Hanle‐Zeeman Redistribution Matrix. II. Comparison of Classical and Quantum Electrodynamic Approaches

Sampoorna, M.; Nagendra, K. N.; Stenflo, J. O.

doi:10.1086/522562

Cited by 22 publications

(16 citation statements)

References 8 publications

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“…Therefore, we need to use appropriate PRD matrices in our LSA approach. The relevant expressions can either be taken from Domke & Hubeny (1988), or computed from our HanleZeeman theory with B = 0 (see Sampoorna et al 2007aSampoorna et al , 2007b. Further, we now need to generalize Equation (1), which was formulated for frequency coherent scattering in the laboratory frame by Stenflo (1982).…”

Section: Model For the Nonmagnetic Scattering Polarizationmentioning

confidence: 99%

“…For the scattering redistribution matrix elements R i1 with i = 1, 2, 3 we use the HanleZeeman theory (see Sampoorna et al 2007aSampoorna et al , 2007b), although we may also use approximation II of Bommier (1997). Note that in a plane-parallel atmosphere the continuum polarization contribution to the U/I is zero.…”

Section: Model For Magnetic Scattering Polarizationmentioning

confidence: 99%

“…This leads us to the rather unexpected conclusion that the Hanle effect cannot explain the observed wing effects, which suggests that the spatial variations of the wing polarization have a nonmagnetic origin. For the scattering theory we use the recently developed Hanle-Zeeman AD PRD matrices for arbitrary magnetic fields (Sampoorna et al 2007a(Sampoorna et al , 2007b; see also Sampoorna et al 2009). …”

Section: Introductionmentioning

confidence: 99%

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ORIGIN OF SPATIAL VARIATIONS OF SCATTERING POLARIZATION IN THE WINGS OF THE Ca I 4227 Å line

Sampoorna¹,

Stenflo²,

Nagendra³

et al. 2009

ApJ

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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).

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Section: Model For the Nonmagnetic Scattering Polarizationmentioning

confidence: 99%

Section: Model For Magnetic Scattering Polarizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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ORIGIN OF SPATIAL VARIATIONS OF SCATTERING POLARIZATION IN THE WINGS OF THE Ca I 4227 Å line

Sampoorna¹,

Stenflo²,

Nagendra³

et al. 2009

ApJ

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“…Therefore, we obtain a maximum degree of linear polarization, namely Q=I ¼ À1. We refer to this case as 'Zeeman scattering' or equivalently 'Rayleigh scattering in strong magnetic fields' (see also [11,23]). Fig.…”

Section: The Pure Magnetic Field Casementioning

confidence: 99%

Scattering polarization in the presence of magnetic and electric fields

Sampoorna

Nagendra

et al. 2007

Journal of Quantitative Spectroscopy and Radiative Transfer

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The polarization of radiation by scattering on an atom embedded in combined external quadrupole electric and uniform magnetic fields is studied theoretically. Limiting cases of scattering under Zeeman effect, and Hanle effect in weak magnetic fields are discussed. The theory is general enough to handle scattering in intermediate magnetic fields (Hanle-Zeeman effect) and for arbitrary orientation of magnetic field. The quadrupolar electric field produces asymmetric line shifts, and causes interesting level-crossing phenomena either in the absence of an ambient magnetic field, or in its presence. It is shown that the quadrupolar electric field produces an additional depolarization in the Q=I profiles and rotation of the plane of polarization in the U=I profile over and above that arising from magnetic field itself. This characteristic may have a diagnostic potential to detect steady-state and time-varying electric fields that surround radiating atoms in solar atmospheric layers. r

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“…Since 1997, great progress has been made to properly include the Hanle and Zeeman effects (see e.g. Bommier 1997b; Sampoorna et al 2007). Systematic theories for multi-level atoms incorporating PRD effects are still under development.…”

Section: Introductionmentioning

confidence: 99%

Spectral line polarization with angle-dependent partial frequency redistribution

Frisch¹

2010

A&A

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Context. The linear polarization of a strong resonance lines observed near the solar limb is created by a multiple-scattering process. Partial frequency redistribution (PRD) effects must be accounted for to explain the polarization profiles. The redistribution matrix describing the scattering process is a sum of terms, each containing a PRD function multiplied by a Rayleigh type phase matrix. A standard approximation made in calculating the polarization is to average the PRD functions over all the scattering angles, because the numerical work needed to take the angle-dependence of the PRD functions into account is large and not always needed for reasonable evaluations of the polarization. Aims. This paper describes a Stokes parameters decomposition method, that is applicable in plane-parallel cylindrically symmetrical media, which aims at simplifying the numerical work needed to overcome the angle-average approximation. Methods. The decomposition method relies on an azimuthal Fourier expansion of the PRD functions associated to a decomposition of the phase matrices in terms of the Landi Degl'Innocenti irreducible spherical tensors for polarimetry T K Q (i, Ω) (i Stokes parameter index, Ω ray direction). The terms that depend on the azimuth of the scattering angle are retained in the phase matrices. Results. It is shown that the Stokes parameters I and Q, which have the same cylindrical symmetry as the medium, can be expressed in terms of four cylindrically symmetrical componentsThe components with Q = 1, 2 are created by the angular dependence of the PRD functions. They go to zero at disk center, ensuring that Stokes Q also goes to zero. Each component I K Q is a solution to a standard radiative transfer equation. The source term S K Q are significantly simpler than the source terms corresponding to I and Q. They satisfy a set of integral equations that can be solved by an accelerated lambda iteration (ALI) method.

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Hanle‐Zeeman Redistribution Matrix. II. Comparison of Classical and Quantum Electrodynamic Approaches

Cited by 22 publications

References 8 publications

ORIGIN OF SPATIAL VARIATIONS OF SCATTERING POLARIZATION IN THE WINGS OF THE Ca I 4227 Å line

ORIGIN OF SPATIAL VARIATIONS OF SCATTERING POLARIZATION IN THE WINGS OF THE Ca I 4227 Å line

Scattering polarization in the presence of magnetic and electric fields

Spectral line polarization with angle-dependent partial frequency redistribution

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