Author name code: anusha
ADS astronomy entries on 2022-09-14
=author:"Anusha, L.S." 
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Title: Chromospheric extension of the MURaM code
Authors: Przybylski, D.; Cameron, R.; Solanki, S. K.; Rempel, M.;
   Leenaarts, J.; Anusha, L. S.; Witzke, V.; Shapiro, A. I.
Bibcode: 2022A&A...664A..91P
Altcode: 2022arXiv220403126P
  Context. Detailed numerical models of the chromosphere and corona are
  required to understand the heating of the solar atmosphere. An accurate
  treatment of the solar chromosphere is complicated by the effects
  arising from non-local thermodynamic equilibrium (NLTE) radiative
  transfer. A small number of strong, highly scattering lines dominate the
  cooling and heating in the chromosphere. Additionally, the recombination
  times of ionised hydrogen are longer than the dynamical timescales,
  requiring a non-equilibrium (NE) treatment of hydrogen ionisation. <BR
  /> Aims: We describe a set of necessary additions to the MURaM code that
  allow it to handle some of the important NLTE effects. We investigate
  the impact on solar chromosphere models caused by NLTE and NE effects in
  radiation magnetohydrodynamic simulations of the solar atmosphere. <BR
  /> Methods: The MURaM code was extended to include the physical
  process required for an accurate simulation of the solar chromosphere,
  as implemented in the Bifrost code. This includes a time-dependent
  treatment of hydrogen ionisation, a scattering multi-group radiation
  transfer scheme, and approximations for NLTE radiative cooling. <BR />
  Results: The inclusion of NE and NLTE physics has a large impact on the
  structure of the chromosphere; the NE treatment of hydrogen ionisation
  leads to a higher ionisation fraction and enhanced populations in
  the first excited state throughout cold inter-shock regions of the
  chromosphere. Additionally, this prevents hydrogen ionisation from
  buffering energy fluctuations, leading to hotter shocks and cooler
  inter-shock regions. The hydrogen populations in the ground and first
  excited state are enhanced by 10<SUP>2</SUP>-10<SUP>3</SUP> in the
  upper chromosphere and by up to 10<SUP>9</SUP> near the transition
  region. <BR /> Conclusions: Including the necessary NLTE physics
  leads to significant differences in chromospheric structure and
  dynamics. The thermodynamics and hydrogen populations calculated using
  the extended version of the MURaM code are consistent with previous
  non-equilibrium simulations. The electron number and temperature
  calculated using the non-equilibrium treatment of the chromosphere
  are required to accurately synthesise chromospheric spectral
  lines. <P />Movies associated to Fig. 2 are only available at <A
  href="https://www.aanda.org/10.1051/0004-6361/202141230/olm">https://www.aanda.org</A>

Title: MPS-ATLAS: A fast all-in-one code for synthesising stellar
    spectra
Authors: Witzke, V.; Shapiro, A. I.; Cernetic, M.; Tagirov, R. V.;
   Kostogryz, N. M.; Anusha, L. S.; Unruh, Y. C.; Solanki, S. K.; Kurucz,
   R. L.
Bibcode: 2021A&A...653A..65W
Altcode: 2021arXiv210513611W
  Context. Stellar spectral synthesis is essential for various
  applications, ranging from determining stellar parameters to
  comprehensive stellar variability calculations. New observational
  resources as well as advanced stellar atmosphere modelling, taking three
  dimensional effects from radiative magnetohydrodynamics calculations
  into account, require a more efficient radiative transfer. <BR /> Aims:
  For accurate, fast and flexible calculations of opacity distribution
  functions (ODFs), stellar atmospheres, and stellar spectra, we developed
  an efficient code building on the well-established ATLAS9 code. The new
  code also paves the way for easy and fast access to different elemental
  compositions in stellar calculations. <BR /> Methods: For the generation
  of ODF tables, we further developed the well-established DFSYNTHE code
  by implementing additional functionality and a speed-up by employing
  a parallel computation scheme. In addition, the line lists used can be
  changed from Kurucz's recent lists. In particular, we implemented the
  VALD3 line list. <BR /> Results: A new code, the Merged Parallelised
  Simplified ATLAS, is presented. It combines the efficient generation of
  ODF, atmosphere modelling, and spectral synthesis in local thermodynamic
  equilibrium, therefore being an all-in-one code. This all-in-one code
  provides more numerical functionality and is substantially faster
  compared to other available codes. The fully portable MPS-ATLAS code
  is validated against previous ATLAS9 calculations, the PHOENIX code
  calculations, and high-quality observations.

Title: Radiative Transfer with Opacity Distribution Functions:
    Application to Narrowband Filters
Authors: Anusha, L. S.; Shapiro, A. I.; Witzke, V.; Cernetic, M.;
   Solanki, S. K.; Gizon, L.
Bibcode: 2021ApJS..255....3A
Altcode: 2021arXiv210413661A
  Modeling of stellar radiative intensities in various spectral passbands
  plays an important role in stellar physics. At the same time, direct
  calculation of the high-resolution spectrum and then integration of it
  over the given spectral passband is computationally demanding due to
  the vast number of atomic and molecular lines. This is particularly so
  when employing three-dimensional (3D) models of stellar atmospheres. To
  accelerate the calculations, one can employ approximate methods, e.g.,
  the use of opacity distribution functions (ODFs). Generally, ODFs
  provide a good approximation of traditional spectral synthesis, i.e.,
  computation of intensities through filters with strictly rectangular
  transmission functions. However, their performance strongly deteriorates
  when the filter transmission noticeably changes within its passband,
  which is the case for almost all filters routinely used in stellar
  physics. In this context, the aims of this paper are (a) to generalize
  the ODFs method for calculating intensities through filters with
  arbitrary transmission functions, and (b) to study the performance of
  the standard and generalized ODFs methods for calculating intensities
  emergent from 3D models of stellar atmospheres. For this purpose we
  use the newly developed MPS-ATLAS radiative transfer code to compute
  intensities emergent from 3D cubes simulated with the radiative
  magnetohydrodynamics code MURaM. The calculations are performed
  in the 1.5D regime, i.e., along many parallel rays passing through
  the simulated cube. We demonstrate that the generalized ODFs method
  allows accurate and fast syntheses of spectral intensities and their
  center-to-limb variations.

Title: Nonequilibrium Equation of State in Stellar Atmospheres
Authors: Anusha, L. S.; van Noort, M.; Cameron, R. H.
Bibcode: 2021ApJ...911...71A
Altcode: 2021arXiv210413650A
  In the stellar chromospheres, radiative energy transport is dominated by
  only the strongest spectral lines. For these lines, the approximation of
  local thermodynamic equilibrium (LTE) is known to be very inaccurate,
  and a state of equilibrium cannot be assumed in general. To calculate
  the radiative energy transport under these conditions, the population
  evolution equation must be evaluated explicitly, including all
  time-dependent terms. We develop a numerical method to solve the
  evolution equation for the atomic-level populations in a time-implicit
  way, keeping all time-dependent terms to first order. We show that
  the linear approximation of the time dependence of the populations
  can handle very large time steps without losing accuracy. We
  reproduce the benchmark solutions from earlier, well-established
  works in terms of non-LTE kinetic equilibrium solutions and typical
  ionization/recombination timescales in the solar chromosphere.

