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Numerical solutions to linear transfer problems of polarized radiation III. Parallel preconditioned Krylov solver tailored for modeling PRD effects
Context. The polarization signals produced by the scattering of anistropic radiation in strong resonance lines encode important information about the elusive magnetic fields in the outer layers of the solar atmosphere. An accurate modeling of these signals is a very challenging problem from the computational point of view, in particular when partial frequency redistribution (PRD) effects in scattering processes are accounted for with a general angle-dependent treatment. Aims. We aim at solving the radiative transfer problem for polarized radiation in nonlocal thermodynamic equilibrium conditions, taking angle-dependent PRD effects into account. The problem is formulated for a two-level atomic model in the presence of arbitrary magnetic and bulk velocity fields. The polarization produced by scattering processes and the Zeeman effect is considered. Methods. The proposed solution strategy is based on an algebraic formulation of the problem and relies on a convenient physical assumption, which allows its linearization. We applied a nested matrix-free GMRES iterative method. Effective preconditioning is obtained in a multifidelity framework by considering the light-weight description of scattering processes in the limit of complete frequency redistribution (CRD). Results. Numerical experiments for a one-dimensional (1D) atmospheric model show near optimal strong and weak scaling of the proposed CRD-preconditioned GMRES method, which converges in few iterations, independently of the discretization parameters. A suitable parallelization strategy and high-performance computing tools lead to competitive run times, providing accurate solutions in a few minutes. Conclusions. The proposed solution strategy allows the fast systematic modeling of the scattering polarization signals of strong resonance lines, taking angle-dependent PRD effects into account together with the impact of arbitrary magnetic and bulk velocity fields. Almost optimal strong and weak scaling results suggest that this strategy is applicable to realistic 3D models. Moreover, the proposed strategy is general, and applications to more complex atomic models are possible.
On the lithium abundance of the visual binary components ξ Boo A (G8V) and ξ Boo B (K5V)
A spectroscopic investigation of the lithium resonance doublet in ξ Boo A and ξ Boo B in terms of both abundance and isotopic ratio is presented. We obtained new R = 130,000 spectra with a signal-to-noise ratio (S/N) per pixel of up to 3200 using the 11.8 m LBT and PEPSI. From fits with synthetic line profiles based on 1D-LTE MARCS model atmospheres and 3D-NLTE corrections, we determine the abundances of both isotopes. For ξ Boo A, we find A(Li) = 2.40 ± 0.03 dex and 6Li/7Li <1.5 ± 1.0% in 1D-LTE, which increases to ≈2.45 for the 3D-NLTE case. For ξ Boo B we obtain A(Li) = 0.37 ± 0.09 dex in 1D-LTE with an unspecified 6Li/7Li level. Therefore, no 6Li is seen on any of the two stars. We consider a spot model for the Li fit for ξ Boo B and find A(Li) = 0.45 ± 0.09 dex. The 7Li abundance is 23 times higher for ξ Boo A than the Sun's, but three times lower than the Sun's for ξ Boo B while both fit the trend of single stars in the similar-aged M35 open cluster. Effective temperatures are redetermined from the TiO band head strength. We note that the best-fit global metallicities are −0.13 ± 0.01 dex for ξ Boo A but +0.13 ± 0.02 dex for ξ Boo B. Lithium abundance for the K5V benchmark star 61 Cyg A was obtained to A(Li) ≈ 0.53 dex when including a spot model but to ≈0.15 dex without a spot model.