Resonance Line Polarization Research Articles

Polarized resonance line transfer in a spherically symmetric medium with angle-dependent partial frequency redistribution

ABSTRACT In a stellar atmosphere, the resonance line polarization arises from scattering of limb-darkened radiation field by atoms. This spectral line polarization gets affected particularly in the wings, when the line photons suffer scattering on electrons in thermal motion. Scattering of line photons by atoms and electrons are, respectively, described by the atomic and Thomson electron scattering redistribution functions, which in general depend on both the frequencies and directions of incident and scattered photons. In this paper, we consider the polarized spectral line formation in spherically symmetric extended and expanding media accounting for the angle-dependent partial frequency redistribution (AD-PRD) in scattering on both atoms and electrons. We solve this computationally demanding polarized transfer problem using an accelerated lambda iteration method and a method based on orders of scattering approach. In the case of expanding spherical medium, the concerned transfer problem is solved in the comoving frame. Because of the computational limitations, we consider optically thin isothermal spherically symmetric media of different extensions for the static case as well as when the velocity fields are present. For the considered model, we show that the AD-PRD effects on the linear polarization profiles are significant and have to be accounted for.

Influence of Thomson Electron Scattering Redistribution on Spectral Line Polarization Formed in Spherically Symmetric Extended and Expanding Atmospheres

Scattering of line photons by ambient electrons in thermal motion in the stellar atmosphere modifies the wings of both intensity and linear polarization profiles of the spectral lines. The aim of the present paper is to investigate in detail the influence of Thomson electron scattering redistribution on resonance line polarization formed in spherically symmetric extended and expanding atmospheres. A comoving frame method based on the accelerated lambda iteration technique is used to solve the concerned spherically symmetric polarized transfer equation including both the atomic and Thomson electron scattering redistribution functions. Our numerical studies highlight the importance of accounting for Thomson electron scattering redistribution in spectral line polarization problems.

The Transfer of Resonance Line Polarization with Partial Frequency Redistribution in the General Hanle–Zeeman Regime

Abstract The spectral line polarization encodes a wealth of information about the thermal and magnetic properties of the solar atmosphere. Modeling the Stokes profiles of strong resonance lines is, however, a complex problem both from a theoretical and computational point of view, especially when partial frequency redistribution (PRD) effects need to be taken into account. In this work, we consider a two-level atom in the presence of magnetic fields of arbitrary intensity (Hanle–Zeeman regime) and orientation, both deterministic and micro-structured. Working within the framework of a rigorous PRD theoretical approach, we have developed a numerical code that solves the full non-LTE radiative transfer problem for polarized radiation, in one-dimensional models of the solar atmosphere, accounting for the combined action of the Hanle and Zeeman effects, as well as for PRD phenomena. After briefly discussing the relevant equations, we describe the iterative method of solution of the problem and the numerical tools that we have developed and implemented. We finally present some illustrative applications to two resonance lines that form at different heights in the solar atmosphere, and provide a detailed physical interpretation of the calculated Stokes profiles. We find that magneto-optical effects have a strong impact on the linear polarization signals that PRD effects produce in the wings of strong resonance lines. We also show that the weak-field approximation has to be used with caution when PRD effects are considered.

Polarization of Resonance Lines in the Case of Partially Polarized Primary Radiation Sources

The transfer of polarized radiation in a resonance line in a semi-infinite plane-parallel nonmagnetic atmosphere is examined. It is assumed that scattering takes place with complete frequency redistribution within the line and continuum absorption is taken into account. The primary radiation sources in the atmosphere are assumed to be partially polarized; here the function describing these sources is given by the product of a polynomial and an exponential of the optical depth. The Stokes vector of the emerging radiation is found using a general analytic theory of I ˆ -matrices (the I -matrix is a generalization of the scalar Chandrasekhar H-function). It is shown that the Stokes vector of the radiation emerging from an atmosphere in which primary sources of this form are distributed can be expressed in terms of the solution of a single, so-called standard problem.

The transfer of resonance line polarization with partial frequency redistribution andJ-state interference

The linear polarization signals produced by scattering processes in strong resonance lines are rich in information on the magnetic and thermal structure of the chromosphere and transition region of the Sun and of other stars. A correct modeling of these signals requires accounting for partial frequency redistribution effects, as well as for the impact of quantum interference between different fine structure levels (J-state interference). In this paper, we present a theoretical approach suitable for modeling the transfer of resonance line polarization when taking these effects into account, along with an accurate numerical method of solution of the problem's equations. We consider a two-term atom with unpolarized lower term and infinitely sharp lower levels, in the absence of magnetic fields. We show that by making simple formal substitutions on the quantum numbers, the theoretical approach derived here for a two-term atom can also be applied to describe a two-level atom with hyperfine structure. An illustrative application to the MgII doublet around 2800A is presented.

