to within 2%. The models converge towards the
  central, strong input field at speeds that differ by a factor of one
  million per iteration step. The fastest-converging, best-performing
  model for these analytical test cases is the Wheatland, Sturrock, and
  Roumeliotis (2000) optimization algorithm as implemented by Wiegelmann
  (2004).

Title: Quantifying the Performance of Force-free Extrapolation
    Methods Using Known Solutions
Authors: Barnes, G.; Leka, K. D.; Wheatland, M. S.
Bibcode: 2006ApJ...641.1188B
Altcode:
  We outline a method for quantifying the performance of extrapolation
  methods for magnetic fields. We extrapolate the field for two
  model cases, using a linear force-free approach and a nonlinear
  approach. Each case contains a different topological feature of
  the field that may be of interest in solar energetic events. We are
  able to determine quantitatively whether either method is capable
  of reproducing the topology of the field. In one of our examples, a
  subjective evaluation of the performance of the extrapolation suggests
  that it has performed quite well, while our quantitative score shows
  that this is not the case, indicating the importance of being able
  to quantify the performance. Our method may be useful in determining
  which extrapolation techniques are best able to reproduce a force-free
  field and which topological features can be recovered.

Title: An Improved Virial Estimate of Solar Active Region Energy
Authors: Wheatland, M. S.; Metcalf, Thomas R.
Bibcode: 2006ApJ...636.1151W
Altcode: 2005astro.ph..9652W
  The MHD virial theorem may be used to estimate the magnetic energy of
  active regions on the basis of vector magnetic fields measured at the
  photosphere or chromosphere. However, the virial estimate depends on
  the measured vector magnetic field being force-free. Departure from the
  force-free condition leads to an unknown systematic error in the virial
  energy estimate and an origin dependence of the result. We present a
  method for estimating the systematic error by assuming that magnetic
  forces are confined to a thin layer near the photosphere. If vector
  magnetic field measurements are available at two levels in the low
  atmosphere (e.g., the photosphere and the chromosphere), the systematic
  error may be directly calculated using the observed horizontal and
  vertical field gradients, resulting in an energy estimate that is
  independent of the choice of origin. If (as is generally the case)
  measurements are available at only one level, the systematic error
  may be approximated using the observed horizontal field gradients
  together with a simple linear force-free model for the vertical
  field gradients. The resulting ``improved'' virial energy estimate
  is independent of the choice of origin but depends on the choice of
  the model for the vertical field gradients, i.e., the value of the
  linear force-free parameter α. This procedure is demonstrated for
  five vector magnetograms, including a chromospheric magnetogram.

Title: Understanding Solar Flare Statistics
Authors: Wheatland, M. S.
Bibcode: 2005AGUFMSM33E..06W
Altcode:
  A review is presented of work aimed at understanding solar flare
  statistics, with emphasis on the well known flare power-law size
  distribution. Although avalanche models are perhaps the favoured model
  to describe flare statistics, their physical basis is unclear, and
  they are divorced from developing ideas in large-scale reconnection
  theory. An alternative model, aimed at reconciling large-scale
  reconnection models with solar flare statistics, is revisited. The
  solar flare waiting-time distribution has also attracted recent
  attention. Observed waiting-time distributions are described, together
  with what they might tell us about the flare phenomenon. Finally,
  a practical application of flare statistics to flare prediction is
  described in detail, including the results of a year of automated
  (web-based) predictions from the method.

Title: Power-spectrum analyses of Super-Kamiokande solar neutrino
data: Variability and its implications for solar physics and neutrino
    physics
Authors: Sturrock, P. A.; Caldwell, D. O.; Scargle, J. D.; Wheatland,
   M. S.
Bibcode: 2005PhRvD..72k3004S
Altcode: 2004hep.ph....8017S
  Since rotational or similar modulation of the solar neutrino flux
  would seem to be incompatible with the currently accepted theoretical
  interpretation of the solar neutrino deficit, it is important to
  determine whether or not such modulation occurs. There have been
  conflicting claims as to whether or not power-spectrum analysis
  of the Super-Kamiokande solar neutrino data yields indication of
  variability. Comparison of these claims is complicated by the fact that
  the relevant articles may use different data sets, different methods of
  analysis, and different procedures for significance estimation. The
  purpose of this article is to clarify the role of power-spectrum
  analysis. To this end, we analyze primarily the Super-Kamiokande 5-day
  data set, and we use a standard procedure for significance estimation as
  used by the Super-Kamiokande collaboration. We then analyze this data
  set, with this method of significance estimation, using six methods
  of power-spectrum analysis. Five of these have been used in published
  articles, and the other is a method that might have been used. We
  find that, with one exception, the results of these calculations are
  consistent with those of previously published analyses. We find that
  the power of the principal modulation (that at 9.43yr<SUP>-1</SUP>)
  is greater in analyses that take account of error estimates than in
  the basic Lomb-Scargle analysis that does not take account of error
  estimates. The corresponding significance level ranges between 98%
  and 99.3%, depending on the details of the analysis. Concerning the
  recent article by Koshio, we find that we can reproduce the results
  of his power-spectrum analysis but not the results of his Monte
  Carlo simulations, and we have a suggestion that may account for
  the difference. We also comment on a recent article by Yoo et al. We
  discuss, in terms of subdominant processes, possible neutrino-physics
  interpretations of the apparent variability of the Super-Kamiokande
  measurements, and we suggest steps that could be taken to resolve the
  question of variability of the solar neutrino flux.

Title: A Simple Dynamical Model for Filament Formation in the
    Solar Corona
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2005ApJ...630..587L
Altcode:
  Filament formation in the solar atmosphere is considered. In the limit
  of sub-Alfvénic but supersonic motion, plasma flow in the solar corona
  is driven via the induction equation by a slow evolution of force-free
  magnetic fields. Methods for solving the relevant magnetohydrodynamic
  equations are presented and applied to filament modeling in two and
  three dimensions. An illustrative two-dimensional example is given,
  which is based on a potential magnetic field with a dip. The example
  describes the formation of a normal filament between two bipolar
  regions on the Sun. Next a detailed three-dimensional calculation is
  presented, which uses linear force-free magnetic fields. The boundary
  conditions are chosen to resemble the qualitative ``head-to-tail''
  linkage model for the formation of filaments, suggested by Martens &amp;
  Zwaan. Consistent with this model, dense formations, reminiscent of
  filament pillars, are shown to appear in the corona above the region of
  converging and canceling magnetic bipoles. The numerical results are
  consistent with the principal role of magnetic field in the dynamical
  processes of dense plasma accumulation and support in filaments,
  advocated by Martens &amp; Zwaan.

Title: A statistical solar flare forecast method
Authors: Wheatland, M. S.
Bibcode: 2005SpWea...3.7003W
Altcode: 2005SpWea...307003W; 2005astro.ph..5311W
  A Bayesian approach to solar flare prediction has been developed which
  uses only the event statistics of flares already observed. The method
  is simple and objective and makes few ad hoc assumptions. It is argued
  that this approach should be used to provide a baseline prediction for
  certain space weather purposes, upon which other methods, incorporating
  additional information, can improve. A practical implementation of
  the method for whole-Sun prediction of Geostationary Observational
  Environment Satellite (GOES) events is described in detail and is
  demonstrated for 4 November 2003, the day of the largest recorded GOES
  flare. A test of the method is described on the basis of the historical
  record of GOES events (1975-2003), and a detailed comparison is made
  with U.S. National Oceanic and Atmospheric Administration (NOAA)
  predictions for 1987-2003. Although the NOAA forecasts incorporate
  a variety of other information, the present method outperforms the
  NOAA method in predicting mean numbers of event days for both M-X
  and X events. Skill scores and other measures show that the present
  method is slightly less accurate at predicting M-X events than the
  NOAA method but substantially more accurate at predicting X events,
  which are important contributors to space weather.

Title: Combined and Comparative Analysis of Power Spectra
Authors: Sturrock, P. A.; Scargle, J. D.; Walther, G.; Wheatland, M. S.
Bibcode: 2005SoPh..227..137S
Altcode: 2005astro.ph..2050S
  In solar physics, especially in exploratory stages of research,
  it is often necessary to compare the power spectra of two or more
  time series. One may, for instance, wish to estimate what the power
  spectrum of the combined data sets might have been, or one may wish to
  estimate the significance of a particular peak that shows up in two
  or more power spectra. One may also on occasion need to search for a
  complex of peaks in a single power spectrum, such as a fundamental and
  one or more harmonics, or a fundamental plus sidebands, etc. Visual
  inspection can be revealing, but it can also be misleading. This
  leads one to look for one or more ways of forming statistics,
  which readily lend themselves to significance estimation, from two
  or more power spectra. We derive formulas for statistics formed from
  the sum, the minimum, and the product of two or more power spectra. A
  distinguishing feature of our formulae is that, if each power spectrum
  has an exponential distribution, each statistic also has an exponential
  distribution. The statistic formed from the minimum power of two or more
  power spectra is well known and has an exponential distribution. The
  sum of two or more powers also has a well-known distribution that is
  not exponential, but a simple operation does lead to an exponential
  distribution. Concerning the product of two or more power spectra,
  we find an analytical expression for the case n = 2, and a procedure
  for computing the statistic for n &gt; 2. We also show that some quite
  simple expressions give surprisingly good approximations.