Title: Power spectrum of turbulent convection in the solar photosphere
Authors: Yelles Chaouche, L.; Cameron, R. H.; Solanki, S. K.;
   Riethmüller, T. L.; Anusha, L. S.; Witzke, V.; Shapiro, A. I.;
   Barthol, P.; Gandorfer, A.; Gizon, L.; Hirzberger, J.; van Noort,
   M.; Blanco Rodríguez, J.; Del Toro Iniesta, J. C.; Orozco Suárez,
   D.; Schmidt, W.; Martínez Pillet, V.; Knölker, M.
Bibcode: 2020A&A...644A..44Y
Altcode: 2020arXiv201009037Y
  The solar photosphere provides us with a laboratory for understanding
  turbulence in a layer where the fundamental processes of transport
  vary rapidly and a strongly superadiabatic region lies very closely
  to a subadiabatic layer. Our tools for probing the turbulence are
  high-resolution spectropolarimetric observations such as have recently
  been obtained with the two balloon-borne SUNRISE missions, and numerical
  simulations. Our aim is to study photospheric turbulence with the
  help of Fourier power spectra that we compute from observations
  and simulations. We also attempt to explain some properties of the
  photospheric overshooting flow with the help of its governing equations
  and simulations. We find that quiet-Sun observations and smeared
  simulations are consistent with each other and exhibit a power-law
  behavior in the subgranular range of their Doppler velocity power
  spectra with a power-law index of ≈ - 2. The unsmeared simulations
  exhibit a power law that extends over the full range between the
  integral and Taylor scales with a power-law index of ≈ - 2.25. The
  smearing, reminiscent of observational conditions, considerably reduces
  the extent of the power-law-like portion of the power spectra. This
  suggests that the limited spatial resolution in some observations
  might eventually result in larger uncertainties in the estimation of
  the power-law indices. The simulated vertical velocity power spectra
  as a function of height show a rapid change in the power-law index
  (at the subgranular range) from roughly the optical depth unity layer,
  that is, the solar surface, to 300 km above it. We propose that the
  cause of the steepening of the power-law index is the transition from
  a super- to a subadiabatic region, in which the dominant source of
  motions is overshooting convection. A scale-dependent transport of
  the vertical momentum occurs. At smaller scales, the vertical momentum
  is more efficiently transported sideways than at larger scales. This
  results in less vertical velocity power transported upward at small
  scales than at larger scales and produces a progressively steeper
  vertical velocity power law below 180 km. Above this height, the
  gravity work progressively gains importance at all relevant scales,
  making the atmosphere progressively more hydrostatic and resulting
  in a gradually less steep power law. Radiative heating and cooling of
  the plasma is shown to play a dominant role in the plasma energetics
  in this region, which is important in terms of nonadiabatic damping
  of the convective motions.

Title: Fast Iterative Techniques for Polarized Radiative Transfer
    in Spherically Symmetric Moving Media
Authors: Megha, A.; Sampoorna, M.; Nagendra, K. N.; Anusha, L. S.;
   Sankarasubramanian, K.
Bibcode: 2020ApJ...903....6M
Altcode:
  For a more precise modeling of polarized spectral lines formed in
  extended and expanding stellar atmospheres, the solution of the
  radiative transfer equation for the Stokes vectors must be obtained
  in a spherical geometry rather than in a planar geometry. In this
  paper, we present the modern iterative techniques based on operator
  perturbation to solve the spherically symmetric polarized radiative
  transfer equation with velocity fields. We consider scattering on a
  two-level atom and account for partial frequency redistribution. An
  accurate numerical solution to such problems requires the use of
  spatial grids with higher resolution. Consequently, Jacobi-based
  methods lead to slower convergence rate. The convergence rate can be
  improved by a factor of 2 or more when fast iterative schemes based
  on Gauss-Seidel (GS) and successive overrelaxation (SOR) methods are
  used over the Jacobi-based method. Here we present the Jacobi, GS,
  and SOR iterative techniques for solving the abovementioned problem,
  and discuss their convergence behavior.

Title: The Dimmest State of the Sun
Authors: Yeo, K. L.; Solanki, S. K.; Krivova, N. A.; Rempel, M.;
   Anusha, L. S.; Shapiro, A. I.; Tagirov, R. V.; Witzke, V.
Bibcode: 2020GeoRL..4790243Y
Altcode: 2021arXiv210209487Y
  How the solar electromagnetic energy entering the Earth's atmosphere
  varied since preindustrial times is an important consideration in
  the climate change debate. Detrimental to this debate, estimates
  of the change in total solar irradiance (TSI) since the Maunder
  minimum, an extended period of weak solar activity preceding the
  industrial revolution, differ markedly, ranging from a drop of 0.75
  W m<SUP>-2</SUP> to a rise of 6.3 W m<SUP>-2</SUP>. Consequently, the
  exact contribution by solar forcing to the rise in global temperatures
  over the past centuries remains inconclusive. Adopting a novel approach
  based on state-of-the-art solar imagery and numerical simulations, we
  establish the TSI level of the Sun when it is in its least-active state
  to be 2.0 ± 0.7 W m<SUP>-2</SUP> below the 2019 level. This means TSI
  could not have risen since the Maunder minimum by more than this amount,
  thus restricting the possible role of solar forcing in global warming.

Title: Importance of Angle-dependent Partial Frequency Redistribution
    in Hyperfine Structure Transitions Under the Incomplete Paschen-Back
    Effect Regime
Authors: Nagendra, K. N.; Sowmya, K.; Sampoorna, M.; Stenflo, J. O.;
   Anusha, L. S.
Bibcode: 2020ApJ...898...49N
Altcode: 2020arXiv200704044N
  Angle-frequency coupling in scattering of polarized light on atoms is
  represented by the angle-dependent (AD) partial frequency redistribution
  (PRD) matrices. There are several lines in the linearly polarized
  solar spectrum, for which PRD combined with quantum interference
  between hyperfine structure states play a significant role. Here we
  present the solution of the polarized line transfer equation including
  the AD-PRD matrix for scattering on a two-level atom with hyperfine
  structure splitting and an unpolarized lower level. We account for
  the effects of arbitrary magnetic fields (including the incomplete
  Paschen-Back effect regime) and elastic collisions. For exploratory
  purposes we consider a self-emitting isothermal planar atmosphere and
  use atomic parameters that represent an isolated Na I D<SUB>2</SUB>
  line. For this case we show that the AD-PRD effects are significant
  for field strengths below about 30 G, but that the computationally
  much less demanding approximation of angle-averaged PRD may be used
  for stronger fields.

Title: Resonance Line Polarization in Spherically Symmetric Moving
Media: a Parametric Study
Authors: Megha, A.; Sampoorna, M.; Nagendra, K. N.; Anusha, L. S.;
   Sankarasubramanian, K.
Bibcode: 2020arXiv200106201M
Altcode:
  In the present paper we consider the problem of resonance
  line polarization formed in the spherically symmetric expanding
  atmospheres. For the solution of the concerned polarized transfer
  equation we use the comoving frame formulation, and apply the
  Accelerated Lambda Iteration (ALI) method. We restrict ourselves to
  the non-relativistic regime of velocities wherein mainly Doppler shift
  effects are significant. For our studies, we consider the scattering
  on a two-level atom, including the effects of partial frequency
  redistribution (PFR). We present the dependence of linearly polarized
  profiles on different atmospheric and atomic parameters.

Title: Polarized Line Formation in Arbitrary Strength Magnetic Fields:
    The Case of a Two-level Atom with Hyperfine Structure Splitting
Authors: Sampoorna, M.; Nagendra, K. N.; Sowmya, K.; Stenflo, J. O.;
   Anusha, L. S.
Bibcode: 2019ApJ...883..188S
Altcode: 2019arXiv191010913S
  Quantum interference effects, together with partial frequency
  redistribution (PFR) in line scattering, produce subtle signatures in
  the so-called Second Solar Spectrum (the linearly polarized spectrum of
  the Sun). These signatures are modified in the presence of arbitrary
  strength magnetic fields via the Hanle, Zeeman, and Paschen-Back
  effects. In the present paper we solve the problem of polarized line
  formation in a magnetized atmosphere taking into account scattering in a
  two-level atom with hyperfine structure splitting together with PFR. To
  this end we incorporate the collisionless PFR matrix derived in Sowmya
  et al. in the polarized transfer equation. We apply the scattering
  expansion method to solve this transfer equation. We study the combined
  effects of PFR and the Paschen-Back effect on polarized line profiles
  formed in an isothermal one-dimensional planar atmosphere. For this
  purpose, we consider the cases of D<SUB>2</SUB> lines of Li I and Na I.

