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

Abstract

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.

Effect of Cross-Redistribution on the Resonance Scattering Polarization of O I Line at 1302 Å

“…Unlike the intensity profiles, the fractional linear polarization profiles are sensitive to the structuring in the atmosphere. The spatial variation due to inhomogeneities of the MHD atmosphere in the lower layers shows itself in the near-wings of the line which are formed in these layers (see Anusha & Nagendra 2013). The spatial distribution of linear polarization shows significant differences between the ordinary PRD and XRD cases.…”

“…The method of solution used in this paper to compute the fractional linear polarization in the O i resonance line is the same as that explained in Anusha & Nagendra (2013, and references cited therein). For completeness we summarize the method briefly in this section.…”

“…The elements of the matrices M II,III (B, λ, λ ′ ) for the Hanle effect are derived in Bommier (1997a,b). The functions r II and r III are the angle-averaged PRD functions of Hummer (1962), keeping the same notation as Anusha & Nagendra (2013).Ŵ is a diagonal matrix written aŝ Computing the mean intensity vector is an important step in which linear polarization is generated from the unpolarized intensity vector. This step is the link between the multi-level atom unpolarized radiative transfer code (RH-code) and the two-level atom polarized radiative transfer code that computes linear polarization at 1302Å .…”

The influence of NLTE effects in Fe I lines on an inverted atmosphere

“…Since then, 3D NLTE computations on 3D model atmospheres have been used to compute spectral lines of, for example, lithium (Asplund et al 2003), oxygen (Kiselman & Nordlund 1995;Asplund et al 2004Asplund et al , 2005Pereira et al 2009;Prakapavičius et al 2013;Steffen et al 2015), iron (Lind et al 2017), manganese (Bergemann et al 2019), and barium (Gallagher et al 2020) to determine their abundances in solar and other stellar atmospheres. Recently, forward-modeling of chromospheric lines such as the Ca ii 8542 Å line (Leenaarts et al 2009), the Na i D1 line (Leenaarts et al 2010), the Hα line (Leenaarts et al 2012(Leenaarts et al , 2015, the Mg ii h and k lines (Leenaarts et al 2013), and the Ca ii H and K lines (Anusha & Nagendra 2013;Bjørgen et al 2018) were carried out in 3D NLTE to understand the line formation and to study different chromospheric features that are observed with these lines. Sukhorukov & Leenaarts (2017) synthesized the Mg ii h and k, Lyα, and Lyβ lines taking the complexities of partial frequency redistribution in 3D NLTE into account.…”

Numerical solutions to linear transfer problems of polarized radiation II. Krylov methods and matrix-free implementation

“…For the sake of simplicity, these papers are limited to the study of hypothetical lines in isothermal atmospheric models. Finally, Anusha & Nagendra (2013) used the BICGSTAB method to model the Ca ii K 3993 Å resonance line using an ad-hoc 3D atmospheric model, and Sampoorna et al (2019) applied the GMRES method to model the D 2 lines of Li i and Na i, taking the hyperfine structure of these atoms into account. However, Krylov methods have not been fully exploited in the numerical solution of transfer of polarized radiation.…”