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.

Manuscript figures and benchmarks

Scripts for reproducing the [SolRaT manuscript] figures and benchmark comparisons are mapped in README_MANUSCRIPT.md.

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 LTE variants of both descriptions, selectable without rewriting the surrounding code.
• Magnetic fields across regimes: linear Zeeman splitting in the multi-level atom, and linear Zeeman through incomplete and complete Paschen-Back splitting in the multi-term atom by exact diagonalization of the atomic Hamiltonian. Both descriptions capture the Hanle effect at weak fields,
• Radiation field $J^K_Q$ either prescribed (LTE Planck, or Allen/[ATL08]-style anisotropic ${n, w}$ values for coronal/chromospheric lines) or solved self-consistently for the non-LTE scattering problem [TM99].

Atmospheres and synthesis

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

The synthesis flow separates the atmosphere choice, the atomic description, the radiation-field treatment, and the final RTE integration; in self-consistent non-LTE runs the formal solution feeds back into the radiation tensor used by the SEE. Figure from Yakovkin (2026), arXiv:2609.32850, licensed under CC BY 4.0.

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 atomic data include He I D3 in multi-term and multi-level forms, and LTE-oriented multi-term models for Mn I 5432.5 Å, Ni I 5435.9 Å, and Fe I 5434.523 Å.

Scope and limitations

SolRaT a forward model. 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. Please refer to [SolRaT preprint] for more details on limitations.

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

If SolRaT has found use in your research, please cite the arXiv preprint:

Yakovkin I. I. 2026, SolRaT: polarized spectral line modeling with multi-term and multi-level atoms, arXiv:2609.32850

References

[SolRaT preprint] Yakovkin, I. I. 2026, SolRaT: polarized spectral line modeling with multi-term and multi-level atoms, arXiv:2609.32850

[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.

[TM99] 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