explanation blue bibcodes open ADS page with paths to full text
Author name code: anusha
ADS astronomy entries on 2022-09-14
=author:"Anusha, L.S."
---------------------------------------------------------
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 & 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