Title: Resonance Line Polarization in Spherically Symmetric Moving
Media: a Parametric Study.
Authors: Megha, A.; Sampoorna, M.; Nagendra, K. N.; Anusha, L. S.;
   Sankarasubramanian, K.
Bibcode: 2019spw..confE..14M
Altcode:
  No abstract at ADS

Title: Polarized Line Transfer in the Incomplete Paschen-Back Effect
    Regime with Angle-dependent Partial Frequency Redistribution.
Authors: Nagendra, K. N.; Sowmya, K.; Sampoorna, M.; Stenflo, J. O.;
   Anusha, L. S.
Bibcode: 2019spw..confE..13N
Altcode:
  No abstract at ADS

Title: Polarized Line Formation in Spherically Symmetric Expanding
    Atmospheres
Authors: Megha, A.; Sampoorna, M.; Nagendra, K. N.; Anusha, L. S.;
   Sankarasubramanian, K.
Bibcode: 2019ASPC..519...27M
Altcode:
  We consider the problem of polarized line formation in the spherically
  symmetric expanding atmospheres. The velocity fields in line forming
  regions produce Doppler shift, aberration of photons and also gives
  rise to advection. These in turn can modify the amplitudes and
  shapes of the emergent Stokes profiles. However, here we consider
  only non-relativistic regime, wherein mainly Doppler shift effects
  are significant. Thus only Doppler shift terms are considered in
  the polarized transfer equation. For the solution of the concerned
  polarized transfer equation we use the comoving frame formulation,
  and apply the Accelerated Lambda Iteration (ALI) method. We present the
  results by considering the scattering on a two-level atom, including the
  effects of partial frequency redistribution (PFR). The polarized line
  profiles are shown for few velocity laws, representative of expanding
  spherical atmospheres. It is shown that the degree of polarization in
  the lines depends sensitively on the extendedness R of the spherical
  atmosphere. We also present a comparison of polarized profiles computed
  under complete frequency redistribution (CFR) and PFR in the case of
  static as well as expanding atmospheres.

Title: Polarized Line Formation with Incomplete Paschen-Back Effect
    and Partial Frequency Redistribution
Authors: Sampoorna, M.; Nagendra, K. N.; Sowmya, K.; Stenflo, J. O.;
   Anusha, L. S.
Bibcode: 2019ASPC..519..113S
Altcode:
  Quantum interference between the hyperfine structure states is
  known to depolarize the cores of some of the lines in the linearly
  polarized spectrum of the Sun (the Second Solar Spectrum). The
  presence of external magnetic fields in the line forming regions
  modify these signatures through the Hanle, Zeeman, and incomplete/
  complete Paschen-Back effects (PBE), depending on the strength of the
  magnetic field. In an earlier paper, Sowmya et al. (2014) derived the
  relevant collisionless partial frequency redistribution (PFR) matrix
  for scattering on a two-level atom with hyperfine structure splitting
  (HFS) and in the presence of arbitrary strength magnetic fields
  (including the PBE regime). In the present paper we solve the problem
  of polarized line transfer in a magnetized atmosphere, including this
  PFR matrix. For this purpose, we apply a scattering expansion method
  which is based on orders of scattering approach. We present the results
  on the combined effects of PBE and PFR on the polarized line profiles
  using the atomic parameters relevant to the Na I D<SUB>2</SUB> line.

Title: Solution of Multi-dimensional Polarized Radiative Transfer
    Equation with PFR
Authors: Anusha, L. S.
Bibcode: 2019ASPC..519..105A
Altcode:
  Solar observations and numerical simulations have proved the existence
  of enormous inhomogeneous structures in the solar atmosphere. Solving
  polarized radiative transfer (RT) equation is a powerful means of
  understanding the effects of these inhomogeneities on the spectrum
  emerging from the Sun. To take spatial inhomogeneities into account,
  a solution of the transfer equation in multi-dimensional (multi-D)
  geometries is necessary. Here we present a summary of the developments
  we carried out in a series of papers, to solve multidimensional
  polarized RT equation with partial frequency redistribution (PFR)
  and the application of these methods to analyze the observations.

Title: Polarized Line Formation in Spherically Symmetric Atmospheres
    with Velocity Fields
Authors: Megha, A.; Sampoorna, M.; Nagendra, K. N.; Anusha, L. S.;
   Sankarasubramanian, K.
Bibcode: 2019ApJ...879...48M
Altcode:
  The plane-parallel approximation of the stellar atmospheres cannot
  be applied to model the formation of optically thick lines formed in
  extended atmospheres. To a good approximation these atmospheres can be
  represented by a spherically symmetric medium. Such extended stellar
  atmospheres are dynamic, in general, due to the systematic motions
  present in their layers. Macroscopic velocity fields in the spectral
  line forming regions produce Doppler shift, aberration of photons,
  and also give rise to advection. All of these effects can modify
  the amplitudes and shapes of the emergent Stokes profiles. In the
  present paper we consider the problem of polarized line formation
  in spherically symmetric media, in the presence of velocity
  fields. Solving the radiative transfer problem in the observer’s
  frame is a straightforward approach to handle the presence of velocity
  fields. This method, however, becomes computationally prohibitive when
  large velocity fields are considered, particularly in the case of the
  line formation with partial frequency redistribution (PFR). In this
  paper we present a polarized comoving frame method to solve the problem
  at hand. We consider nonrelativistic radial velocity fields, thereby
  accounting only for Doppler shift effects and neglecting advection
  and aberration of photons. We study the effects of extendedness,
  velocity fields, and PFR on the polarized line profiles formed in
  highly extended atmospheres.

Title: Estimation of the Magnetic Flux Emergence Rate in the Quiet
    Sun from Sunrise Data
Authors: Smitha, H. N.; Anusha, L. S.; Solanki, S. K.; Riethmüller,
   T. L.
Bibcode: 2017ApJS..229...17S
Altcode: 2016arXiv161106432S
  Small-scale internetwork (IN) features are thought to be the major
  source of fresh magnetic flux in the quiet Sun. During its first science
  flight in 2009, the balloon-borne observatory Sunrise captured images of
  the magnetic fields in the quiet Sun at a high spatial resolution. Using
  these data we measure the rate at which the IN features bring magnetic
  flux to the solar surface. In a previous paper it was found that the
  lowest magnetic flux in small-scale features detected using the Sunrise
  observations is 9 × 10<SUP>14</SUP> Mx. This is nearly an order of
  magnitude smaller than the smallest fluxes of features detected in
  observations from the Hinode satellite. In this paper, we compute the
  flux emergence rate (FER) by accounting for such small fluxes, which
  was not possible before Sunrise. By tracking the features with fluxes
  in the range {10}<SUP>15</SUP>{--}{10}<SUP>18</SUP> Mx, we measure an
  FER of 1100 {Mx} {{cm}}<SUP>-2</SUP> {{day}}<SUP>-1</SUP>. The smaller
  features with fluxes ≤slant {10}<SUP>16</SUP> Mx are found to be the
  dominant contributors to the solar magnetic flux. The FER found here
  is an order of magnitude higher than the rate from Hinode, obtained
  with a similar feature tracking technique. A wider comparison with the
  literature shows, however, that the exact technique of determining the
  rate of the appearance of new flux can lead to results that differ by
  up to two orders of magnitude, even when applied to similar data. The
  causes of this discrepancy are discussed and first qualitative
  explanations proposed.

Title: Statistical evolution of quiet-Sun small-scale magnetic
    features using Sunrise observations
Authors: Anusha, L. S.; Solanki, S. K.; Hirzberger, J.; Feller, A.
Bibcode: 2017A&A...598A..47A
Altcode: 2016arXiv160808499A
  The evolution of small magnetic features in quiet regions of the Sun
  provides a unique window for probing solar magneto-convection. Here
  we analyze small-scale magnetic features in the quiet Sun, using the
  high resolution, seeing-free observations from the Sunrise balloon
  borne solar observatory. Our aim is to understand the contribution of
  different physical processes, such as splitting, merging, emergence
  and cancellation of magnetic fields to the rearrangement, addition
  and removal of magnetic flux in the photosphere. We have employed a
  statistical approach for the analysis and the evolution studies are
  carried out using a feature-tracking technique. In this paper we provide
  a detailed description of the feature-tracking algorithm that we have
  newly developed and we present the results of a statistical study
  of several physical quantities. The results on the fractions of the
  flux in the emergence, appearance, splitting, merging, disappearance
  and cancellation qualitatively agrees with other recent studies. To
  summarize, the total flux gained in unipolar appearance is an order of
  magnitude larger than the total flux gained in emergence. On the other
  hand, the bipolar cancellation contributes nearly an equal amount to
  the loss of magnetic flux as unipolar disappearance. The total flux
  lost in cancellation is nearly six to eight times larger than the
  total flux gained in emergence. One big difference between our study
  and previous similar studies is that, thanks to the higher spatial
  resolution of Sunrise, we can track features with fluxes as low as
  9 × 10<SUP>14</SUP> Mx. This flux is nearly an order of magnitude
  lower than the smallest fluxes of the features tracked in the highest
  resolution previous studies based on Hinode data. The area and flux
  of the magnetic features follow power-law type distribution, while
  the lifetimes show either power-law or exponential type distribution
  depending on the exact definitions used to define various birth and
  death events. We have also statistically determined the evolution
  of the flux within the features in the course of their lifetime,
  finding that this evolution depends very strongly on the birth and
  death process that the features undergo.