Title: Initial Test of a Bayesian Approach to Solar Flare Prediction
Authors: Wheatland, Michael S.
Bibcode: 2005PASA...22..153W
Altcode: 2004astro.ph.10723W
  A test of a new Bayesian approach to solar flare prediction is
  presented. The approach uses the past history of flaring together
  with phenomenological rules of flare statistics to make a prediction
  for the probability of occurrence of a large flare within an interval
  of time, or to refine an initial prediction (which may incorporate
  other information). The test of the method is based on data from the
  Geostationary Observational Environmental Satellites, and involves
  whole-Sun prediction of soft X-ray flares for 1976-2003. The results
  show that the method somewhat over-predicts the probability of all
  events above a moderate size, but performs well in predicting large
  events.

Title: A Parallel Approach to Nonlinear Force-Free Fields
Authors: Wheatland, M. S.
Bibcode: 2004ASPC..325..131W
Altcode:
  A new procedure for calculating nonlinear force-free fields is briefly
  described, which is similar in approach to Sakurai (1981) but which
  differs in the method of solution of the problem. The present method is
  designed to be implemented on parallel computers. Preliminary results
  are shown.

Title: Parallel Construction of Nonlinear Force-Free Fields
Authors: Wheatland, M. S.
Bibcode: 2004SoPh..222..247W
Altcode:
  A numerical approach to calculating nonlinear force-free fields
  is presented. The approach is similar to Sakurai (1981) being a
  current-field iteration scheme using the integral solution to Ampere's
  law (the Biot-Savart law). However, the method of solution presented
  here is simpler than Sakurai's approach, in that the field is directly
  constructed on a grid without the intermediate solution of a large
  system of nonlinear equations. The method also permits straightforward
  implementation on parallel computers. Results of applying the method
  to a number test cases, including boundary conditions with substantial
  currents, are presented.

Title: A Bayesian Approach to Solar Flare Prediction
Authors: Wheatland, M. S.
Bibcode: 2004ApJ...609.1134W
Altcode: 2004astro.ph..3613W
  A number of methods of flare prediction rely on classification of
  physical characteristics of an active region, in particular optical
  classification of sunspots, and historical rates of flaring for a
  given classification. However, these methods largely ignore the number
  of flares the active region has already produced, in particular the
  number of small events. The past history of occurrence of flares (of
  all sizes) is an important indicator of future flare production. We
  present a Bayesian approach to flare prediction, which uses the flaring
  record of an active region together with phenomenological rules of flare
  statistics to refine an initial prediction for the occurrence of a big
  flare during a subsequent period of time. The initial prediction is
  assumed to come from one of the extant methods of flare prediction. The
  theory of the method is outlined, and simulations are presented to
  show how the refinement step of the method works in practice.

Title: Comparative Analysis of Super-Kamiokande 10-day-bin and
    5-day-bin Datasets
Authors: Sturrock, P. A.; Caldwell, D. O.; Scargle, J. D.; Walther,
   G.; Wheatland, M. S.
Bibcode: 2004AAS...204.5301S
Altcode: 2004BAAS...36..755S
  The Super-Kamiokande Collaboration has released two datasets suitable
  for time-series analysis: one packaged in 10-day bins and, more
  recently, one packaged in 5-day bins. We have analyzed both datasets by
  a likelihood power-spectrum procedure that is to be preferred over the
  more usual Lomb-Scargle procedure since it takes account of all of the
  available data, whereas the Lomb-Scargle procedure uses only a fraction
  of the data. Analysis of these two datasets yields power spectra that
  are similar but have some notable differences. Comparative analysis
  of these two datasets shows that the significant differences are due
  to aliasing. Since each dataset represents highly regular sampling,
  a modulation at frequency v<SUB>M</SUB> will be accompanied by alias
  periodicities at frequencies ěrt v<SUB>T</SUB> - v<SUB>M</SUB>
  ěrt and at v<SUB>T</SUB> + v<SUB>M</SUB>, where v<SUB>T</SUB> is the
  sampling frequency. As indications of real oscillations, we have looked
  for peaks in the two power spectra which are strong in both, but for
  which the power in the 5-day power spectrum is larger than that in
  the 10-day power spectrum. This plot identifies three peaks of special
  interest. One of these may be attributed to modulation associated with
  solar rotation, and the other two may be attributed to modulation
  associated with an internal r-mode oscillation. These periodicities
  appear to be statistically significant. We thank the Super-Kamiokande
  consortium for making these datasets available. This work was supported
  by NSF grant AST-0097128 and DOE grant DE-FG03-91ER40618.

Title: Bayesian refinement of solar flare prediction
Authors: Wheatland, M. S.
Bibcode: 2004AAS...204.5415W
Altcode: 2004BAAS...36..760W
  A number of methods of flare prediction rely on classification of
  physical characteristics of an active region, in particular optical
  classification of sunspots, and historical rates of flaring for a given
  classification. However these methods largely ignore how many flares
  the active region has already produced, in particular the number of
  small events. The past history of occurrence of flares (of all sizes)
  is an important indicator to future flare production. We present a
  Bayesian approach to flare prediction, which uses the past history
  of flaring of an active region together with phenomenological rules
  of flare statistics to refine an initial prediction for flaring. The
  initial prediction may come from one of the extant prediction schemes,
  and appears in the method as a prior probability distribution. The
  theory of the new method is outlined, and simulations are presented
  to show how the refinement step works in practice. Construction of
  appropriate prior distributions is also discussed. <P />The author is
  supported by an Australian Research Council QEII Fellowship.

Title: Energy Balance in the Corona over the 22 Year Solar Cycle
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2004SoPh..219..265L
Altcode:
  Wheatland and Litvinenko (2001) presented a model for dynamical
  energy balance in the flaring solar corona which predicts a time
  lag between flare occurrence and the supply of energy to the corona
  (`driving'). They also suggested that an observed net lag between
  flare numbers and sunspot numbers over cycles 21 and 22 might provide
  support for the model. Temmer, Veronig, and Hanslmeier (2003) examined
  data for five individual solar cycles (19-23) and confirmed a lag
  between flare and sunspot numbers for odd solar cycles, but found no
  lag for even cycles. Following the suggestion of Temmer, Veronig, and
  Hanslmeier, the energy balance model is here extended to incorporate
  22-year driving consistent with the phenomenological Gnevyshev—Ohl
  rule. The model is found to exhibit a greater lag for the smaller
  (even) cycles, in contradiction with the findings of Temmer, Veronig,
  and Hanslmeier. A modification to the model is investigated in which
  the flaring rate is proportional to the free energy and to the driving
  rate for small driving rates, but is proportional only to the free
  energy for large driving rates. The modified model can in principle
  account for the observations.

Title: Testing Circuit Models for the Energies of Coronal Magnetic
    Field Configurations
Authors: Wheatland, M. S.; Farvis, F. J.
Bibcode: 2004SoPh..219..109W
Altcode: 2003astro.ph.11018W
  Circuit models involving bulk currents and inductances are often used
  to estimate the energies of coronal magnetic field configurations, in
  particular configurations associated with solar flares. The accuracy
  of circuit models is tested by comparing calculated energies of linear
  force-free fields with specified boundary conditions with corresponding
  circuit estimates. The circuit models are found to provide reasonable
  (order of magnitude) estimates for the energies of the non-potential
  components of the fields, and to reproduce observed functional
  dependences of the energies. However, substantial departure from
  the circuit estimates is observed for large values of the force-free
  parameter, and this is attributed to the influence of the non-potential
  component of the field on the path taken by the current.

