83 research outputs found
Polarized Line Formation in Multi-Dimensional Media.III. Hanle Effect with Partial Frequency Redistribution
In the previous two papers, namely, \citet{anuknn11} and \citet{anuetal11} we
solved the polarized radiative transfer (RT) equation in multi-dimensional
(multi-D) geometries, with partial frequency redistribution (PRD) as the
scattering mechanism. We assumed Rayleigh scattering as the only source of
linear polarization () 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 ,
developed in \citet{anuknn11}, to the case of RT with Hanle effect. A fast
iterative method of solution (based on the Stabilized Preconditioned
Bi-Conjugate-Gradient technique), developed in \citet{anuetal11}, 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 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 profiles, which is more pronounced in the line wings. (3)
The presence of a weak magnetic field modifies the spatial variation of the
emergent profiles in the line core, by producing significant
changes in their magnitudes.Comment: 31 pages, 14 figures, Submitted to ApJ, Under revie
On the Sensitivity of Partial Redistribution Scattering Polarization Profiles to Various Atmospheric Parameters
This paper presents a detailed study of the scattering polarization profiles
formed under partial frequency redistribution (PRD) in two thermal models of
the solar atmosphere. Particular attention is given to understanding the
influence of several atmospheric parameters on the emergent fractional linear
polarization profiles. The shapes of these profiles are interpreted in
terms of the anisotropy of the radiation field, which in turn depends on the
source function gradient that sets the angular variation of the specific
intensity. We define a suitable frequency integrated anisotropy factor for PRD
that can be directly related to the emergent linear polarization. We show that
complete frequency redistribution is a good approximation to model weak
resonance lines. We also show that the emergent linear polarization profiles
can be very sensitive to the thermal structure of the solar atmosphere and, in
particular, to spatial variations of the damping parameter.Comment: 45 pages, 16 figures, accepted for publication in the Astrophysical
Journal (2010
Hanle effect in the solar Ba II D2 line: a diagnostic tool for chromospheric weak magnetic fields
The physics of the solar chromosphere depends in a crucial way on its
magnetic structure. However there are presently very few direct magnetic field
diagnostics available for this region. Here we investigate the diagnostic
potential of the Hanle effect on the Ba II D2 line resonance polarization for
the determination of weak chromospheric turbulent magnetic fields......Comment: In press in astronomy and astrophysic
Hanle effect in the CN violet system with LTE modeling
Weak entangled magnetic fields with mixed polarity occupy the main part of
the quiet Sun. The Zeeman effect diagnostics fails to measure such fields
because of cancellation in circular polarization. However, the Hanle effect
diagnostics, accessible through the second solar spectrum, provides us with a
very sensitive tool for studying the distribution of weak magnetic fields on
the Sun. Molecular lines are very strong and even dominate in some regions of
the second solar spectrum. The CN system is
one of the richest and most promising systems for molecular diagnostics and
well suited for the application of the differential Hanle effect method. The
aim is to interpret observations of the CN
system using the Hanle effect and to obtain an estimation of the magnetic field
strength. We assume that the CN molecular layer is situated above the region
where the continuum radiation is formed and employ the single-scattering
approximation. Together with the Hanle effect theory this provides us with a
model that can diagnose turbulent magnetic fields. We have succeeded in fitting
modeled CN lines in several regions of the second solar spectrum to
observations and obtained a magnetic field strength in the range from 10--30 G
in the upper solar photosphere depending on the considered lines.Comment: Accepted for publication in Astronomy and Astrophysic
Determining the Magnetization of the Quiet Sun Photosphere from the Hanle Effect and Surface Dynamo Simulations
The bulk of the quiet solar photosphere is thought to be significantly
magnetized, due to the ubiquitous presence of a tangled magnetic field at
subresolution scales with an average strength ~ 100 G. This conclusion was
reached through detailed three-dimensional (3D) radiative transfer modeling of
the Hanle effect in the Sr I 4607 line, using the microturbulent field
approximation and assuming that the shape of the probability density function
of the magnetic field strength is exponential. Here we relax both
approximations by modeling the observed scattering polarization in terms of the
Hanle effect produced by the magnetic field of a 3D photospheric model
resulting from a (state-of-the-art) magneto-convection simulation with surface
dynamo action. We show that the scattering polarization amplitudes observed in
the Sr I 4607 line can be explained only after enhancing the magnetic strength
of the photospheric model by a sizable scaling factor, F=10, which implies
= 130 G in the upper photosphere. We argue also that in order to explain both
the Hanle depolarization of the Sr I 4607 line and the Zeeman signals observed
in Fe I lines we need to introduce a height-dependent scaling factor, such that
the ensuing = 160 G in the low photosphere and = 130 G in the upper
photosphere.Comment: To appear in ApJ Letter
Origin of spatial variations of scattering polarization in the wings of the Ca {\sc i} 4227 \AA line
Polarization that is produced by coherent scattering can be modified by
magnetic fields via the Hanle 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 {\sc i} 4227 \AA line reveals 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
non-magnetic 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 with coherent
scattering in magnetic fields. To model the wing polarization we apply an
extended version of the technique based on the "last scattering approximation".