Title: Flux emergence rate in the quiet Sun from Sunrise data
Authors: Smitha, H. N.; Anusha, L. S.; Solanki, S. K.; Riethmüller,
   T. L.
Bibcode: 2017psio.confE.106S
Altcode:
  No abstract at ADS

Title: Scattering Polarization of the Spectral Lines in the Solar
    Chromosphere
Authors: Anusha, L. S.; Nanjundarao, N. K.
Bibcode: 2015AGUFMSH43B2452A
Altcode:
  Linear polarization produced by scattering of light and its magnetic
  field modification (namely, Hanle effect) in spectral lines can be
  used as diagnostic tools to understand the structuring of the solar
  atmosphere and the physical processes that produce and modify the
  linear, scattering poalrization signals. Modeling observations
  of strong spectral lines such as Ca II K at 3933 A using model
  solar atmosphers can give information on the less understood solar
  chromosphere, where this line is formed. Modeling the observations of
  the scattering poalrization in spectral lines requires the solution
  of polarized radiative transfer equation. Although solution is easier
  in one-dimenion, to be more realistic we must go for multi-dimensional
  geometries. In particular Ca II K line is appropriate for chromospheric
  diagnostics as it contains information on the less understood
  topics such as (1) scattering mechansim called partial frequency
  redistribution, (2) effect of magnetic field on line polarization in
  the chromosphere through Hanle effect, and (3) spatial structuring of
  the chromosphere that cause modifications in line polarization. Our aim
  here is to address these three topics through modeling the observations
  of Ca II K line using different model solar atmospheres.

Title: Modeling the center-to-limb variation of the Ca i 4227 Å
    line using FCHHT models
Authors: Supriya, H. D.; Smitha, H. N.; Nagendra, K. N.; Stenflo,
   J. O.; Bianda, M.; Ravindra, B.; Ramelli, R.; Anusha, L. S.
Bibcode: 2015IAUS..305..381S
Altcode:
  The Ca i 4227 Å is a chromospheric line exhibiting the largest degree
  of linear polarization near the limb, in the visible spectrum of the
  Sun. Modeling the observations of the center-to-limb variations (CLV)
  of different lines in the Second Solar Spectrum helps to sample the
  height dependence of the magnetic field, as the observations made
  at different lines of sight sample different heights in the solar
  atmosphere. Supriya et al. (2014) attempted to simultaneously model
  the CLV of the (I, Q/I) spectra of the Ca i 4227 Å line using the
  standard 1-D FAL model atmospheres. They found that the standard FAL
  model atmospheres and also any appropriate combination of them, fail
  to simultaneously fit the observed Stokes (I, Q/I) profiles at all the
  limb distances (μ) satisfying at the same time all the observational
  constraints. This failure of 1-D modeling approach can probably be
  overcome by using multi-dimensional modeling which is computationally
  expensive. To eliminate an even wider choice of 1-D models, we attempt
  here to simultaneously model the CLV of the (I, Q/I) spectra using the
  FCHHT solar model atmospheres which are updated and recent versions
  of the FAL models. The details of our modeling efforts and the results
  are presented.

Title: Study of resonance scattering polarization in O i 130 nm lines
Authors: Anusha, L. S.; Nagendra, K. N.; Uitenbroek, Han
Bibcode: 2015IAUS..305..234A
Altcode:
  Here we address the importance of frequency cross-redistribution on
  the scattering polarization of the O i line at 130.2 nm. We compute
  the polarized profiles of this line with ordinary partial frequency
  redistribution and cross-redistribution using a two-dimensional
  radiative transfer code.

Title: Evolution of Small Scale Magnetic Structures from Sunrise Data
Authors: Anusha, L. S.; Feller, A.; Hirzberger, J.; Solanki, S. K.
Bibcode: 2014ASPC..489...83A
Altcode:
  We present the results of an analysis of small scale magnetic features
  in the quiet Sun, observed with the Sunrise balloon borne telescope. Our
  aim is to understand the contribution of different physical processes
  that drive the evolution of magnetic features in quiet regions of
  the photosphere. To this end, we study the rearrangement, addition,
  and removal of magnetic flux through splitting, merging, cancellation,
  and emergence of magnetic fields.

Title: Multi-Dimensional Polarized Radiative Transfer: Methods and
    Solar Applications
Authors: Anusha, L. S.; Nagendra, K. N.
Bibcode: 2014ASPC..489..225A
Altcode:
  Observations of the Sun using modern telescopes as well as numerical
  simulations of the Sun reveal existence of enormous inhomogeneous
  structures in the solar atmosphere. The polarized spectrum of the Sun
  (Second Solar Spectrum), produced due to anisotropic scattering helps
  to infer the temperature structure, magnetic fields, and other physical
  properties of the solar atmosphere more accurately. Analysis of the
  Second Solar Spectrum requires solution of the polarized radiative
  transfer equation. To take spatial inhomogeneities into account, a
  solution of the transfer equation in multi-dimensional geometries is
  necessary. In this paper we present a specialized review of recent
  developments in the methods to solve multi-dimensional polarized
  radiative transfer equation and an application of these methods to
  analyze the observations.

Title: Effect of Cross-redistribution on the Resonance Scattering
    Polarization of O I Line at 1302 Å
Authors: Anusha, L. S.; Nagendra, K. N.; Uitenbroek, H.
Bibcode: 2014ApJ...794...17A
Altcode: 2014arXiv1407.8456A
  Oxygen is the most abundant element on the Sun after hydrogen
  and helium. The intensity spectrum of resonance lines of neutral
  oxygen, namely, O I (1302, 1305, and 1306 Å), has been studied
  in the literature for chromospheric diagnostics. In this paper,
  we study the resonance scattering polarization in the O I line at
  1302 Å using two-dimensional (2D) radiative transfer in a composite
  atmosphere constructed using a 2D magneto-hydrodynamical snapshot in
  the photosphere and columns of the one-dimensional FALC atmosphere in
  the chromosphere. The methods developed by us recently in a series
  of papers to solve multi-dimensional polarized radiative transfer
  have been incorporated in our new code POLY2D, which we use for our
  analysis. We find that multi-dimensional radiative transfer including
  XRD effects is important in reproducing the amplitude and shape of
  scattering polarization signals of the O I line at 1302 Å.

Title: Center-to-limb Observations and Modeling of the Ca I 4227
    Å Line
Authors: Supriya, H. D.; Smitha, H. N.; Nagendra, K. N.; Stenflo,
   J. O.; Bianda, M.; Ramelli, R.; Ravindra, B.; Anusha, L. S.
Bibcode: 2014ApJ...793...42S
Altcode: 2014arXiv1407.5461S
  The observed center-to-limb variation (CLV) of the scattering
  polarization in different lines of the Second Solar Spectrum can be used
  to constrain the height variation of various atmospheric parameters, in
  particular the magnetic fields, via the Hanle effect. Here we attempt
  to model the nonmagnetic CLV observations of the Q/I profiles of the
  Ca I 4227 Å line recorded with the Zurich Imaging Polarimeter-3
  at IRSOL. For modeling, we use the polarized radiative transfer
  with partial frequency redistribution with a number of realistic
  one-dimensional (1D) model atmospheres. We find that all the standard
  Fontenla-Avrett-Loeser (FAL) model atmospheres, which we used, fail
  to simultaneously fit the observed (I, Q/I) at all the limb distances
  (μ). However, an attempt is made to find a single model which can
  provide a fit to at least the CLV of the observed Q/I instead of a
  simultaneous fit to the (I, Q/I) at all μ. To this end we construct a
  new 1D model by combining two of the standard models after modifying
  their temperature structures in the appropriate height ranges. This
  new combined model closely reproduces the observed Q/I at all μ but
  fails to reproduce the observed rest intensity at different μ. Hence
  we find that no single 1D model atmosphere succeeds in providing a
  good representation of the real Sun. This failure of 1D models does
  not, however, cause an impediment to the magnetic field diagnostic
  potential of the Ca I 4227 Å line. To demonstrate this we deduce the
  field strength at various μ positions without invoking the use of
  radiative transfer.