Title: Toward a Reconnection Model for Solar Flare Statistics
Authors: Wheatland, M. S.; Craig, I. J. D.
Bibcode: 2003ApJ...595..458W
Altcode:
  A model to account for observed solar flare statistics in terms of
  a superposition of independent random flaring elements (assumed to
  be sites of magnetic reconnection in the coronal magnetic field
  and hence termed ``separators'') is described. A separator of
  length l is assumed to flare as a Poisson process in time, with a
  rate ν(l) inversely proportional to the Alfvén transit time for
  the structure. It is shown that a relationship E~l<SUP>κ</SUP>
  between the mean energy of events E at a separator and the separator
  length implies a relationship E~τ<SUP>κ</SUP> between individual
  waiting times τ and energies E of events at the separator. The most
  plausible κ=2 model is found to be compatible with simple pictures for
  magnetohydrodynamic energy storage prior to magnetic reconnection in a
  current sheet with anomalous (turbulent) resistivity. Formal inversion
  of the observed flare frequency-energy distribution is shown to imply
  a distribution P(l)~l<SUP>-1</SUP> of the separator lengths in active
  regions. A simulation confirms the basic results of the model. It is
  also demonstrated that a model comprising time-dependent separator
  numbers N=N(t) can reproduce an observed power-law tail in the flare
  waiting-time distribution, for large waiting times.

Title: Statistics of the Chi-Square Type, with Application to the
    Analysis of Multiple Time-Series Power Spectra
Authors: Sturrock, P. A.; Wheatland, M. S.
Bibcode: 2003astro.ph..7353S
Altcode:
  It is often necessary to compare the power spectra of two or more
  time series: one may, for instance, wish to estimate what the power
  spectrum of the combined data sets might have been, or one may wish
  to estimate the significance of a particular peak that shows up in two
  or more power spectra. Also, one may occasionally need to search for a
  complex of peaks in a single power spectrum, such as a fundamental and
  one or more harmonics, or a fundamental plus sidebands, etc. Visual
  inspection can be revealing, but it can also be misleading. This
  leads one to look for one or more ways of forming statistics, which
  readily lend themselves to significance estimation, from two or more
  power spectra. The familiar chi-square statistic provides a convenient
  mechanism for combining variables drawn from normal distributions, and
  one may generalize the chi-square statistic to be any function of any
  number of variables with arbitrary distributions. In dealing with power
  spectra, we are interested mainly in exponential distributions. One
  well-known statistic, formed from the sum of two or more variables
  with exponential distributions, satisfies the gamma distribution. We
  show that a transformation of this statistic has the convenient
  property that it has an exponential distribution. We introduce two
  additional statistics formed from two or more variables with exponential
  distributions. For certain investigations, we may wish to study the
  minimum power (as a function of frequency) drawn from two or more
  power spectra. In other investigations, it may be helpful to study
  the product of the powers. We give numerical examples and an example
  drawn from our solar-neutrino research.

Title: The Coronal Mass Ejection Waiting-Time Distribution
Authors: Wheatland, M. S.
Bibcode: 2003SoPh..214..361W
Altcode: 2003astro.ph..3019W
  The distribution of times Δt between coronal mass ejections (CMEs) in
  the Large Angle and Spectrometric Coronagraph (LASCO) CME catalog for
  the years 1996-2001 is examined. The distribution exhibits a power-law
  tail ∼(Δt)<SUP>γ</SUP> with an index γ≈−2.36±0.11 for large
  waiting times (Δt&gt;10 hours). The power-law index of the waiting-time
  distribution varies with the solar cycle: for the years 1996-1998 (a
  period of low activity), the power-law index is γ≈−1.86±0.14,
  and for the years 1999-2001 (a period of higher activity), the index
  is γ≈−2.98±0.20. The observed CME waiting-time distribution,
  and its variation with the cycle, may be understood in terms of CMEs
  occurring as a time-dependent Poisson process. The CME waiting-time
  distribution is compared with that for greater than C1 class solar
  flares in the Geostationary Operational Environmental Satellite (GOES)
  catalog for the same years. The flare and CME waiting-time distributions
  exhibit power-law tails with very similar indices and time variation.

Title: Interpretation of Statistical Flare Data using Magnetic
    Reconnection Models
Authors: Craig, I. J. D.; Wheatland, M. S.
Bibcode: 2002SoPh..211..275C
Altcode:
  The ability of magnetic reconnection solutions to explain statistical
  flare data is discussed. It is assumed that flares occur at
  well-defined, isolated sites within an active region, determined by
  the null points and separators of the coronal magnetic field (Craig,
  2001). Statistical flare observations then derive from a multiplicity
  of independent sites, flaring in parallel, that produce events of
  widely varying output (Wheatland, 2002). Given that the `separator
  length' at an individual site controls the event frequency and the mean
  energy release, it is shown that the observed frequency-energy spectrum
  N(E)can be inverted to yield a source function that relates directly
  to the distribution of separator lengths. It is also pointed out that,
  under the parallel flaring model, inferred waiting-time distributions
  are naturally interpreted as a superposition of individual point
  processes. Only a modest number of flaring separators is required to
  mimic a Poisson process.

Title: Understanding Solar Flare Waiting-Time Distributions
Authors: Wheatland, M. S.; Litvinenko, Y. E.
Bibcode: 2002SoPh..211..255W
Altcode:
  The observed distribution of waiting times Δt between X-ray solar
  flares of greater than C1 class listed in the Geostationary Operational
  Environmental Satellite (GOES) catalog exhibits a power-law tail
  ∼(Δt)<SUP>γ</SUP> for large waiting times (Δt&gt;10 hours). It is
  shown that the power-law index γ varies with the solar cycle. For
  the minimum phase of the cycle the index is γ=−1.4±0.1, and
  for the maximum phase of the cycle the index is −3.2±0.2. For
  all years 1975-2001, the index is −2.2±0.1. We present a simple
  theory to account for the observed waiting-time distributions
  in terms of a Poisson process with a time-varying rate λ(t). A
  common approximation of slow variation of the rate with respect to a
  waiting time is examined, and found to be valid for the GOES catalog
  events. Subject to this approximation the observed waiting-time
  distribution is determined by f(λ), the time distribution of the rate
  λ. If f(λ) has a power-law form ∼λ<SUP>α</SUP> for low rates,
  the waiting time-distribution is predicted to have a power-law tail
  ∼(Δt)<SUP>−(3+α)</SUP> (α&gt;−3). Distributions f(λ) are
  constructed from the GOES data. For the entire catalog a power-law index
  α=−0.9±0.1 is found in the time distribution of rates for low rates
  (λ&lt;0.1 hours<SUP>−1</SUP>). For the maximum and minimum phases
  power-law indices α=−0.1±0.5 and α=−1.7±0.2, respectively,
  are observed. Hence, the Poisson theory together with the observed time
  distributions of the rate predict power-law tails in the waiting-time
  distributions with indices −2.2±0.1 (1975-2001), −2.9±0.5
  (maximum phase) and −1.3±0.2 (minimum phase), consistent with the
  observations. These results suggest that the flaring rate varies in an
  intrinsically different way at solar maximum by comparison with solar
  minimum. The implications of these results for a recent model for flare
  statistics (Craig, 2001) and more generally for our understanding of
  the flare process are discussed.

Title: Distribution of Flare Energies Based on Independent
    Reconnecting Structures
Authors: Wheatland, M. S.
Bibcode: 2002SoPh..208...33W
Altcode:
  A model is presented to explain the observed frequency distribution of
  flare energies, based on independent flaring at a number of distinct
  topological structures (separators) within active-region magnetic
  fields. The model is a modification and generalization of a recent
  model due to Craig (2001), and reconciles that model with the observed
  flare waiting-time distribution, and the observed absence of a flare
  waiting-time versus energy relationship. The basic assumptions of the
  model are that flares of energy E∼<SUP>2</SUP> occur at separators
  of length , and that the frequency of flaring at a separator is
  defined by the Alfvén transit time of the structure. To reproduce
  the observed distribution of flare energies the model requires a
  probability distribution P()∼<SUP>−1</SUP> of separator lengths
  within active regions. This prediction of the model is in principle
  testable. A theoretical origin for this distribution is also discussed.