SCATTERING POLARIZATION IN SOLAR FLARES

There is ongoing debate about the origin and even the very existence of a high degree of linear polarization of some chromospheric spectral lines observed in solar flares. The standard explanation of these measurements is in terms of the impact polarization caused by non-thermal proton and/or electron beams. In this work, we study the possible role of resonance line polarization due to radiation anisotropy in the inhomogeneous medium of the flare ribbons. We consider a simple two-dimensional model of the flaring chromosphere and we self-consistently solve the non-LTE problem taking into account the role of resonant scattering polarization and of the Hanle effect. Our calculations show that the horizontal plasma inhomogeneities at the boundary of the flare ribbons can lead to a significant radiation anisotropy in the line formation region and, consequently, to a fractional linear polarization of the emergent radiation of the order of several percent. Neglecting the effects of impact polarization, our model can provide a clue for resolving some of the common observational findings, namely: (1) why a high degree of polarization appears mainly at the edges of the flare ribbons; (2) why polarization can also be observed during the gradual phase of a flare; and (3) why polarization is mostly radial or tangential. We conclude that radiation transfer in realistic multi-dimensional models of solar flares needs to be considered as an essential ingredient for understanding the observed spectral line polarization.

Spectral line polarization with angle-dependent partial frequency redistribution

Context. The linear polarization of strong resonance lines observed in the solar spectrum is created by the scattering of the photospheric radiation field. This polarization is sensitive to the form of the partial frequency redistribution (PRD) function used in the line radiative transfer equation. Observations have been analyzed until now with angle-averaged PRD functions. With an increase in the polarimetric sensitivity and resolving power of the present-day telescopes, it will become possible to detect finer effects caused by the angle dependence of the PRD functions. Aims. We devise new efficient numerical methods to solve the polarized line transfer equation with angle-dependent PRD, in planeparallel cylindrically symmetrical media. We try to bring out the essential differences between the polarized spectra formed under angle-averaged and the more realistic case of angle-dependent PRD functions. Methods. We use a recently developed Stokes vector decomposition technique to formulate three different iterative methods tailored for angle-dependent PRD functions. Two of them are of the accelerated lambda iteration type, one is based on the core-wing approach, and the other one on the frequency by frequency approach suitably generalized to handle angle-dependent PRD. The third one is based on a series expansion in the mean number of scattering events (Neumann series expansion). Results. We show that all these methods work well on this difficult problem of polarized line formation with angle-dependent PRD. We present several benchmark solutions with isothermal atmospheres to show the performance of the three numerical methods and to analyze the role of the angle-dependent PRD effects. For weak lines, we find no significant effects when the angle-dependence of the PRD functions is taken into account. For strong lines, we find a significant decrease in the polarization, the largest effect occurring in the near wing maxima.

Effect of continuum absorption on the polarization of resonance lines

Multiple resonance scattering of radiation in a spectrum line with absorption in the continuum is examined. It is assumed that the scattering atmosphere is semi-infinite and that there is no magnetic field or continuum emission at the frequencies of the spectrum line. The polarization characteristics of the emerging radiation are determined for unpolarized primary radiation sources distributed uniformly within an atmosphere in the case of a Voigt absorption profile. The calculations employ an iterative solution of the Ambartsumyan-Chandrasekhar matrix integral equation.

Spectropolarimetry and polarization-dependent fringes

An account is given of the formation of polarization-dependent fringes, the “enemies" of spectropolarimetry, present practically in all polarization devices. Typically, multiple reflections give rise to secondary beams coherent with the main beam, but with wavelength-dependent phase differences. Polarized fringes may appear in any particular Stokes parameter or their combinations, and may (or may not) be seen in the intensity. The mechanism of formation of fringes in polarization is demonstrated. Fringes of analyzers, beam-splitter and retarders are evaluated. Flat-fielding techniques are discussed and ways for the removal of polarized fringes are suggested. Techniques that are efficient in removing fringes in intensity may be inadequate or insufficient for polarization. Anti-reflection coating, for instance, may reduce fringes, but not below 10-3 of the intensity. This level would often be acceptable for intensity measurements but not necessarily for polarization, where one may often need to evaluate signals down to the level of 10-5, as in the observation of resonance line polarization and the second solar spectrum. Flat-fielding, by observing disk center, may be satisfactory to remove fringes for solar observations but this is not appropriate for stellar observations. The understanding of how these fringes are formed is essential both for the design of polarimeters and for their proper use.