Title: Multi-dimensional Radiative Transfer to Analyze Hanle Effect
    in Ca II K Line at 3933 Å
Authors: Anusha, L. S.; Nagendra, K. N.
Bibcode: 2013ApJ...767..108A
Altcode: 2013arXiv1308.3437A
  Radiative transfer (RT) studies of the linearly polarized spectrum of
  the Sun (the second solar spectrum) have generally focused on line
  formation, with an aim to understand the vertical structure of the
  solar atmosphere using one-dimensional (1D) model atmospheres. Modeling
  spatial structuring in the observations of the linearly polarized
  line profiles requires the solution of multi-dimensional (multi-D)
  polarized RT equation and a model solar atmosphere obtained by
  magnetohydrodynamical (MHD) simulations of the solar atmosphere. Our
  aim in this paper is to analyze the chromospheric resonance line Ca
  II K at 3933 Å using multi-D polarized RT with the Hanle effect and
  partial frequency redistribution (PRD) in line scattering. We use an
  atmosphere that is constructed by a two-dimensional snapshot of the
  three-dimensional MHD simulations of the solar photosphere, combined
  with columns of a 1D atmosphere in the chromosphere. This paper
  represents the first application of polarized multi-D RT to explore
  the chromospheric lines using multi-D MHD atmospheres, with PRD as the
  line scattering mechanism. We find that the horizontal inhomogeneities
  caused by MHD in the lower layers of the atmosphere are responsible for
  strong spatial inhomogeneities in the wings of the linear polarization
  profiles, while the use of horizontally homogeneous chromosphere
  (FALC) produces spatially homogeneous linear polarization in the line
  core. The introduction of different magnetic field configurations
  modifies the line core polarization through the Hanle effect and can
  cause spatial inhomogeneities in the line core. A comparison of our
  theoretical profiles with the observations of this line shows that
  the MHD structuring in the photosphere is sufficient to reproduce the
  line wings and in the line core, but only line center polarization
  can be reproduced using the Hanle effect. For a simultaneous modeling
  of the line wings and the line core (including the line center),
  MHD atmospheres with inhomogeneities in the chromosphere are required.

Title: An efficient decomposition technique to solve angle-dependent
    Hanle scattering problems
Authors: Supriya, H. D.; Sampoorna, M.; Nagendra, K. N.; Ravindra,
   B.; Anusha, L. S.
Bibcode: 2013JQSRT.119...67S
Altcode: 2013arXiv1304.5321S
  Hanle scattering is an important diagnostic tool to study weak solar
  magnetic fields. Partial frequency redistribution (PRD) is necessary
  to interpret the linear polarization observed in strong resonance
  lines. Usually angle-averaged PRD functions are used to analyze
  linear polarization. However, it is established that angle-dependent
  PRD functions are often necessary to interpret polarization profiles
  formed in the presence of weak magnetic fields. Our aim is to present
  an efficient decomposition technique, and the numerical method to solve
  the concerned angle-dependent line transfer problem. Together with the
  standard Stokes decomposition technique, we employ Fourier expansion
  over the outgoing azimuth angle to express in a more convenient form,
  the angle-dependent PRD function for the Hanle effect. It allows the
  use of angle-dependent frequency domains of Bommier to solve the Hanle
  transfer problem. Such an approach is self-consistent and accurate
  compared to a recent approach where angle-averaged frequency domains
  were used to solve the same problem. We show that it is necessary to
  incorporate angle-dependent frequency domains instead of angle-averaged
  frequency domains to solve the Hanle transfer problem accurately,
  especially for the Stokes U parameter. The importance of using
  angle-dependent domains has been highlighted by taking the example
  of Hanle effect in the case of line transfer with vertical magnetic
  fields in a slab atmosphere. We have also studied the case of polarized
  line formation when micro-turbulent magnetic fields are present. The
  difference between angle-averaged and angle-dependent solutions is
  enhanced by the presence of micro-turbulent fields.

Title: Forward-scattering Hanle effect in the solar Ca I 4227 Å line
Authors: Frisch, H.; Anusha, L. S.; Bianda, M.; Holzreuter, R.;
   Nagendra, K. N.; Ramelli, R.; Sampoorna, M.; Smitha, H. N.; Stenflo,
   J. O.
Bibcode: 2012EAS....55...59F
Altcode:
  High sensitivity spectropolarimetric observations of the four Stokes
  parameters of the solar Ca I 4227 Å line have been performed in
  October 2010 at IRSOL with the ZIMPOL polarimeter, near the disk center,
  outside an active region (Bianda et al. 2011). They were analyzed in
  Anusha et al. 2011 with a combination of detailed radiative transfer
  modelling of the Hanle effect for the linear polarization and weak
  field Zeeman approximation for the circular polarization. This approach
  made possible a unique determination of the magnetic field vector at
  various positions along the slit of the spectrograph. A summary of
  the observations and of their analysis is presented here.

Title: J-state interference signatures in the second solar
    spectrum. Modeling the Cr i triplet at 5204-5208 Å
Authors: Smitha, H. N.; Nagendra, K. N.; Stenflo, J. O.; Bianda, M.;
   Sampoorna, M.; Ramelli, R.; Anusha, L. S.
Bibcode: 2012A&A...541A..24S
Altcode: 2012arXiv1203.4934S
  The scattering polarization in the solar spectrum is traditionally
  modeled with each spectral line treated separately, but this is
  generally inadequate for multiplets where J-state interference
  plays a significant role. Through simultaneous observations of all
  the 3 lines of a Cr i triplet, combined with realistic radiative
  transfer modeling of the data, we show that it is necessary to include
  J-state interference consistently when modeling lines with partially
  interacting fine structure components. Polarized line formation theory
  that includes J-state interference effects together with partial
  frequency redistribution for a two-term atom is used to model the
  observations. Collisional frequency redistribution is also accounted
  for. We show that the resonance polarization in the Cr i triplet is
  strongly affected by the partial frequency redistribution effects in
  the line core and near wing peaks. The Cr i triplet is quite sensitive
  to the temperature structure of the photospheric layers. Our complete
  frequency redistribution calculations in semi-empirical models of the
  solar atmosphere cannot reproduce the observed near wing polarization or
  the cross-over of the Stokes Q/I line polarization about the continuum
  polarization level that is due to the J-state interference. When
  however partial frequency redistribution is included, a good fit to
  these features can be achieved. Further, to obtain a good fit to the
  far wings, a small temperature enhancement of the FALF model in the
  photospheric layers is necessary.

Title: Polarized Line Formation in Multi-dimensional Media. V. Effects
    of Angle-dependent Partial Frequency Redistribution
Authors: Anusha, L. S.; Nagendra, K. N.
Bibcode: 2012ApJ...746...84A
Altcode: 2013arXiv1308.3443A
  The solution of polarized radiative transfer equation with
  angle-dependent (AD) partial frequency redistribution (PRD) is a
  challenging problem. Modeling the observed, linearly polarized strong
  resonance lines in the solar spectrum often requires the solution of
  the AD line transfer problems in one-dimensional or multi-dimensional
  (multi-D) geometries. The purpose of this paper is to develop an
  understanding of the relative importance of the AD PRD effects and the
  multi-D transfer effects and particularly their combined influence on
  the line polarization. This would help in a quantitative analysis of the
  second solar spectrum (the linearly polarized spectrum of the Sun). We
  consider both non-magnetic and magnetic media. In this paper we reduce
  the Stokes vector transfer equation to a simpler form using a Fourier
  decomposition technique for multi-D media. A fast numerical method
  is also devised to solve the concerned multi-D transfer problem. The
  numerical results are presented for a two-dimensional medium with a
  moderate optical thickness (effectively thin) and are computed for
  a collisionless frequency redistribution. We show that the AD PRD
  effects are significant and cannot be ignored in a quantitative fine
  analysis of the line polarization. These effects are accentuated by the
  finite dimensionality of the medium (multi-D transfer). The presence
  of magnetic fields (Hanle effect) modifies the impact of these two
  effects to a considerable extent.