Title: Variability of the Solar Neutrino Flux
Authors: Sturrock, P. A.; Scargle, J. D.; Walther, G.; Weber, M. A.;
   Wheatland, M. S.
Bibcode: 2002AAS...200.8904S
Altcode: 2002BAAS...34..791S
  Several tests of the available data provide evidence for variability of
  the solar neutrino flux. The variance of the Homestake measurements is
  larger than expected of a constant flux, and varies with heliographic
  latitude. The Homestake power spectrum contains a peak at 12.88
  y<SUP>-1</SUP> (period 28.4 days), corresponding to a sidereal
  rotation frequency of 440 nHz, close to that of the radiative zone. The
  power spectrum of GALLEX-GNO data contains the 12.88 y<SUP>-1</SUP>
  peak and a stronger peak at 13.59 y<SUP>-1</SUP> (period 26.9 days),
  corresponding to a sidereal rotation frequency of 462 nHz, that of the
  equatorial convection zone at normalized radius 0.85. Further evidence
  for time variation comes from the bimodality of the GALLEX-GNO and SAGE
  histograms. Joint spectrum analysis of the Homestake and GALLEX-GNO
  data yields evidence for the influence of r-mode oscillations [with
  l = 3, m = \{1,2,3\}] associated with the same sidereal rotation rate
  (13.88 y<SUP>-1</SUP> or 440 nHz) found previously. The periods of these
  oscillations (158, 79, and 53 days, respectively) are close to those of
  known Rieger-type oscillations, and therefore point to the radiative
  zone as the source of these oscillations. A subset of these tests,
  selected to be independent, yield results that could arise by chance
  from a constant flux with probabilities ranging from 0.1 to 0.0001. If
  there are no relevant experimental systematic effects, and if the tests
  are valid and statistically independent, the combined estimates yield a
  probability of 10<SUP>-15</SUP> that the results are compatible with a
  constant flux. A variable flux implies that neutrinos have a significant
  magnetic moment, and that neutrino measurements may be used to probe
  the Sun's internal magnetic field and internal dynamics. This work
  was supported by NASA grants NAS 8-37334 and NAG 5-9784, NSF grant
  AST-0097128, and the NASA Applied Information Systems Research Program.

Title: Distribution of Flare Energies Based On Independent
    Reconnecting Structures
Authors: Wheatland, M. S.
Bibcode: 2002AAS...200.2909W
Altcode: 2002BAAS...34..682W
  An explanation for the observed frequency distribution of flare
  energies is given, based on independent flaring at a number of
  distinct topological structures (separators) within active region
  magnetic fields. The approach modifies and generalises a recent model
  due to Craig (2001), and reconciles that model with the observed
  flare waiting-time distribution, and the observed absence of a flare
  waiting-time vs. energy relationship. The basic assumptions of the
  model are that flares of energy E l<SUP>2</SUP> occur at separators
  of length l, and that the frequency of flaring at a separator is
  defined by the Alfvén transit time of the structure. To reproduce the
  observed distribution of flare energies the model requires a probability
  distribution P(l) l<SUP>-1</SUP> of separator lengths l within active
  regions. This prediction of the model is in principle testable. A
  theoretical origin for this distribution is also discussed. The
  author acknowledges the support of an Australian Research Council
  QEII Fellowship.

Title: Solar Neutrino Flux: Evidence for Intrinsic Variability
Authors: Sturrock, P.; Walther, G.; Weber, M.; Scargle, J.;
   Wheatland, M.
Bibcode: 2002APS..APR.X7001S
Altcode:
  Analyses of Homestake and GALLEX-GNO data yield persuasive evidence for
  rotational modulation and related modulations of the solar neutrino
  flux. We find in Homestake data evidence that (1) the variance is
  significantly larger than that found in Monte Carlo simulations; (2)
  the power spectrum contains a significant peak at 12.88 y<SUP>-1</SUP>
  (period 28.4 days); (3) the spectrum also contains four sidebands
  displaced by ± 1 y<SUP>-1</SUP> and ± 2 y<SUP>-1</SUP>; (4) the
  variance of the data shows a significant heliographic N/S asymmetry;
  (5) a time series reconstructed from power spectrum analysis exhibits a
  heliographic-latitude-dependent variance; and (6) the spectrum formed
  from the variance of the reconstructed flux has a notable peak at
  1 y<SUP>-1</SUP>. We find from analysis of GALLEX-GNO data that (7)
  there is a significant periodicity at 13.59 y<SUP>-1</SUP> (period
  26.9 days); and (8) the histogram is bimodal. From a comparative
  analysis of Homestake and GALLEX-GNO data, we find (9) evidence for
  variations attributable to r-mode oscillations with l = 3, m = 1,2,3
  in a region with synodic rotation rate 12.88 y<SUP>-1</SUP>. From
  analysis of X-ray data acquired by the SXT instrument on Yohkoh, we
  find that the corona exhibits two discrete rotation rates, and that
  (10) the coronal rotation frequencies are virtually identical to the
  principal frequencies in the Homestake and GALLEX-GNO spectra.

Title: Energy Balance in the Flaring Solar Corona
Authors: Wheatland, M. S.; Litvinenko, Y. E.
Bibcode: 2001AGUFMSH42A0778W
Altcode:
  Assuming only that flares derive their energy from a coronal source
  and that flaring is the dominant mechanism for depleting that source,
  the global coronal response time (time for flares to remove available
  coronal energy) is about 9 months. A detailed model for dynamic
  energy balance in the solar corona over the solar cycle is presented
  to describe how the magnetic free energy in the solar corona varies
  in response to changes in the supply of energy to the system and to
  changes in the flaring rate. The model predicts that both the flaring
  rate and the free energy of the system should lag behind the driving
  of the system because of the coronal response time (the model gives a
  lag of ~ 11 months). This effect may account for hysteresis phenomena
  between certain solar activity indices. For example, analysis of time
  series of monthly sunspot numbers and monthly numbers of soft X-ray
  flares over the years 1976 to 1999 indicates a tendency for flare
  numbers to lag behind sunspot numbers by ~ 6 months.

Title: Rates of Flaring in Individual Active Regions
Authors: Wheatland, M. S.
Bibcode: 2001SoPh..203...87W
Altcode:
  Rates of flaring in individual active regions on the Sun during the
  period 1981-1999 are examined using United States Air Force/Mount Wilson
  (USAF/MWL) active-region observations together with the Geostationary
  Operational Environmental Satellite (GOES) soft X-ray flare catalog. Of
  the flares in the catalog above C1 class, 61.5% are identified with
  an active region. Evidence is presented for obscuration, i.e. that
  the increase in soft X-ray flux during a large flare decreases the
  likelihood of detection of soft X-ray events immediately following
  the large flare. This effect means that many events are missing
  from the GOES catalog. It is estimated that in the absence of
  obscuration the number of flares above C1 class would be higher by
  (75±23) %. A second observational selection effect - an increased
  tendency for larger flares to be identified with an active region -
  is also identified. The distributions of numbers of flares produced
  by individual active regions and of mean flaring rate among active
  regions are shown to be approximately exponential, although there are
  excess numbers of active regions with low flare numbers and low flaring
  rates. A Bayesian procedure is used to analyze the time history of the
  flaring rate in the individual active regions. A substantial number
  of active regions appear to exhibit variation in flaring rate during
  their transit of the solar disk. Examples are shown of regions with
  and without rate variation, illustrating the different distributions of
  times between events (waiting-time distributions) that are observed. A
  piecewise constant Poisson process is found to provide a good model
  for the observed waiting-time distributions. Finally, applications of
  analysis of the rate of flaring to understanding the flare mechanism
  and to flare prediction are discussed.

Title: Energy Balance in the Flaring Solar Corona
Authors: Wheatland, M. S.; Litvinenko, Yuri E.
Bibcode: 2001ApJ...557..332W
Altcode:
  Assuming only that flares derive their energy from a coronal source
  and that flaring is the dominant mechanism for depleting that source,
  the global coronal response time (time for flares to remove available
  coronal energy) is about 9 months. A detailed model for dynamic
  energy balance in the solar corona over the solar cycle is presented
  to describe how the magnetic free energy in the solar corona varies
  in response to changes in the supply of energy to the system and to
  changes in the flaring rate. The model predicts that both the flaring
  rate and the free energy of the system should lag behind the driving
  of the system because of the coronal response time (the detailed model
  gives a lag of ~11 months). This effect may account for hysteresis
  phenomena between certain solar activity indices. A specific example is
  presented in support of the model. Analysis of time series of monthly
  sunspot numbers and monthly numbers of soft X-ray flares over the
  years 1976-1999 indicates a tendency for flare numbers to lag behind
  sunspot numbers by ~6 months.

