3D radiative transfer modeling of scattering polarization with partial frequency redistribution I. Verification and disk-center results for the solar Ca I 4227 Å line

TL;DR

The paper addresses modeling of scattering polarization in strong solar resonance lines using 3D non-LTE radiative transfer with partial frequency redistribution (PRD). It introduces TRIP, a parallel code verified against PORTA in the CRD limit and applied to the Ca I 4227 line in a realistic 3D RMHD-based solar atmosphere, solving a large linear system with a physics-based Krylov preconditioner. Key findings show that PRD plus 3D structure produce disk-center wing polarization signals that are sensitive to magneto-optical effects and velocity gradients, while CRD underestimates line-core amplitudes; bulk velocities can amplify core signals and shift their shapes. This work enables quantitative comparisons between synthetic and observational polarization data for chromospheric magnetism diagnostics and sets the stage for broader line diagnostics in larger atmospheric models.

Abstract

Several strong solar resonance lines show observable linear scattering polarization signals, holding a great potential for investigating the magnetism of the outer solar atmosphere. Accurately modeling these signals requires solving the radiative transfer (RT) problem for polarized radiation in comprehensive 3D models of the solar atmosphere, in non-local thermodynamic equilibrium, accounting for partial frequency redistribution (PRD) effects. This problem has so far been computationally inaccessible. We present the first scientific application of TRIP, a novel software for the massively parallel solution of the 3D non-LTE RT problem for polarized radiation, including scattering polarization and PRD. We aim to verify the code and explore the combined action of PRD and the 3D structure of the solar atmosphere on scattering polarization. We run TRIP to synthesize the Stokes profiles of the Ca I line at 4227 Å in a 3D model of the solar atmosphere extracted from a radiation magneto-hydrodynamic simulation. We efficiently solve the resulting large-scale problem, with up to $4 \times 10^{10}$ degrees of freedom, with a state-of-the-art preconditioned Krylov method, using up to 20 thousand parallel CPUs. After including verification tests, we find that the joint impact of PRD effects and the detailed 3D structure of the atmospheric model produce disk-center scattering polarization signals in the line wings. These signals are sensitive to the magnetic field, via magneto-optical effects, and to bulk velocity gradients. We also show that the CRD approximation underestimates the amplitude of disk-center line-core signals. This achievement represents a crucial step forward for diagnosing the magnetism of the solar chromosphere and transition region through the quantitative comparisons of synthetic and observational data.

Figures (13)

• Figure 1: From left to right: temperature maps at $z=-0.114$ Mm of (i) the original model from the 3D R-MHD simulation by carlsson16; (ii) a zoomed-in model, corresponding to the green square in the original model; (iii) the same zoomed-in model, but with halved spatial resolution in the $x$ and $y$ axes; and (iv) Model-63 obtained by mirroring the half-resolution zoomed-in model with respect to the right and top boundaries.
• Figure 2: Scatter plots of the absolute discrepancy between TRIP and PORTA emergent fractional polarization as a function of TRIP fractional polarization, for all $N_x N_y N_{\Omega^+} = 63 \cdot 63 \cdot 64\simeq0.25M$ spatial points and emerging LOSs. Dashed lines represent different relative discrepancies $\delta_S$. The colorbar indicates the density of points per grid element, for a $100\times100$ grid of the shown $(\widehat{S},\widehat{\Delta}_S)$ planes.
• Figure 3: Scatter plots of the absolute discrepancy between the emergent fractional polarization obtained with $N_\Omega=128$ and $N_\Omega=200$ as a function of the fractional polarization for $N_\Omega = 200$. Each plot contains $N_{\widetilde{\Omega}}N_x N_y = 15\cdot63 \cdot 63 \simeq 60$ K points, one for each spatial point and common LOS ($N_{\widetilde{\Omega}}=15$ is the number of common LOSs considered for the comparison). Dashed lines represent different relative discrepancies $\delta_S$. Solid lines represent linear regression with corresponding slope $\delta_S$. The colorbar indicates the density of points per grid element, for a $100\times100$ grid of the shown $(\widehat{S},\widehat{\Delta}_S)$ planes.
• Figure 4: Emergent Stokes profiles at spatial point $(x,y)=(1.43,0.38)$ Mm with indices $(i,j)=(16,5)$ and LOS $(\mu,\chi)=(0.149,0.157)$, calculated with different angular grid sizes.
• Figure 5: Upper panels: Ca i 4227 line-center emergent intensity (in erg cm$^{-2}$ s$^{-1}$ Hz$^{-1}$ sr$^{-1}$) at $\mu=1$ (left); line-center formation height (FH) at $\mu=1$ (middle); Model-63 temperature at the line-center FH (right). Here, $I$ and $z_{\rm FH}$ are calculated neglecting magnetic and bulk velocity fields. Lower panels: Model-63 magnetic field strength (left), inclination (middle), and azimuth (right) at the line-center FH.