Title: Polarized Line Formation in Multi-dimensional Media. IV. A
    Fourier Decomposition Technique to Formulate the Transfer Equation
    with Angle-dependent Partial Frequency Redistribution
Authors: Anusha, L. S.; Nagendra, K. N.
Bibcode: 2011ApJ...739...40A
Altcode: 2013arXiv1308.3447A
  To explain the linear polarization observed in spatially resolved
  structures in the solar atmosphere, the solution of polarized radiative
  transfer (RT) equation in multi-dimensional (multi-D) geometries is
  essential. For strong resonance lines, partial frequency redistribution
  (PRD) effects also become important. In a series of papers, we have been
  investigating the nature of Stokes profiles formed in multi-D media
  including PRD in line scattering. For numerical simplicity, so far we
  have restricted our attention to the particular case of PRD functions
  which are averaged over all the incident and scattered directions. In
  this paper, we formulate the polarized RT equation in multi-D media
  that takes into account the Hanle effect with angle-dependent PRD
  functions. We generalize here to the multi-D case the method for Fourier
  series expansion of angle-dependent PRD functions originally developed
  for RT in one-dimensional geometry. We show that the Stokes source
  vector S = (S<SUB>I</SUB> , S<SUB>Q</SUB> , S<SUB>U</SUB> )<SUP> T
  </SUP> and the Stokes vector I = (I, Q, U)<SUP> T </SUP> can be expanded
  in terms of infinite sets of components \tilde{S}^(k), \tilde{I}^(k),
  respectively, k in [0, +∞). We show that the components \tilde{S}^(k)
  become independent of the azimuthal angle (phiv) of the scattered ray,
  whereas the components \tilde{I}^(k) remain dependent on phiv due to the
  nature of RT in multi-D geometry. We also establish that \tilde{S}^(k)
  and \tilde{I}^(k) satisfy a simple transfer equation, which can be
  solved by any iterative method such as an approximate Lambda iteration
  or a Bi-Conjugate Gradient-type projection method provided we truncate
  the Fourier series to have a finite number of terms.

Title: Polarized Line Formation in Multi-dimensional Media. III. Hanle
    Effect with Partial Frequency Redistribution
Authors: Anusha, L. S.; Nagendra, K. N.
Bibcode: 2011ApJ...738..116A
Altcode: 2011arXiv1105.4052A
  In two previous papers, we solved the polarized radiative transfer
  (RT) equation in multi-dimensional (multi-D) geometries with partial
  frequency redistribution as the scattering mechanism. We assumed
  Rayleigh scattering as the only source of linear polarization (Q/I,
  U/I) in both these papers. In this paper, we extend these previous
  works to include the effect of weak oriented magnetic fields (Hanle
  effect) on line scattering. We generalize the technique of Stokes
  vector decomposition in terms of the irreducible spherical tensors
  {T}^K_Q, developed by Anusha &amp; Nagendra, to the case of RT with
  Hanle effect. A fast iterative method of solution (based on the
  Stabilized Preconditioned Bi-Conjugate-Gradient technique), developed
  by Anusha et al., is now generalized to the case of RT in magnetized
  three-dimensional media. We use the efficient short-characteristics
  formal solution method for multi-D media, generalized appropriately to
  the present context. The main results of this paper are the following:
  (1) a comparison of emergent (I, Q/I, U/I) profiles formed in
  one-dimensional (1D) media, with the corresponding emergent, spatially
  averaged profiles formed in multi-D media, shows that in the spatially
  resolved structures, the assumption of 1D may lead to large errors in
  linear polarization, especially in the line wings. (2) The multi-D RT
  in semi-infinite non-magnetic media causes a strong spatial variation
  of the emergent (Q/I, U/I) profiles, which is more pronounced in the
  line wings. (3) The presence of a weak magnetic field modifies the
  spatial variation of the emergent (Q/I, U/I) profiles in the line core,
  by producing significant changes in their magnitudes.

Title: Analysis of the Forward-scattering Hanle Effect in the Ca I
    4227 Å Line
Authors: Anusha, L. S.; Nagendra, K. N.; Bianda, M.; Stenflo, J. O.;
   Holzreuter, R.; Sampoorna, M.; Frisch, H.; Ramelli, R.; Smitha, H. N.
Bibcode: 2011ApJ...737...95A
Altcode:
  Coherent scattering of limb-darkened radiation is responsible for the
  generation of the linearly polarized spectrum of the Sun (the Second
  Solar Spectrum). This Second Solar Spectrum is usually observed near the
  limb of the Sun, where the polarization amplitudes are largest. At the
  center of the solar disk the linear polarization is zero for an axially
  symmetric atmosphere. Any mechanism that breaks the axial symmetry (like
  the presence of an oriented magnetic field, or resolved inhomogeneities
  in the atmosphere) can generate a non-zero linear polarization. In the
  present paper we study the linear polarization near the disk center
  in a weakly magnetized region, where the axisymmetry is broken. We
  present polarimetric (I, Q/I, U/I, and V/I) observations of the Ca
  I 4227 Å line recorded around μ = cos θ = 0.9 (where θ is the
  heliocentric angle) and a modeling of these observations. The high
  sensitivity of the instrument (ZIMPOL-3) makes it possible to measure
  the weak polarimetric signals with great accuracy. The modeling of
  these high-quality observations requires the solution of the polarized
  radiative transfer equation in the presence of a magnetic field. For
  this we use standard one-dimensional model atmospheres. We show that the
  linear polarization is mainly produced by the Hanle effect (rather than
  by the transverse Zeeman effect), while the circular polarization is due
  to the longitudinal Zeeman effect. A unique determination of the full
  \bm {B} vector may be achieved when both effects are accounted for. The
  field strengths required for the simultaneous fitting of Q/I, U/I, and
  V/I are in the range 10-50 G. The shapes and signs of the Q/I and U/I
  profiles are highly sensitive to the orientation of the magnetic field.

Title: Observations of the forward scattering Hanle effect in the
    Ca I 4227 Å line
Authors: Bianda, M.; Ramelli, R.; Anusha, L. S.; Stenflo, J. O.;
   Nagendra, K. N.; Holzreuter, R.; Sampoorna, M.; Frisch, H.; Smitha,
   H. N.
Bibcode: 2011A&A...530L..13B
Altcode: 2011arXiv1105.2157B
  Chromospheric magnetic fields are notoriously difficult to measure. The
  chromospheric lines are broad, while the fields are producing
  a minuscule Zeeman-effect polarization. A promising diagnostic
  alternative is provided by the forward-scattering Hanle effect, which
  can be recorded in chromospheric lines such as the He i 10 830 Å
  and the Ca i 4227 Å lines. We present a set of spectropolarimetric
  observations of the full Stokes vector obtained near the center of the
  solar disk in the Ca i 4227 Å line with the ZIMPOL polarimeter at the
  IRSOL observatory. We detect a number of interesting forward-scattering
  Hanle effect signatures, which we model successfully using polarized
  radiative transfer. Here we focus on the observational aspects, while
  a separate companion paper deals with the theoretical modeling.

Title: Linear Polarization of the Solar Ca I 4227 Å Line: Modeling
    with Radiative Transfer and Last Scattering Approximation
Authors: Anusha, L. S.; Stenflo, J. O.; Frisch, H.; Bianda, M.;
   Holzreuter, R.; Nagendra, K. N.; Sampoorna, M.; Ramelli, R.
Bibcode: 2011ASPC..437...57A
Altcode:
  To model the Ca I 4227 Å line polarization, radiative transfer
  effects with partial frequency redistribution (PRD) must be taken into
  account. The numerical solution of the relevant polarized radiative
  transfer (RT) equations is computationally very demanding. The
  “last scattering approximation” (LSA) is a concept allowing
  faster methods to be devised. It is based on the remark that a single
  scattering of the radiation field is sufficient for creating most
  of the polarization. Its key ingredient is the anisotropy of the
  radiation field. If the anisotropy is extracted from the observed
  center to limb variation of the intensity profile, only the wings
  of the Q/I spectrum can be modeled (Sampoorna et al. 2009). We show
  here that the core region may be modeled as well if one takes into
  account the depth variation of the anisotropy which is obtained from
  an unpolarized multilevel RT (Anusha et al. 2010). After a validation
  of the LSA approach by comparison with a polarized RT calculation, we
  apply both approaches to model recent observations of the Ca I 4227 Å
  line polarization taken on the quiet Sun. Apart from a global scaling
  factor, both approaches give a very good fit to the Q/I spectrum for
  all the wavelengths. As the LSA is 8 times faster than the RT approach,
  we can recommend it as an efficient method to analyze other strong
  resonance lines in the second solar spectrum.