Title: YOHKOH/HXT Evidence for a Hyperhot Loop-Top Source in The
    Pre-Impulsive Phase of a Loop Flare
Authors: Uchida, Y.; Wheatland, M. S.; Haga, R.; Yoshitake, I.;
   Melrose, D.
Bibcode: 2001SoPh..202..117U
Altcode:
  A loop flare that occurred on 22 April 1993 near the disk center is
  examined using the Yohkoh Hard X-ray Telescope (HXT). We specifically
  looked into the faint early phase of the flare prior to the start of
  the strong impulsive phase. The pre-impulsive phase, though weak in
  intensity, is expected to contain essential clues to the mechanism
  of loop flares according to the causality principle, but it has
  not received attention previously, probably due to the insufficient
  dynamic range and cadence of observations by the instruments on earlier
  satellites. Observations with Yohkoh/HXT can clarify what occurs in
  this phase. This flare, like many other flares of this type, shows a
  relatively weak emission with a smooth and gradual increase during
  this pre-impulsive phase, followed by impulsive bursts, and then
  turns into a smooth decay phase without impulsive bursts. First, we
  found that the spectrum for the initial smooth rise part is consistent
  with a thin-thermal source at a temperature around 80 MK. Imaging of
  this phase in the HXT/L and M bands shows a single source between the
  footpoint sources that will come up in the impulsive phase following
  this phase, suggesting that this hyperhot source is located at a
  high part of the loop between the footpoints, since this flare takes
  a form of a loop. Furthermore, as we go up to the earliest times of
  the flare before this `hyperhot' source phase, two fainter sources
  are found near the footpoint sources that will appear later in the
  impulsive phase. The spectra of these sources at this earliest time of
  the flare, in contrast to the `hyperhot' source, cannot be determined
  from the HXT because the instrument was not in flare mode, and HXT/M1,
  M2, and H-band data are, unfortunately, not available at this very
  initial time. We can guess, however, that they are also of thermal
  character because the time profile is smooth without any spikes just as
  in the following `hyperhot' thermal phase, and in the post-impulsive
  `superhot' thermal phase coming up much later. These findings suggest
  that there is an important, and probably dynamic, early phase in loop
  flares that has been unnoticed in the still dark pre-impulsive phase,
  because the very early footpoint sources change into the loop top
  source in a matter of 20-30 s, comparable to the dynamic Alfvén time
  scale. Some implications of our new findings are discussed.

Title: The local Poisson hypothesis for solar flares
Authors: Wheatland, M. S.
Bibcode: 2001astro.ph..7147W
Altcode:
  The question of whether flares occur as a Poisson process has
  important consequences for flare physics. Recently Lepreti et
  al. presented evidence for local departure from Poisson statistics
  in the Geostationary Operational Environmental Satellite (GOES)
  X-ray flare catalog. Here it is argued that this effect arises from
  a selection effect inherent in the soft X-ray observations; namely
  that the slow decay of enhanced flux following a large flare makes
  detection of subsequent flares less likely. It is also shown that the
  power-law tail of the GOES waiting-time distribution varies with the
  solar cycle. This counts against any intrinsic significance to the
  appearance of a power law, or to the value of its index.

Title: Modeling the Rate of Occurrence of Solar Flares
Authors: Litvinenko, Yuri E.; Wheatland, M. S.
Bibcode: 2001ApJ...550L.109L
Altcode:
  Dimensional considerations are used to analyze the distribution of
  times between solar flares (the flare waiting-time distribution). An
  analytical estimate for the mean flaring rate λ<SUB>0</SUB>
  is obtained, based on the idea that the rate reflects a balance
  between the processes of energy input into the corona and energy
  dissipation by flaring. The estimate is shown to be in good agreement
  with observations of flares by Geostationary Operational Environmental
  Satellite detectors. The analytic result is confirmed using the master
  equation (probability balance equation) formalism. Analysis of time
  variation leads to a differential equation describing how the free
  energy in the corona changes when the rates of driving of the system
  and of flaring vary. This equation may be used to describe the global
  energy balance in the corona over the solar cycle.

Title: Metastable Magnetic Configurations and Their Significance
    for Solar Eruptive Events
Authors: Sturrock, Peter A.; Weber, Mark; Wheatland, Michael S.;
   Wolfson, Richard
Bibcode: 2001ApJ...548..492S
Altcode:
  Solar flares and coronal mass ejections (CMEs) involve the sudden
  release of magnetic energy that can lead to the ejection from the Sun of
  large masses of gas with entrained magnetic field. In dynamical systems,
  such sudden events are characteristic of metastable configurations that
  are stable against small perturbations but unstable to sufficiently
  large perturbations. Linear stability analysis indicates whether
  or not the first requirement is met, and energetic analysis can
  indicate whether or not the second requirement is met: if a magnetic
  configuration that is stable against small perturbations can make a
  transition to a lower energy state, then it is metastable. In this
  paper, we consider a long twisted flux tube, anchored at both ends
  in the photosphere and restrained by an overlying magnetic arcade. We
  argue from a simple order-of-magnitude calculation that, for appropriate
  parameter values, it is energetically favorable for part of the flux
  tube to erupt into interplanetary space, even when the configuration
  is stable according to linear MHD stability theory. The properties
  of metastable magnetic configurations may be relevant to CMEs and to
  other explosive astrophysical events such as solar flares.

Title: A Test to Confirm the Source of Energy for Solar Flares
Authors: Wheatland, M. S.
Bibcode: 2001PASA...18..351W
Altcode:
  A test of the hypothesis that flares derive their energy from
  large scale current systems inferred from active region vector
  magnetograms is proposed. The test involves a statistical comparison
  of the flare-related change in coronal magnetic energy (based on
  the magnetohydrodynamic virial theorem) and an independent measure
  of the energy of the flare. A simulation suggests that - assuming
  the hypothesis is correct - the test requires around 50 flares with
  energy greater than 5×10<SUP>23</SUP> J to return a significant
  result. Existing archives of vector magnetograms should provide
  sufficient data for such a study.

Title: The Origin of the Solar Flare Waiting-time Distribution
Authors: Wheatland, M. S.
Bibcode: 2000SPD....31.0256W
Altcode: 2000BAAS...32.1291W
  It was recently pointed out that the distribution of times between
  solar flares (the flare waiting-time distribution) follows a power
  law, for long waiting times. Based on 25 years of soft X-ray flares
  observed by Geostationary Operational Environmental Satellite (GOES)
  instruments it is shown that 1. the waiting-time distribution of
  flares is consistent with a time-dependent Poisson process, and
  2. the fraction of time the Sun spends with different flaring rates
  approximately follows an exponential distribution. The second result
  is a new phenomenological law for flares. It is shown analytically how
  the observed power-law behavior of the waiting times originates in the
  exponential distribution of flaring rates. These results are argued
  to be consistent with a non-stationary avalanche model for flares.

Title: An Optimization Approach to Reconstructing Force-free Fields
Authors: Wheatland, M. S.; Sturrock, P. A.; Roumeliotis, G.
Bibcode: 2000ApJ...540.1150W
Altcode:
  A new method for reconstructing force-free magnetic fields from their
  boundary values, based on minimizing the global departure of an initial
  field from a force-free and solenoidal state, is presented. The method
  is tested by application to a known nonlinear solution. We discuss
  the obstacles to be overcome in the application of this method to the
  solar case: the reconstruction of force-free fields in the corona from
  measurements of the vector magnetic field in the low atmosphere.

Title: The Origin of the Solar Flare Waiting-Time Distribution
Authors: Wheatland, M. S.
Bibcode: 2000ApJ...536L.109W
Altcode: 2000astro.ph..5121W
  It was recently pointed out that the distribution of times between solar
  flares (the flare waiting-time distribution) follows a power law for
  long waiting times. Based on 25 years of soft X-ray flares observed by
  Geostationary Operational Environmental Satellite instruments, it is
  shown that (1) the waiting-time distribution of flares is consistent
  with a time-dependent Poisson process and (2) the fraction of time
  the Sun spends with different flaring rates approximately follows an
  exponential distribution. The second result is a new phenomenological
  law for flares. It is shown analytically how the observed power-law
  behavior of the waiting times originates in the exponential distribution
  of flaring rates. These results are argued to be consistent with a
  nonstationary avalanche model for flares.

Title: Flare Frequency-Size Distributions for Individual Active
    Regions
Authors: Wheatland, M. S.
Bibcode: 2000ApJ...532.1209W
Altcode:
  It is well known that the size (peak count rate of emission, or
  inferred energy) distribution of flares observed on the Sun follows
  a power law. However, the distributions that are constructed include
  flares from different active regions that have a variety of physical
  properties. In this paper cumulative peak count rate distributions
  are constructed for individual active regions using events listed in
  the WATCH solar X-ray burst catalog. The individual distributions are
  found to be consistent with the distribution constructed from events
  in all active regions named in the catalog. This result suggests that
  the flare power-law size distribution reflects an intrinsic property
  of the flare mechanism and is not a product of the distributions of
  physical parameters between active regions. The result is consistent
  with the avalanche model for flares and more generally argues against
  macroscopic flare models.

