SolRaT

SolRaT (Solar Radiative Transfer) is a forward-modeling code for the polarized, non-LTE transfer of spectral-line radiation in magnetized stellar atmospheres. It is built on the density-matrix formalism of [LL04] and written so that each statistical-equilibrium and radiative-transfer expression reads close to the equation it implements. The aim is a model that is transparent enough to inspect and verify, and flexible enough to adapt to a specific line or context rather than used as a black box.

Physical model

• Density-matrix formalism in the irreducible spherical statistical tensors $\rho^K_Q$, with atomic level polarization fully included [LL04].
• Interchangeable atomic models in a single pipeline: multi-term, multi-level, and a semi-LTE multi-term model, selectable without rewriting the surrounding code.
• Magnetic fields of arbitrary strength: Zeeman, Hanle, and the Paschen-Back regime by exact diagonalization of the atomic Hamiltonian (multi-term atom; Zeeman and Hanle for the multi-level atom).
• Radiation field $J^K_Q$ either prescribed (LTE Planck, or the anisotropic ${n, w}$ parametrization of [ATL08] for coronal/chromospheric lines) or solved self-consistently for the non-LTE scattering problem [TB99].

Atmospheres and synthesis

• Constant-property slabs, optionally stacked into a multi-slab stratification under anisotropic illumination.
• Height-stratified atmosphere in which temperature, absorber number density, the magnetic-field vector, microturbulence, Voigt damping, and the vector macroscopic velocity vary continuously with geometric height. The scattering $J^K_Q$ is solved self-consistently by $\Lambda$-iteration on a depth grid, with the Stokes transfer solved by the DELO method.
• Emergent Stokes profiles for a chosen line of sight at arbitrary spectral resolution.

Design

SolRaT is organized in three layers:

• a public API to run the built-in models;
• a modeling API to extend a model or build a new one by analogy with the shipped ones;
• the SolRaT engine, a vectorized meta-language in which the angular algebra and rate expressions are written close to their mathematical form, with the bookkeeping and optimization handled underneath.

Pre-configured lines: He I D3, Mn I 5432.5 Å, Ni I 5435.9 Å, Fe I 5434.523 Å.

Scope and limitations

SolRaT is a forward model. Its non-LTE solution is collisionless (pure scattering) by default, so scattering-polarization amplitudes are then upper limits; an optional parametrized-collision extension for the multi-level atom adds inelastic (transfer) and elastic (depolarizing) rates that bridge the scattering limit to LTE. Line formation assumes complete frequency redistribution (CRD). Physical collisional rates from cross-sections, partial frequency redistribution, and 3D geometry are out of scope for the current version.

Installation

Install SolRaT directly from PyPi by running pip install solrat.

Documentation

Detailed documentation is available at https://solrat.readthedocs.io/. A quick-start example is available at https://solrat.readthedocs.io/latest/quickstart.html. Additional demos and validation against [LL04] and [HAZEL2] are available in demos.

Citing

A journal article is in preparation. In the meantime, if SolRaT has found use in your research, please cite it as

Yakovkin I. I. SolRaT (2023) [computer software]. Retrieved from https://www.yakovkinii.com/solrat/

References

[LL04] Landi Degl’Innocenti, E., & Landolfi, M. 2004, Polarization in Spectral Lines (Dordrecht: Kluwer)

[ATL08] Asensio Ramos, A., Trujillo Bueno, J., & Landi Degl’Innocenti, E. (2008). Advanced Forward Modeling and Inversion of Stokes Profiles Resulting from the Joint Action of the Hanle and Zeeman Effects. The Astrophysical Journal, 683(1), 542–565.

[TB99] Trujillo Bueno, J., & Manso Sainz, R. (1999). Iterative Methods for the Non-LTE Transfer of Polarized Radiation: Resonance Line Polarization in One-dimensional Atmospheres. The Astrophysical Journal, 516(1), 436–450.

[HAZEL2] Link

Keywords:

Non-LTE, Stokes Profiles, Synthesis, Paschen-Back, Hanle, Zeeman, Magnetic Fields, Sun, Solar Atmosphere, Radiative Transfer, Spectral Line Polarization, Spectral Lines, Multi-Term Atom Model, Multi-Level Atom Model, Atomic Polarization.

Copyright (2023) Ivan I. Yakovkin