Title: Observations of the Solar Ca I 4227 Å Line
Authors: Bianda, M.; Ramelli, R.; Stenflo, J. O.; Anusha, L. S.;
   Nagendra, K. N.; Sampoorna, M.; Holzreuter, R.; Frisch, H.
Bibcode: 2011ASPC..437...67B
Altcode:
  Our aim is to understand some interesting polarization features
  observed in the solar Ca I 4277 Å line. Here we only discuss the
  observational aspects. Observations have also been made in other
  chromospheric lines within a few hours of those in the Ca I 4227 Å
  line, in the same region near the north solar limb, to illustrate the
  potential of simultaneous observations in different lines.

Title: Polarized Line Formation in Multi-dimensional Media. II. A
    Fast Method to Solve Problems with Partial Frequency Redistribution
Authors: Anusha, L. S.; Nagendra, K. N.; Paletou, F.
Bibcode: 2011ApJ...726...96A
Altcode:
  In the previous paper of this series, we presented a formulation of
  the polarized radiative transfer equation for resonance scattering
  with partial frequency redistribution (PRD) in multi-dimensional
  media for a two-level atom model with unpolarized ground level, using
  the irreducible spherical tensors {T}^K_Q(i,Ω) for polarimetry. We
  also presented a polarized approximate lambda iteration method to
  solve this equation using the Jacobi iteration scheme. The formal
  solution used was based on a simple finite volume technique. In this
  paper, we develop a faster and more efficient method which uses the
  projection techniques applied to the radiative transfer equation (the
  Stabilized Preconditioned Bi-Conjugate Gradient method). We now use a
  more accurate formal solver, namely the well-known two-dimensional (2D)
  short characteristics method. Using the numerical method developed in
  Paper I, we can consider only simpler cases of finite 2D slabs due to
  computational limitations. Using the method developed in this paper,
  we could compute PRD solutions in 2D media in the more difficult
  context of semi-infinite 2D slabs also. We present several solutions
  which may serve as benchmarks in future studies in this area.

Title: Polarized Line Formation in Multi-dimensional
    Media. I. Decomposition of Stokes Parameters in Arbitrary Geometries
Authors: Anusha, L. S.; Nagendra, K. N.
Bibcode: 2011ApJ...726....6A
Altcode:
  The solution of the polarized line radiative transfer (RT) equation in
  multi-dimensional geometries has been rarely addressed and only under
  the approximation that the changes of frequencies at each scattering
  are uncorrelated (complete frequency redistribution). With the
  increase in the resolution power of telescopes, being able to handle
  RT in multi-dimensional structures becomes absolutely necessary. In
  the present paper, our first aim is to formulate the polarized RT
  equation for resonance scattering in multi-dimensional media, using the
  elegant technique of irreducible spherical tensors {T}^K_Q(i, Ω). Our
  second aim is to develop a numerical method of a solution based on the
  polarized approximate lambda iteration (PALI) approach. We consider both
  complete frequency redistribution and partial frequency redistribution
  (PRD) in the line scattering. In a multi-dimensional geometry, the
  radiation field is non-axisymmetrical even in the absence of a symmetry
  breaking mechanism such as an oriented magnetic field. We generalize
  here to the three-dimensional (3D) case, the decomposition technique
  developed for the Hanle effect in a one-dimensional (1D) medium which
  allows one to represent the Stokes parameters I, Q, U by a set of six
  cylindrically symmetrical functions. The scattering phase matrix is
  expressed in terms of {T}^K_Q(i, Ω) (i=0,1,2, K=0,1,2, -K ≤ Q ≤
  +K), with Ω being the direction of the outgoing ray. Starting from the
  definition of the source vector, we show that it can be represented
  in terms of six components S<SUP>K</SUP> <SUB>Q</SUB> independent of
  Ω. The formal solution of the multi-dimensional transfer equation
  shows that the Stokes parameters can also be expanded in terms of
  {T}^K_Q(i, Ω). Because of the 3D geometry, the expansion coefficients
  I<SUP>K</SUP> <SUB>Q</SUB> remain Ω-dependent. We show that each
  I<SUP>K</SUP> <SUB>Q</SUB> satisfies a simple transfer equation with a
  source term S<SUP>K</SUP> <SUB>Q</SUB> and that this transfer equation
  provides an efficient approach for handling the polarized transfer in
  multi-dimensional geometries. A PALI method for 3D, associated with
  a core-wing separation method for treating PRD, is developed. It is
  tested by comparison with 1D solutions, and several benchmark solutions
  in the 3D case are given.

Title: Generalization of the Last Scattering Approximation for the
Second Solar Spectrum Modeling: The Ca I 4227 Å Line as a Case Study
Authors: Anusha, L. S.; Nagendra, K. N.; Stenflo, J. O.; Bianda, M.;
   Sampoorna, M.; Frisch, H.; Holzreuter, R.; Ramelli, R.
Bibcode: 2010ApJ...718..988A
Altcode:
  To model the second solar spectrum (the linearly polarized spectrum
  of the Sun that is due to coherent scattering processes), one needs
  to solve the polarized radiative transfer (RT) equation. For strong
  resonance lines, partial frequency redistribution (PRD) effects must be
  accounted for, which make the problem computationally demanding. The
  "last scattering approximation" (LSA) is a concept that has been
  introduced to make this highly complex problem more tractable. An
  earlier application of a simple LSA version could successfully model
  the wings of the strong Ca I 4227 Å resonance line in Stokes Q/I
  (fractional linear polarization), but completely failed to reproduce
  the observed Q/I peak in the line core. Since the magnetic field
  signatures from the Hanle effect only occur in the line core, we need
  to generalize the existing LSA approach if it is to be useful for the
  diagnostics of chromospheric and turbulent magnetic fields. In this
  paper, we explore three different approximation levels for LSA and
  compare each of them with the benchmark represented by the solution of
  the full polarized RT, including PRD effects. The simplest approximation
  level is LSA-1, which uses the observed center-to-limb variation of
  the intensity profile to obtain the anisotropy of the radiation field
  at the surface, without solving any transfer equation. In contrast,
  the next two approximation levels use the solution of the unpolarized
  transfer equation to derive the anisotropy of the incident radiation
  field and use it as an input. In the case of LSA-2, the anisotropy
  at level τ<SUB>λ</SUB> = μ, the atmospheric level from which an
  observed photon is most likely to originate, is used. LSA-3, on the
  other hand, makes use of the full depth dependence of the radiation
  anisotropy. The Q/I formula for LSA-3 is obtained by keeping the
  first term in a series expansion of the Q-source function in powers
  of the mean number of scattering events. Computationally, LSA-1 is 21
  times faster than LSA-2, which is 5 times faster than the more general
  LSA-3, which itself is 8 times faster than the polarized RT approach. A
  comparison of the calculated Q/I spectra with the RT benchmark shows
  excellent agreement for LSA-3, including good modeling of the Q/I
  core region with its PRD effects. In contrast, both LSA-1 and LSA-2
  fail to model the core region. The RT and LSA-3 approaches are then
  applied to model the recently observed Q/I profile of the Ca I 4227
  Å line in quiet regions of the Sun. Apart from a global scale factor
  both give a very good fit to the Q/I spectra for all the wavelengths,
  including the core peak and blend line depolarizations. We conclude
  that LSA-3 is an excellent substitute for the full polarized RT and
  can be used to interpret the second solar spectrum, including the
  Hanle effect with PRD. It also allows the techniques developed for
  unpolarized three-dimensional RT to be applied to the modeling of the
  second solar spectrum.

Title: Recent Developments in Polarized Line Formation in Magnetic
    Fields
Authors: Nagendra, K. N.; Sampoorna, M.; Anusha, L. S.
Bibcode: 2010ASSP...17..139N
Altcode: 2010rast.conf..139N; 2010rasp.book..139N
  The nature of solar surface magnetism has been an open problem in
  solar physics. In this paper we address three frontline problems
  of spectropolarimetry of the Sun. We first review the theoretical
  formulation and numerical solutions of Zeeman absorption and then the
  Hanle scattering phenomena in 'turbulent magnetic fields'. We show that
  the mean emergent Stokes profiles cannot be obtained by simply averaging
  the scattering and absorption opacities, respectively, over a given
  distribution of the random field (except when the micro-turbulence
  prevails). A new formulation of the transfer equation is necessary
  to study the astrophysically interesting meso-turbulence case. Such
  formulations of the stochastic polarized radiative transfer problems for
  absorbing and scattering media are developed only in recent years. We
  review them and show some results computed by our new formulations.Until
  recent years the solution of the polarized line radiative transfer
  equation in LTE (Zeeman absorption in strong fields), and its NLTE
  counterpart (Hanle scattering in weak fields), were treated as two
  disparate problems. The reason for this artificial division was more
  due to the theoretical and numerical difficulties encountered in the
  solution of the combined Hanle-Zeeman radiative transfer equation. A
  very general form of the transfer equation was formulated only a
  decade ago, for the case of complete frequency redistribution. A
  more difficult case of partial frequency redistribution is explored
  by us recently. We review these developments through a study of the
  Hanle-Zeeman effect in arbitrary strength magnetic fields.