Title: Are Electric Currents in Solar Active Regions Neutralized?
Authors: Wheatland, M. S.
Bibcode: 2000ApJ...532..616W
Altcode:
  Models for energy storage in the solar corona due to the twisting of
  coronal magnetic fields by subphotospheric flows imply that coronal
  currents should be neutralized (i.e., observed currents over a given
  polarity of the magnetic field should sum to zero). The neutralized
  current hypothesis is quantitatively tested by examining vector
  magnetic field data from 21 active regions observed by the Solar
  Magnetic Field Telescope of the Huairou Solar Observing Station of
  Beijing Astronomical Observatory. For each active region, the current
  over the positive polarity of the field, I<SUB>+</SUB>, is estimated,
  as well as the current over the negative polarity, I<SUB>-</SUB>, and
  the total current over both polarities, I<SUB>tot</SUB>. In no case
  is the total current I<SUB>tot</SUB> significantly different from
  zero. The currents I<SUB>+</SUB> and I<SUB>-</SUB> are found to be
  significantly different from zero (at the 3 σ level) in more than half
  of the active regions studied, implying that large-scale currents in
  active regions are typically unneutralized. The implications of this
  result and the relationship of this study to related studies (e.g.,
  of current helicity) are discussed.

Title: Do Solar Flares Exhibit AN Interval-Size Relationship?
Authors: Wheatland, M. S.
Bibcode: 2000SoPh..191..381W
Altcode:
  Some models for flare statistics predict or assume that there is
  a relationship between the times between flares and the energy of
  flares. This question is examined observationally using the WATCH
  solar X-ray burst catalogue. A rank correlation test applied to the
  data finds strong evidence for a correlation between the time since the
  last event, t<SUB>b</SUB>, and the size (peak count rate) of an event,
  and for a correlation between the time to the next event, t<SUB>a</SUB>,
  and the size of an event. A more sophisticated statistical test, taking
  into account a probable bias in event selection, does not support the
  hypothesis that event size depends on t<SUB>b</SUB> or t<SUB>a</SUB>.

Title: Models for Flare Statistics and the Waiting-time Distribution
    of Solar Flare Hard X-ray Bursts
Authors: Wheatland, M. S.; Edney, S. D.
Bibcode: 1999spro.proc..357W
Altcode:
  In a previous study (Wheatland, Sturrock, McTiernan 1998), a
  waiting-time distribution was constructed for solar flare hard X-ray
  bursts observed by the ICE/ISEE-3 spacecraft. A comparison of the
  observed distribution with that of a time-dependent Poisson process
  indicated an overabundance of short waiting times (10~s -- 10~min),
  implying that the hard X-ray bursts are not independent events. Models
  for flare statistics assume or predict that flares are independent
  events -- in particular the avalanche model makes this specific
  prediction. The results of the previous study may be reconciled with
  the avalanche picture if individual flares produce several distinct
  bursts of hard X-ray emission. A detailed comparison of the avalanche
  model and the ICE/ISEE-3 waiting-time distribution is presented here.

Title: Rotational Signature and Possible R-Mode Signature in the
    GALLEX Solar Neutrino Data
Authors: Sturrock, P. A.; Scargle, J. D.; Walther, G.; Wheatland, M. S.
Bibcode: 1999ApJ...523L.177S
Altcode: 1999astro.ph..4278S
  Recent analysis of the Homestake data has yielded evidence that the
  solar neutrino flux varies in time--more specifically, that it exhibits
  a periodic variation that may be attributed to rotational modulation
  occurring deep in the solar interior, either in the tachocline or
  in the radiative zone. Here we present a spectral analysis of the
  GALLEX data that yields supporting evidence for this rotational
  modulation. The most prominent peak in the power spectrum occurs
  at the synodic frequency of 13.08 yr<SUP>-1</SUP> (cycles per year)
  and is estimated to be significant at the 0.1% level. It appears that
  the most likely interpretation of this modulation is that the electron
  neutrinos have nonzero magnetic moment, so that they oscillate between
  left-hand (detectable) and right-hand (nondetectable) chiralities
  as they traverse the Sun's internal magnetic field. This oscillation
  could account for the neutrino deficit. The second strongest peak in
  the GALLEX spectrum has a period of 52 days, and this period occurs
  in other solar data as well. We suggest that this periodicity and also
  the Rieger 154 day periodicity, which shows up in many solar parameters
  and in the Homestake data, are due to r-mode oscillations.

Title: Frequency-energy distributions of flares and active region
    transient brightenings
Authors: Wheatland, M. S.; Uchida, Y.
Bibcode: 1999SoPh..189..163W
Altcode:
  In 1988, Uchida and Shibata proposed a model for compact loop
  flares as due to the collision of two large amplitude torsional
  Alfvén wave packets coming up along a coronal magnetic loop,
  leaking out from the subphotospheric convective layers of the solar
  atmosphere. We investigate the possibility that active region transient
  brightenings occur when a single torsional Alfvén wave packet transits
  a coronal loop. Assuming this related origin for flares and transient
  brightenings, the statistics of the two phenomena must also be closely
  related. It is shown that the observed power-law frequency-energy
  distributions of flares and transient brightenings may be accounted
  for in a natural way if the energy distribution of the underlying
  torsional Alfvén wave packets is itself a power law.

Title: A Better Linear Force-free Field
Authors: Wheatland, M. S.
Bibcode: 1999ApJ...518..948W
Altcode:
  Linear force-free fields are often used as approximate models for
  magnetic fields in the solar corona, calculated on the basis of boundary
  values measured in the low atmosphere. The problem that is set up and
  solved does not have a unique solution, however, and various particular
  solutions--motivated in large part by mathematical convenience--appear
  in the literature. A method is presented for calculating the linear
  force-free field that is consistent with the observed component of
  the magnetic field normal to the solar surface and has a minimum
  difference between the components tangent to the surface and the
  observed tangential field. The method is tested by application to a
  known nonlinear solution.

Title: Topological Differences Between Force-Free Field Models
Authors: Hudson, T. S.; Wheatland, M. S.
Bibcode: 1999SoPh..186..301H
Altcode:
  The potential and linear force-free field models for the magnetic field
  in the solar corona are often used in the analysis of flares. The
  field is calculated using boundary values measured in the low solar
  atmosphere. The topology of the field calculated using these models
  is then compared to the position of flare emissions. We demonstrate
  that the topology of the field according to each of these models,
  with the same boundary conditions in place, is not in general even
  qualitatively equivalent. An argument is given for a similar discrepancy
  between a linear force-free field solution and a nonlinear force-free
  field solution.

Title: Rotational and Related Periodicities in the Homestake and
    GALLEX Neutrino Data
Authors: Sturrock, P. A.; Walther, G.; Wheatland, M. S.
Bibcode: 1999HEAD....4.3908S
Altcode: 1999BAAS...31..743S
  If neutrinos have a sufficiently strong magnetic moment, the solar
  neutrino flux will be modulated by the Sun's internal magnetic field. We
  have spectrum-analyzed the Homestake data, looking for evidence of
  periodic modulation in the range 12.6 - 13.3 y(-1) due to structures
  in the radiative zone that has a sidereal rotation rate in the range
  13.6 - 14.3 y(-1) . We find a peak at 12.88 y(-1) . The estimated
  probability of finding such a peak in the search band by chance is
  about 3%. We also find sidebands at 11.88, 12.88, 14.88 and 15.88 y(-1)
  , attributable to a seasonal modulation due to the tilt of the solar
  axis. The estimated probability of this combination occurring by chance
  is about 0.2%. We have more recently examined the GALLEX data and find
  that the strongest peak in the range 1 to 20 cycles per year occurs
  at 13.10 y(-1) , close to the value found in the Homestake data. The
  estimated probability of finding such a periodicity in the search band
  by chance is less than 0.1%. There is evidence for some other well
  known solar periodicities in the neutrino data: a peak at 2.32 cycles
  per year (period = 157 days) in the Homestake data, and a peak at 7.00
  cycles per year (period = 52 days) in the GALLEX data. We propose that
  these periodicities [together with another well known periodicity at
  4.67 cycles per year (period = 78 days)] are due to internal r-mode
  oscillations. We suggest that these modulations in the neutrino flux may
  be understood in terms of the RSFP (resonant spin flavor precession)
  mechanism proposed by Akhmedov and others. This interpretation leads
  to an estimate of Delta m(2) and to a lower limit for the neutrino
  magnetic moment. This work was supported in part by Air Force grant
  F49620-95-1-008 and NASA grants NAS 8-37334 and NAGW-5-4038.