The effect of angle-dependent non-coherent electron scattering and partial redistribution on the polarization of resonance lines

The polarized radiative transfer equation is solved when angle-dependent partial redistribution and non-coherent electron scattering are included as line-scattering mechanisms. A static atmosphere with plane parallel symmetry is assumed. Test calculations are used to illustrate the effects of the electron-scattering coefficient, the thermalization parameter and the continuous absorption coefficient on the line polarization. Results of angle-averaged and angle-dependent redistribution functions are compared and it is shown that angle-dependent functions should be used to model the wing polarization of optically thin lines. The lower the continuous absorption compared with the electron scattering, the higher the wing polarization.

Iterative Methods for the Non‐LTE Transfer of Polarized Radiation: Resonance Line Polarization in One‐dimensional Atmospheres

This paper shows how to generalize to non-LTE polarization transfer some operator splitting methods that were originally developed for solving unpolarized transfer problems. These are the Jacobi-based accelerated Λ-iteration (ALI) method of Olson, Auer, & Buchler and the iterative schemes based on Gauss-Seidel and successive overrelaxation (SOR) iteration of Trujillo Bueno and Fabiani Bendicho. The theoretical framework chosen for the formulation of polarization transfer problems is the quantum electrodynamics (QED) theory of Landi Degl'Innocenti, which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. This first paper establishes the grounds of our numerical approach to non-LTE polarization transfer by concentrating on the standard case of scattering line polarization in a gas of two-level atoms, including the Hanle effect due to a weak microturbulent and isotropic magnetic field. We begin demonstrating that the well-known Λ-iteration method leads to the self-consistent solution of this type of problem if one initializes using the exact solution corresponding to the unpolarized case. We show then how the above-mentioned splitting methods can be easily derived from this simple Λ-iteration scheme. We show that our SOR method is 10 times faster than the Jacobi-based ALI method, while our implementation of the Gauss-Seidel method is 4 times faster. These iterative schemes lead to the self-consistent solution independently of the chosen initialization. The convergence rate of these iterative methods is very high; they do not require either the construction or the inversion of any matrix, and the computing time per iteration is similar to that of the Λ-iteration method.

THEORETICAL AND OBSERVATIONAL CONSEQUENCES OF STELLAR ROTATION AND MAGNETIC FIELDS FOR STELLAR WINDS

ABSTRACT My dissertation concerns the study of stellar wind structure from (1) the theoretical modeling of stellar rotation and magnetic fields and (2) the development of observational diagnostics. First, I have investigated the effects of stellar rotation for the wind structure of stars across the H-R Diagram using principles from the Wind Compressed Disk (WCD) model. Relative to a spherical wind, the effect of rotation is to increase the wind density at the equator while decreasing the density near the poles. An investigation of mild equatorial density enhancements has led to the development of the Wind Compressed Zone (WCZ) model. The WCZ model predicts that equatorial wind compressions are most likely to occur for stellar winds with low terminal speeds and/or radial velocity distributions that increase gradually from the base of the wind. In favorable cases stellar rotation can produce significant equatorial density enhancements in the winds of Wolf-Rayet stars, B~supergiants, Asymptotic Giant Branch stars, and even some novae at moderate stellar rotations of 20-30% break-up. A spectral line diagnostic based on multiline observations at Infrared wavelengths has been developed to measure the velocity law in the Wolf-Rayet winds, to determine whether they are likely susceptible to wind compression effects. The second major part of the thesis relates to the result that the WCZ model predicts the magnetic field structure in the wind, if the field strength is relatively weak. However, there are generally no good spectral diagnostics of sub-kiloGauss stellar magnetic fields. Magnetic fields at these low strengths are difficult to measure with the Zeeman effect, because the Zeeman line splitting is significantly smaller than the Doppler broadening. Thus, I have explored applications of the Hanle effect, that is sensitive to weaker magnetic fields than is the Zeeman effect, for probing the magnetic properties of stellar winds. The Hanle effect concerns the modification of resonance line polarization by the magnetic field. It has been used in studies of the Solar atmosphere, but not in other stars. Solutions for the Hanle effect in optically thin axisymmetric extended stellar envelopes have been derived. Relative to the zero field case, the Hanle effect can result in significant changes of the total line polarization. Consequences of the Hanle effect for the polarization of line profiles is also investigated, and analytic results are presented for a few special cases. A magnetic field can cause strong variations of the polarized line profile shape as compared to the case without a magnetic field. With multiline observations the Hanle effect will be a valuable diagnostic of stellar magnetic fields in the range 1-1000 Gauss.