Title: The Hanle Effect as Diagnostic Tool for Turbulent Magnetic
    Fields
Authors: Anusha, L. S.; Sampoorna, M.; Frisch, H.; Nagendra, K. N.
Bibcode: 2010ASSP...19..390A
Altcode: 2010mcia.conf..390A
  The Hanle effect is calculated for a random magnetic field characterized
  by a finite correlation length and a probability density function
  of the magnetic field vector. It is shown that linear polarization
  is essentially independent of the magnetic field correlation length,
  but strongly depends on the distribution of the field strength.

Title: Preconditioned Bi-conjugate Gradient Method for Radiative
    Transfer in Spherical Media
Authors: Anusha, L. S.; Nagendra, K. N.; Paletou, F.; Léger, L.
Bibcode: 2009ApJ...704..661A
Altcode: 2009arXiv0906.2926A
  A robust numerical method called the Preconditioned Bi-Conjugate
  Gradient (Pre-BiCG) method is proposed for the solution of the radiative
  transfer equation in spherical geometry. A variant of this method called
  Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also
  presented. These are iterative methods based on the construction of a
  set of bi-orthogonal vectors. The application of the Pre-BiCG method
  in some benchmark tests shows that the method is quite versatile,
  and can handle difficult problems that may arise in astrophysical
  radiative transfer theory.

Title: The Hanle effect in a random magnetic field. Dependence of
    the polarization on statistical properties of the magnetic field
Authors: Frisch, H.; Anusha, L. S.; Sampoorna, M.; Nagendra, K. N.
Bibcode: 2009A&A...501..335F
Altcode:
  Context: The Hanle effect is used to determine weak turbulent magnetic
  fields in the solar atmosphere, usually assuming that the angular
  distribution is isotropic, the magnetic field strength constant, and
  that micro-turbulence holds, i.e. that the magnetic field correlation
  length is much less than a photon mean free path. <BR />Aims: To
  examine the sensitivity of turbulent magnetic field measurements
  to these assumptions, we study the dependence of Hanle effect on
  the magnetic field correlation length, its angular, and strength
  distributions. <BR />Methods: We introduce a fairly general random
  magnetic field model characterized by a correlation length and a
  magnetic field vector distribution. Micro-turbulence is recovered
  when the correlation length goes to zero and macro-turbulence when it
  goes to infinity. Radiative transfer equations are established for
  the calculation of the mean Stokes parameters and they are solved
  numerically by a polarized approximate lambda iteration method. <BR
  />Results: We show that optically thin spectral lines and optically
  very thick ones are insensitive to the correlation length of the
  magnetic field, while spectral lines with intermediate optical depths
  (around 10-100) show some sensitivity to this parameter. The result is
  interpreted in terms of the mean number of scattering events needed to
  create the surface polarization. It is shown that the single-scattering
  approximation holds good for thin and thick lines but may fail for lines
  with intermediate thickness. The dependence of the polarization on the
  magnetic field vector probability density function (PDF) is examined
  in the micro-turbulent limit. A few PDFs with different angular and
  strength distributions, but equal mean value of the magnetic field,
  are considered. It is found that the polarization is in general quite
  sensitive to the shape of the magnetic field strength PDF and somewhat
  to the angular distribution. <BR />Conclusions: The mean field derived
  from Hanle effect analysis of polarimetric data strongly depends on
  the choice of the field strength distribution used in the analysis. It
  is shown that micro-turbulence is in general a safe approximation.

Title: Origin of Spatial Variations of Scattering Polarization in
    the Wings of the Ca I 4227 Å Line
Authors: Sampoorna, M.; Stenflo, J. O.; Nagendra, K. N.; Bianda, M.;
   Ramelli, R.; Anusha, L. S.
Bibcode: 2009ApJ...699.1650S
Altcode: 2009arXiv0906.1184S
  Polarization that is produced by coherent scattering can be modified
  by magnetic fields via the Hanle effect. This has opened a window to
  explorations of solar magnetism in parameter domains not accessible to
  the Zeeman effect. According to standard theory the Hanle effect should
  only be operating in the Doppler core of spectral lines but not in the
  wings. In contrast, our observations of the scattering polarization
  in the Ca I 4227 Å line reveal the existence of spatial variations
  of the scattering polarization throughout the far line wings. This
  raises the question whether the observed spatial variations in wing
  polarization have a magnetic or nonmagnetic origin. A magnetic origin
  may be possible if elastic collisions are able to cause sufficient
  frequency redistribution to make the Hanle effect effective in the wings
  without causing excessive collisional depolarization, as suggested by
  recent theories for partial frequency redistribution (PRD) with coherent
  scattering in magnetic fields. To model the wing polarization we bypass
  the problem of solving the full polarized radiative transfer equations
  and instead apply an extended version of the technique based on the
  "last scattering approximation." It assumes that the polarization
  of the emergent radiation is determined by the anisotropy of the
  incident radiation field at the last scattering event. We determine
  this anisotropy from the observed limb darkening as a function of
  wavelength throughout the spectral line. The empirical anisotropy
  profile is used together with the single-scattering redistribution
  matrix, which contains all the PRD, collisional, and magnetic field
  effects. The model further contains a continuum opacity parameter,
  which increasingly dilutes the polarized line photons as we move away
  from the line center, and a continuum polarization parameter that
  represents the observed polarization level far from the line. This
  model is highly successful in reproducing the observed Stokes Q/I
  polarization (linear polarization parallel to the nearest solar
  limb), including the location of the wing polarization maxima and the
  minima around the Doppler core, but it fails to reproduce the observed
  spatial variations of the wing polarization in terms of magnetic field
  effects with frequency redistribution. This null result points in the
  direction of a nonmagnetic origin in terms of local inhomogeneities
  (varying collisional depolarization, radiation-field anisotropies,
  and deviations from a plane-parallel atmospheric stratification).

Title: Polarization : Proving ground for methods in radiative
    transfer.
Authors: Nagendra, K. N.; Anusha, L. S.; Sampoorna, M.
Bibcode: 2009MmSAI..80..678N
Altcode:
  Polarization of solar lines arises due to illumination of radiating
  atom by anisotropic (limb darkened/brightened) radiation. Modelling
  the polarized spectra of the Sun and stars requires solution of the
  line radiative transfer problem in which the relevant polarizing
  physical mechanisms are incorporated. The purpose of this paper is to
  describe in what different ways the polarization state of the radiation
  `complicates' the numerical methods originally designed for scalar
  radiative transfer. We present several interesting situations involving
  the solution of polarized line transfer to prove our point. They are
  (i) Comparison of the polarized approximate lambda iteration (PALI)
  methods with new approaches like Bi-conjugate gradient method that
  is faster, (ii) Polarized Hanle scattering line radiative transfer in
  random magnetic fields, (iii) Difficulties encountered in incorporating
  polarized partial frequency redistribution (PRD) matrices in line
  radiative transfer codes, (iv) Technical difficulties encountered
  in handling polarized specific intensity vector, some components of
  which are sign changing, (v) Proving that scattering polarization is
  indeed a boundary layer phenomenon. We provide credible benchmarks in
  each of the above studies. We show that any new numerical methods can
  be tested in the best possible way, when it is extended to include
  polarization state of the radiation field in line scattering.

Title: Projection methods for line radiative transfer in spherical
    media.
Authors: Anusha, L. S.; Nagendra, K. N.
Bibcode: 2009MmSAI..80..631A
Altcode:
  An efficient numerical method called the Preconditioned Bi-Conjugate
  Gradient (Pre-BiCG) method is presented for the solution of radiative
  transfer equation in spherical geometry. A variant of this method called
  Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also
  presented. These methods are based on projections on the subspaces of
  the n dimensional Euclidean space mathbb {R}<SUP>n</SUP> called Krylov
  subspaces. The methods are shown to be faster in terms of convergence
  rate compared to the contemporary iterative methods such as Jacobi,
  Gauss-Seidel and Successive Over Relaxation (SOR).