Title: The Waiting-Time Distribution of Solar Flare Hard X-Ray Bursts
Authors: Wheatland, M. S.; Sturrock, P. A.; McTiernan, J. M.
Bibcode: 1998ApJ...509..448W
Altcode:
  A waiting-time distribution is constructed for 8 yr of solar flare
  hard X-ray bursts observed by the ICE/ISEE 3 spacecraft. The observed
  distribution is compared with a simulated waiting-time distribution
  produced by a time-dependent Poisson process constructed using rates
  estimated from the observations. The observed distribution shows an
  overabundance of short waiting times (10 s-10 minutes) in comparison
  with the simulation. This result implies that the hard X-ray bursts
  are not independent events. The implications of this result for the
  existence of sympathetic flaring and to models of flare statistics are
  discussed, and the result is compared with previous determinations of
  waiting-time distributions for solar hard X-ray events.

Title: Apparent Latitudinal Modulation of the Solar Neutrino Flux
Authors: Sturrock, P. A.; Walther, G.; Wheatland, M. S.
Bibcode: 1998ApJ...507..978S
Altcode:
  We examine the solar neutrino flux, as measured by the Homestake
  neutrino detector, to search for evidence of a dependence upon the
  solar latitude of the Earth-Sun line that varies from 7.25d south in
  mid-March to 7.25d north in mid-September. Although the flux does
  not obviously show any dependence on latitude, we do find evidence
  for a dependence of the variance of the flux upon latitude. When
  data from 108 runs of the Homestake experiment are divided into four
  quartiles, sorted according to latitude, we find that the northernmost
  quartile exhibits a larger variance than the other three. By applying
  the shuffle test, we estimate the probability that this could have
  occurred by chance to be in the range 1%-2%. <P />For more detailed
  information, we examine a ``reconstructed flux'' formed from our recent
  maximum likelihood spectrum analysis. This procedure indicates that
  the variance is largest at about 6.5d north. We also find that the
  spectrum of the variance of the reconstructed flux has a notable peak
  at 1 cycle y<SUP>-1</SUP> tending to confirm a latitude dependence of
  the variance. We also examine the 12.88 cycle yr periodicity described
  in our recent paper and find that the amplitude of the periodicity is
  greater for the northernmost quartile than for the other quartiles. We
  suggest that these effects may be attributed to resonant spin-flavor
  precession of left-hand-helicity electron neutrinos in the magnetic
  field of the solar radiative zone.

Title: Flare Frequency Distributions Based on a Master Equation
Authors: Wheatland, M. S.; Glukhov, S.
Bibcode: 1998ApJ...494..858W
Altcode:
  The Rosner &amp; Vaiana model for flares is generalized to allow
  for flares that do not deplete all free energy from the system, a
  step that overcomes a number of objections to the original model. We
  obtain a probability balance equation, or master equation, describing
  the free energy E of an active region subject to a prescribed growth
  rate, Ė, and a prescribed distribution, α(E), of stochastic decay
  events. We argue that the solution appropriate to flares involves an
  energy-independent growth rate and a power-law form for α(E), which may
  be the result of an underlying avalanche process. The resulting model
  produces power-law flare frequency distributions below a high-energy
  rollover corresponding to the largest energy the system is likely to
  attain, which is set by the balance between the rate of growth and the
  rate of stochastic decay. There is a close correspondence between the
  resulting model and the avalanche model for flares.

Title: Search for Periodicities in the Homestake Solar Neutrino Data
Authors: Sturrock, P. A.; Walther, G.; Wheatland, M. S.
Bibcode: 1997ApJ...491..409S
Altcode:
  We evaluate a χ<SUP>2</SUP> statistic to test against the Homestake
  data the hypothesis that the neutrino flux from the Sun is constant. We
  use estimates of standard deviations derived 1000 simulations of the
  sequence of 108 runs, and we also use two procedures for deriving
  proxies for the standard deviation from the experimental data. All
  tests indicate that the hypothesis should be rejected; the significance
  level ranges from 5.8% to 0.1%. <P />We also search for evidence of
  periodicities in the neutrino flux by evaluating the log likelihood of
  finding the actual count rates in a model in which the neutrino flux
  is modulated with a sinusoidal term. We consider a range of values of
  the frequency (0-20 cycles yr<SUP>-1</SUP>) and, for each frequency,
  adjust the modulation parameters to maximize the likelihood. We find
  no evidence of modulation at the frequency of the solar cycle. A 1000
  shuffle test and 1000 simulations using error estimates taken from the
  simulations yield no evidence for either the quasi-biennial (2.2 yr)
  periodicity or the Rieger (157 day) periodicity. However, simulations
  based on the experimental error estimates yield significance levels
  of 1% and 2.7% for the quasi-biennial periodicity, and 2% and 0.2%
  for the Rieger periodicity. <P />We have also looked for evidence
  of modulation at a frequency that might be related to the solar
  rotation frequency. We have adopted a search band of 12.4-13.1 cycles
  yr<SUP>-1</SUP>, corresponding to the 1 year lower sideband (synodic
  frequency) of the rotation frequency of the Sun's radiative zone, as
  estimated from helioseismology. There is indeed a peak in that band,
  at 12.88 cycles yr<SUP>-1</SUP>, that according to the simulation test
  is significant at the 3% level. However, we also find evidence of four
  sidebands near 10.88, 11.88, 13.88, and 14.88 cycles yr<SUP>-1</SUP>
  that may be due to the departure of the rotational axis from the
  normal to the ecliptic. We introduce a correlation measure formed
  from the powers at a ``fundamental'' and at four sidebands. None of
  1000 shuffle tests, and only one of 1000 simulations, yield values of
  the correlation measure as large as that formed from the experimental
  data. These tests offer support, at the 0.1% and 0.2% significance
  level, respectively, for the proposition that the neutrino flux
  is modulated at a frequency that could be the synodic frequency
  corresponding to a sidereal rotational frequency of 13.88 cycles
  yr<SUP>-1</SUP> (440 nHz) of the Sun's radiative zone.

Title: Search for Periodicities in the Homestake Solar Neutrino Data
Authors: Sturrock, P. A.; Walther, G.; Wheatland, M. S.
Bibcode: 1997BAAS...29.1121S
Altcode:
  No abstract at ADS

Title: Test for Constancy of the Solar Neutrino Flux as Measured by
    the Homestake Neutrino Experiment
Authors: Walther, G.; Sturrock, P. A.; Wheatland, M. S.
Bibcode: 1997BAAS...29.1121W
Altcode:
  No abstract at ADS

Title: Coronal Heating and the Vertical Temperature Structure of
    the Quiet Corona
Authors: Wheatland, M. S.; Sturrock, P. A.; Acton, L. W.
Bibcode: 1997ApJ...482..510W
Altcode:
  The radial variation of temperature in the inner corona is examined
  using long-exposure Yohkoh images of two regions of diffuse (quiet)
  corona. The results indicate a steady radial increase of temperature for
  both regions, out to 0.7 and 0.95 solar radii above the limb. We find
  that the filter-ratio data for the two regions is well fitted in each
  case by integration over the line of sight of a spherically symmetric
  model atmosphere in hydrostatic equilibrium and with a temperature
  profile due to a conserved inward heat flux. An Abel inversion process
  is also applied to the data, and this gives results consistent with
  the spherically symmetric, conserved-heat flux model. These results
  imply that the nonthermal energy responsible for heating these regions
  of the quiet corona is being deposited beyond the observed range of
  heights. However, the diffuse regions we examined are believed to be
  partly closed-field regions, and so, the radial models require careful
  interpretation. We discuss the implications for coronal heating in
  these regions.

Title: An optimization approach to reconstructing force-free fields
from boundary data: II. Numerical results
Authors: Wheatland, M. S.; Roumeliotis, G.
Bibcode: 1997SPD....28.1604W
Altcode: 1997BAAS...29..920W
  The reconstruction of force-free fields from boundary data is an
  important problem in solar physics. Reliable reconstructions of fields
  in active regions may allow detailed tests of existing theories of the
  physics of solar flares and of coronal heating. A new method, based on
  minimizing a global objective function describing the departure from
  a force-free and solenoidal state, has been presented in a talk at
  this meeting. A computer code to reconstruct arbitrary 3-d fields from
  boundary data, based on this approach, has been written and is being
  tested. We describe the details of the implementation of the method
  and the numerical results obtained. The method has been tested against
  known analytic force-free solutions, which highlight the advantages
  and shortcomings of our approach. We also describe the application
  of the method to real boundary data, and outline particular physical
  problems that we hope to address with our code. This work was supported
  in part by Air Force grant F49620-95-1-008 and NASA grants NAS 8-37334
  and NAGW-2265.