Collisional redistribution effects on line polarization in spherical atmospheres

The polarization of resonance and subordinate lines formed in spherically symmetric media is studied. The effect of collisions is shown by taking a combination of partial redistribution mechanisms represented by the functions RII-A(x,x′) and RIII-A(x,x′), which are well-known redistribution functions that describe interaction of line photons with a two-level model atom. A large number of models are presented, which clearly show the effect of collisions on line polarization, when basic model parameters of a two-level atom are varied one at a time. Thus the grid of models generated serves to establish upper and lower limits on the impact of collisions on line polarization. Some results employing a more accurate treatment of collisional redistribution are also shown. The purpose of this paper is to understand the quantitative behaviour of line polarization when collisional redistribution plays an important role in the transfer of line radiation.

Resonance line polarization in spherical atmospheres: Partial redistribution effects studied with the Domke-Hubeny redistribution matrix

Resonance line polarization in spherical atmospheres: Partial redistribution effects studied with the Domke-Hubeny redistribution matrix

Resonance-line polarization in expanding spherical atmospheres: solution in the comoving frame

Resonance-line polarization in expanding spherical atmospheres: solution in the comoving frame

Resonance-line polarization in a moving medium: solution in the comoving frame with complete frequency redistribution

We study the effect of differential radial velocity on the distribution of line intensities and line polarization along the line of sight of an extended stellar atmosphere stratified in parallel planes. The main purpose of this paper is to understand the behaviour of line polarization in an extended and expanding atmosphere. The atmospheric models could represent the photospheric layers of early-type stars. We consider, for simplicity, complete redistribution of frequency. The velocities of expansion of the medium are set at 5, 20 and 50 mean thermal units with two different velocity laws. The results are compared with that of the static case. It is found that large effects are generated in the polarized radiation field when differential radial expansion is taken into account.

Polarization of resonance lines formed in extenned spherical atmospheres

The problem of polarization of the resonance lines formed in extended spherical atmospheres is studied in detail. In this paper, the atmosphere is assumed to be at rest. The basic problem of resonance line polarization in spherical atmospheres as compared to the conventionally used plane-parallel atmospheres, is studied in Nagendra (1988). Our main interest in this paper is to understand the behaviour of polarized radiation fields in extended model spherical atmospheres so that some constraints can be placed on the model parameters in the modelling work conected with observations of polarization across resonance lines. A comparison of polarized lines formed under three kinds of line-scattering mechanisms is also made. They are CS=coherent scatteirng, CRD=complete redistribution, and PRD=partial frequency redistribution which, in the increasing order of generality, provide a good approximation in the two-level atom approach, to the resonance line polarization. The dependence of polarization on the opacity laws, extendedness and on optical depth is studied in detail. The distribution of line intensity and polarization across the visible disk of an extended model stellar atmosphere is studied, in view of the possible disk-resolved observations in future, of the extended atmospheres of the stars.

Resonance line polarization in spherical atmospheres

The problem of resonance line polarization is studied using simple theoretical models. The medium is assumed to be a finite slab or a finite spherical shell-like atmosphere. A comparison of lines formed under complete redistribution and partial redistribution in frequency is presented, for both plane-parallel and spherically symmetric media. The dependence of the resonance line polarization of physical parameters of the two-level atom formulation, and on the global parameters such as extendedness, the opacity law in a spherical medium, and the boundary conditions are studied. The resonance line polarization by coherent scattering is also discussed.

Electron impact polarization of resonance lines from Lithium-like ions

The Oppenheimer-Penney theory, as developed by Percival and Seaton (1958), is applied to calculate the polarization of resonance lines from Li-like ions. Two laws for the pitch-angle distribution of electrons around the magnetic field are accounted. The degrees of polarization are averaged over the energy of non-thermal electrons generated during the initial phase of solar flares. It is found that for the full space pitch-angle distribution, as adopted by Chandra and Joshi (1984), the degrees of polarization are nearly independent of the atomic number of ion. Whereas for the forward-come distribution used by Haug (1981), they depend on the choice of the free parameterE0. The polarization of the resonance lines from Li-like ions is two times larger than that of the Lα radiations from H-like ions. Hence, under favourable conditions, it may be detected during solar flares.

Non-LTE resonance line polarization with partial redistribution: The solar Ca II K line

The non-LTE equations for the transfer of polarized radiation are solved for a two-level model of the Ca ii K ion in the atmospheric models of Gingerich et al. (1971) and Vernazza et al. (1981). The line formation model treats partial redistribution effects, including collisions. The effects of magnetic fields and of quantum mechanical interference are neglected. The response of the intensity, percentage polarization and Q Stokes parameter to changes in the calcium abundance, van der Waals damping parameter and atmospheric models is discussed.