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

Abstract

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).

MULTI-DIMENSIONAL RADIATIVE TRANSFER TO ANALYZE HANLE EFFECT IN Ca II K LINE AT 3933 Å

“…Further, a strong λ dependence of the spatial distribution shows that the scattering physics described through PRD strongly couples with spatial inhomogeneity of the atmosphere. Spatial variations in the linear polarization profiles are observationally noted in the wings of the well-known chromospheric line, the Ca i 4227 Å (see Bianda et al 2003;Sampoorna et al 2009), which the authors refer to as the "enigmatic wing features." We find such spatial inhomogeneities in the line wings of the Ca ii K line, which is also a chromospheric line.…”

“…However, the solar atmosphere is extremely inhomogeneous to be well represented by 1D stratification of the physical quantities. Observations using ZIMPOL (Gandorfer et al 2004) show strong spatial variation of the linear polarization along the slit, indicating spatial structuring in the atmosphere (see, e.g., Bianda et al 2003;Stenflo 2006;Sampoorna et al 2009). A natural explanation of this spatial structuring in the line core is in terms of the Hanle effect from spatially varying magnetic fields.…”

“…Scattering polarization in strong resonance lines such as Ca i 4227 Å and Ca ii K at 3933 Å can be used to diagnose chromospheric magnetic fields (see, e.g., Faurobert-Scholl 1992;Holzreuter et al 2005;Sampoorna et al 2009;Anusha et al 2010Frisch et al 2012) and also to explore the temperature bifurcation in the chromosphere (Holzreuter et al 2006;Holzreuter & Stenflo 2007a, 2007b. All these studies consider one-dimensional (1D) models of the solar atmosphere such as FALC (Fontenla et al 1993).…”

Polarized line formation with J-state interference in the presence of magnetic fields: A Heuristic treatment of collisional frequency redistribution

“…Such a decomposition is possible in the non-magnetic case. This is because in the absence of a magnetic field, the summations over the magnetic quantum numbers can be analytically performed using Racah algebra as shown in P1 for type-II redistribution and Equation (35) for type-III redistribution. However in the magnetic case, all the summations remain intact and have to be performed numerically.…”

Hanle effect from a dipolar magnetic structure: the case of the solar corona and the case of a star

“…Owing to the weakness of the polarization degree, this approximation is quite valid. Its validity has been extensively studied by Sampoorna et al (2009).…”