Title: An optimization approach to reconstructing force-free fields
from boundary data: I. Theoretical basis.
Authors: Roumeliotis, G.; Wheatland, M. S.
Bibcode: 1997SPD....28.1603R
Altcode: 1997BAAS...29..920R
  The reconstruction of force-free fields from boundary data is an
  important problem in solar physics. Reliable reconstructions of fields
  in active regions may allow detailed tests of existing theories of the
  physics of solar flares and of coronal heating. A new method, based on
  minimizing a global objective function describing the departure from
  a force-free and solenoidal state, will be presented in this talk. A
  computer code to reconstruct arbitrary 3-d fields from boundary data,
  based on this approach, has been written and will be described in
  another talk at this meeting. This work was supported in part by Air
  Force grant F49620-95-1-008 and NASA grants NAS 8-37334 and NAGW-2265.

Title: Avalanche Models of Solar Flares and the Distribution of
    Active Regions
Authors: Wheatland, M. S.; Sturrock, P. A.
Bibcode: 1996ApJ...471.1044W
Altcode:
  Avalanche models of solar flares successfully reproduce the power-law
  distribution of flare frequency as a function of energy. However,
  the model distributions have been produced for a single numerical
  grid, representing a single active region on the Sun. Here we
  convolve the distribution owing to an avalanche grid with each of
  two observationally determined active region size distributions. The
  resulting energy distributions are power laws (with index α ≍ 1.5)
  below about 10<SUP>31</SUP> ergs, but they gradually steepen with
  energy. The resulting distributions are compared with a flare energy
  distribution derived from International Cometary Explorer satellite
  observations. Qualitative agreement is found between the model and
  observed distributions, although the observations favor a simple
  power-law model distribution with a somewhat steeper index (≍1.71).

Title: Coronal Heating in the Quiet Corona
Authors: Wheatland, M.; Sturrock, P.
Bibcode: 1996AAS...188.3308W
Altcode: 1996BAAS...28Q.869W
  The radial variation of temperature in the inner corona is examined
  using long exposure Yohkoh images for two regions of diffuse (quiet)
  corona. The results indicate a steady radial increase of temperature
  for both regions, out to 0.7 and 0.9 solar radii above the limb,
  respectively. We find that the filter ratio data for the two regions
  is well fitted in each case by integration over the line of sight
  of a model radial atmosphere in hydrostatic equilibrium and with
  a temperature profile due to a conserved inward heat flux. An Abel
  inversion process is also applied to the data, and this gives results
  consistent with the radially symmetric, conserved heat flux model. These
  results imply that the non-thermal energy responsible for heating these
  pieces of the quiet corona is being deposited beyond the observed range
  of heights. However, the diffuse regions we examined are believed to be
  mainly closed field regions, and so the radial models require careful
  interpretation. We discuss the implications for coronal heating in these
  regions, and compare this result with other recent determinations of
  the temperature in the inner corona. This work was supported in part
  by NASA grant NAS 8-37334. The authors acknowledge also support from
  Air Force grant F49620-95-1-0008 and NASA grant NAGW-2265.

Title: Yokhoh Soft X-Ray Telescope Images of the Diffuse Solar Corona
Authors: Sturrock, P. A.; Wheatland, M. S.; Acton, L. W.
Bibcode: 1996ApJ...461L.115S
Altcode:
  During the interval 1992 May 3--15, an extended region (out to 1.5
  solar radii) of diffuse, stable corona crossed the northeast limb
  of the Sun. This region underlaid a coronal streamer as revealed by
  the Mauna Loa Coronagraph of the High Altitude Observatory. During
  this passage, the soft X-ray telescope on Yohkoh obtained a number of
  high-quality pairs of images, closely spaced in time, through the two
  thinnest analysis filters. Analysis of these data indicates that (1)
  the temperature increases steadily with height and (2) the variation
  of temperature with radius is consistent with a conserved inward
  heat flux. These results imply that the magnetic field configuration
  was substantially open out to 1.5 solar radii and that there was no
  significant coronal heating below that height in that region. It appears
  that this region was being heated by nonthermal energy deposited beyond
  1.5 solar radii.

Title: Interpretation of SXT Data Concerning the Diffuse Corona
Authors: Sturrock, P. A.; Wheatland, M. S.; Acton, L. W.
Bibcode: 1996mpsa.conf..417S
Altcode: 1996IAUCo.153..417S
  No abstract at ADS

Title: Energy Release in a Prominence-Loaded Flaring Loop
Authors: Wheatland, M. S.; Melrose, D. B.
Bibcode: 1995SoPh..159..137W
Altcode:
  Zaitsev and Stepanov (1991, 1992) proposed a mechanism for energy
  release in solar flares that involves the intrusion of dense prominence
  material into a coronal loop. The resulting non-steady state conditions
  are claimed to increase the resistance of the loop by 8-10 orders of
  magnitude. It is shown here that the dramatic increase in resistance
  calculated by Zaitsev and Stepanov depends on a gross overestimate of
  the of the magnitude of the magnetic force in the loop prior to the
  flare trigger. A more realistic estimate of the increase due to the
  mechanism suggests that it is by no more than about four orders of
  magnitude. As a consequence, the `prominence-loading` mechanism does
  not provide a tenable flare model.

Title: Interpreting YOHKOH Hard and Soft X-Ray Flare Observations
Authors: Wheatland, M. S.; Melrose, D. B.
Bibcode: 1995SoPh..158..283W
Altcode:
  A simple model is presented to account for theYohkoh flare observations
  of Feldmanet al. (1994), and Masuda (1994). Electrons accelerated by
  the flare are assumed to encounter the dense, small regions observed
  by Feldmanet al. at the tops of impulsively flaring coronal magnetic
  loops. The values of electron density and volume inferred by Feldmanet
  al. imply that these dense regions present an intermediate thick-thin
  target to the energised electrons. Specifically, they present a
  thick (thin) target to electrons with energy much less (greater)
  thanE<SUB>c</SUB>, where 15 keV &lt;E<SUB>c</SUB> &lt; 40 keV. The
  electrons are either stopped at the loop top or precipitate down
  the field lines of the loop to the footpoints. Collisional losses
  of the electrons at the loop top produce the heating observed by
  Feldmanet al. and also some hard X-rays. It is argued that this is the
  mechanism for the loop-top hard X-ray sources observed in limb flares
  by Masuda. Adopting a simple model for the energy losses of electrons
  traversing the dense region and the ambient loop plasma, hard X-ray
  spectra are derived for the loop-top source, the footpoint sources
  and the region between the loop top and footpoints. These spectra
  are compared with the observations of Masuda. The model spectra are
  found to qualitatively agree with the data, and in particular account
  for the observed steepening of the loop-top and footpoint spectra
  between 14 and 53 keV and the relative brightnesses of the loop-top
  and footpoint sources.

Title: Coronal Hard X-ray Sources in Solar Flares
Authors: Wheatland, M. S.; Sturrock, P. A.
Bibcode: 1995SPD....26.1321W
Altcode: 1995BAAS...27..991W
  No abstract at ADS

Title: Some topics in the physics of solar flares
Authors: Wheatland, Michael Scott
Bibcode: 1995PhDT.......189W
Altcode:
  No abstract at ADS

Title: Alfvenic fronts and the turning-off of the energy release in
    solar flares
Authors: Wheatland, M. S.; Melrose, D. B.
Bibcode: 1994PASA...11...25W
Altcode: 1994PASAu..11...25W
  The effect of impulsively turning off the dissipation in an existing
  model for energy propagation through Alfvenic fronts into the coronal
  site of enerrgy release in a solar flare is examined. In the optimum
  case of impedance matching, the flux tube re-stresses on a much longer
  timescale than it relaxes, suggesting an explanation for the timescales
  observed in homologous flares.

Title: Cross-field current closure below the solar photosphere
Authors: Wheatland, M. S.; Melrose, D. B.
Bibcode: 1994AuJPh..47..361W
Altcode:
  A simple model is developed to describe how an externally imposed
  current closes as a function of time below the photosphere. A
  vertical current density is assumed to turn on at the photospheric
  boundary. The model implies that the subsequent closure of the current
  in the sub-photosphere depends only on the ratio R<SUB>A</SUB>/R,
  where R<SUB>A</SUB> = mu<SUB>o</SUB>V<SUB>A</SUB> is the Alfvenic
  impedance of the photosphere and R = 1/sigma<SUB>P</SUB> is the
  resistance corresponding to the conductivity sigma<SUB>P</SUB> and
  a characteristic length l. For R<SUB>A</SUB>/R much greater than
  1, current closure occurs at a front, propagating with the Alfven
  speed. For R<SUB>A</SUB>/R much less than 1, current closure is a
  diffusive process ahead and behind a slowly propagating Alfvenic
  front. The first case is the relevant one for the Sun, where
  R<SUB>A</SUB>/R as approximately 10<SUP>8</SUP>/V<SUB>A</SUB>, for
  V<SUB>A</SUB> in kilometers per second.