This model is highly successful in reproducing the observed Stokes
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 non-magnetic
origin in terms of local inhomogeneities (varying collisional depolarization,
radiation-field anisotropies, and deviations from a plane-parallel atmospheric
stratification).Comment: Accepted in May 2009 for publication in The Astrophysical Journa
Quiet Sun Magnetic Field Measurements Based on Lines with Hyperfine Structure
The Zeeman pattern of MnI lines is sensitive to hyperfine structure (HFS)
and, they respond to hG magnetic field strengths differently from the lines
used in solar magnetometry. This peculiarity has been employed to measure
magnetic field strengths in quiet Sun regions. However, the methods applied so
far assume the magnetic field to be constant in the resolution element. The
assumption is clearly insufficient to describe the complex quiet Sun magnetic
fields, biasing the results of the measurements. We present the first syntheses
of MnI lines in realistic quiet Sun model atmospheres. The syntheses show how
the MnI lines weaken with increasing field strength. In particular, kG magnetic
concentrations produce NnI 5538 circular polarization signals (Stokes V) which
can be up to two orders of magnitude smaller than the weak magnetic field
approximation prediction. Consequently, (1) the polarization emerging from an
atmosphere having weak and strong fields is biased towards the weak fields, and
(2) HFS features characteristic of weak fields show up even when the magnetic
flux and energy are dominated by kG fields. For the HFS feature of MnI 5538 to
disappear the filling factor of kG fields has to be larger than the filling
factor of sub-kG fields. Stokes V depends on magnetic field inclination
according to the simple consine law. Atmospheres with unresolved velocities
produce asymmetric line profiles, which cannot be reproduced by simple
one-component model atmospheres. The uncertainty of the HFS constants do not
limit the use of MnI lines for magnetometry.Comment: Accepted for publication in ApJ. 10 pages, 14 figure
The distribution of Quiet Sun magnetic field strengths from 0 to 1800 G
The quiet Sun photospheric plasma has a variety of magnetic field strengths
going from zero to 1800 G. The empirical characterization of these field
strengths requires a probability density function (PDF), i.e., a function P(B)
describing the fraction of quiet Sun occupied by each field strength B. We show
how to combine magnetic field strength measurements based on the Zeeman effect
and the Hanle effect to estimate an unbiased P(B). The application of the
method to real observations renders a set of possible PDFs, which outline the
general characteristics of the quiet Sun magnetic fields. Their most probable
field strength differs from zero. The magnetic energy density is a significant
fraction of the kinetic energy of the granular motions at the base of the
photosphere (larger than 15% or larger than 2 10^{3} erg cm^{-3}). The unsigned
flux density (or mean magnetic field strength) has to be between 130 G and 190
G. A significant part of the unsigned flux (between 10% and 50%) and of the
magnetic energy (between 45% and 85%) are provided by the field strengths
larger than 500 G which, however, occupy only a small fraction of the surface
(between 1% and 10%). The fraction of kG fields in the quiet Sun is even
smaller, but they are important for a number of reasons. The kG fields still
trace a significant fraction of the total magnetic energy, they reach the high
photosphere, and they appear in unpolarized light images. The quiet Sun
photosphere has far more unsigned magnetic flux and magnetic energy than the
active regions and the network all together.Comment: To appear in ApJ. 14 pages, 9 figure
The Hanle Effect in 1D, 2D and 3D
This paper addresses the problem of scattering line polarization and the
Hanle effect in one-dimensional (1D), two-dimensional (2D) and
three-dimensional (3D) media for the case of a two-level model atom without
lower-level polarization and assuming complete frequency redistribution. The
theoretical framework chosen for its formulation is the QED theory of Landi
Degl'Innocenti (1983), which specifies the excitation state of the atoms in
terms of the irreducible tensor components of the atomic density matrix. The
self-consistent values of these density-matrix elements is to be determined by
solving jointly the kinetic and radiative transfer equations for the Stokes
parameters. We show how to achieve this by generalizing to Non-LTE polarization
transfer the Jacobi-based ALI method of Olson et al. (1986) and the iterative
schemes based on Gauss-Seidel iteration of Trujillo Bueno and Fabiani Bendicho
(1995). These methods essentially maintain the simplicity of the
Lambda-iteration method, but their convergence rate is extremely high. Finally,
some 1D and 2D model calculations are presented that illustrate the effect of
horizontal atmospheric inhomogeneities on magnetic and non-magnetic resonance
line polarization signals.Comment: 14 pages and 5 figure
Wavelength-Diverse Polarization Modulators for Stokes Polarimetry
Information about the three-dimensional structure of solar magnetic fields is
encoded in the polarized spectra of solar radiation by a host of physical
processes. To extract this information, solar spectra must be obtained in a
variety of magnetically sensitive spectral lines at high spatial, spectral, and
temporal resolution with high precision. The need to observe many different
spectral lines drives the development of Stokes polarimeters with a high degree
of wavelength diversity. We present a new paradigm for the design of
polarization modulators that operate over a wide wavelength range with near
optimal polarimetric efficiency and are directly applicable to the next
generation of multi-line Stokes polarimeters. These modulators are not
achromatic in the usual sense because their polarimetric properties vary with
wavelength, but they do so in an optimal way. Thus we refer to these modulators
as polychromatic. We present here the theory behind polychromatic modulators,
illustrate the concept with design examples, and present the performance
properties of a prototype polychromatic modulator.Comment: 13 pages, 1 table, 5 figures, accepted for publication in Applied
Optic
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