PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers

Abstract

The interpretation of the intensity and polarization of the spectral line radiation produced in the atmosphere of the Sun and of other stars requires solving a radiative transfer problem that can be very complex, especially when the main interest lies in modeling the spectral line polarization produced by scattering processes and the Hanle and Zeeman effects. One of the difficulties is that the plasma of a stellar atmosphere can be highly inhomogeneous and dynamic, which implies the need to solve the non-equilibrium problem of the generation and transfer of polarized radiation in realistic three-dimensional (3D) stellar atmospheric models. Here we present PORTA, an efficient multilevel radiative transfer code we have developed for the simulation of the spectral line polarization caused by scattering processes and the Hanle and Zeeman effects in 3D models of stellar atmospheres. The numerical method of solution is based on the non-linear multigrid iterative method and on a novel short-characteristics formal solver of the Stokes-vector transfer equation which uses monotonic Bézier interpolation. Therefore, with PORTA the computing time needed to obtain at each spatial grid point the self-consistent values of the atomic density matrix (which quantifies the excitation state of the atomic system) scales linearly with the total number of grid points. Another crucial feature of PORTA is its parallelization strategy, which allows us to speed up the numerical solution of complicated 3D problems by several orders of magnitude with respect to sequential radiative transfer approaches, given its excellent linear scaling with the number of available processors. The PORTA code can also be conveniently applied to solve the simpler 3D radiative transfer problem of unpolarized radiation in multilevel systems.

Formal Solutions for Polarized Radiative Transfer. I. The DELO Family

“…In fact, in both cases, the modified propagation matrix K K K disappears and a parabolic approximation of the source termǫ, supported by a proper conversion to optical depth (see Appendix A), produces an effective third-order numerical scheme. This can be appreciated inŠtěpán & Trujillo Bueno (2013), where the log-log error figure clearly shows the superiority of DELOPAR over DELO-linear for the scalar case. Stěpán & Trujillo Bueno (2013) applied a similar technique to create BESSER, the formal solver used in the PORTA code.…”

“…This can be appreciated inŠtěpán & Trujillo Bueno (2013), where the log-log error figure clearly shows the superiority of DELOPAR over DELO-linear for the scalar case. Stěpán & Trujillo Bueno (2013) applied a similar technique to create BESSER, the formal solver used in the PORTA code. The same argumentation can be applied to it, explaining its second-order accuracy confirmed by Figure 3.…”

“…From the computational point of view, the formal solution is, in most cases, the slowest part of the iterative scheme (e.g., Stěpán & Trujillo Bueno 2013). Moreover, large magnetohydrodynamic simulations of stellar atmospheres call for massive synthesis of Stokes profiles.…”

Polarized radiative transfer in discontinuous media

“…Because parabolic interpolation can be non-monotonic between otherwise monotonic node values, Štěpán & Trujillo Bueno (2013) went even one step further (drawing from an idea of Auer 2003), using quadratic Bézier splines forS (but still linear interpolation forKI). In this case, the interpolant of the source function is strictly monotone for a monotonic sequence of node values and it can be made one times differentiable and it remains continuous as is the interpolant forKI.…”

“…In this case, the interpolant of the source function is strictly monotone for a monotonic sequence of node values and it can be made one times differentiable and it remains continuous as is the interpolant forKI. Štěpán & Trujillo Bueno (2013) called this method of integration enthusiastically BESSER (BEzier Spline SolvER, which is also German for better) and performed some accuracy tests proving the superiority of it.…”