SAETASS: Solver for Astroparticle Equation of Transport Analysis in Spherical Symmetry

TL;DR

SAETASS is an open-source numerical solver designed for modeling the transport of astroparticles in spherically symmetric astrophysical environments, ensuring particle conservation and handling complex physical processes.

Contribution

It introduces a novel, efficient, modular finite-volume solver specifically tailored for spherical symmetry, validated through rigorous tests and applied to cosmic-ray transport scenarios.

Findings

Successfully models cosmic-ray proton transport in astrophysical environments.

Recovers steady-state limits and captures pre-equilibrium dynamics.

Handles steep gradients and discontinuities robustly.

Abstract

In order to model astrophysical environments characterized by radial stratification, such as supernova remnants or expanding superbubbles; correctly understanding the transport of non-thermal particles in astrophysical plasmas is essential. While large-scale Galactic propagation codes exist, they are often optimized for Cartesian or cylindrical geometries and lack the efficiency of one-dimensional spherically symmetric problems. In this work, we present SAETASS (Solver for Astroparticle Equation of Transport Analysis in Spherical Symmetry), a novel, open-source numerical tool designed to solve the time-dependent transport equation for astroparticles. The solver is built upon a conservative finite-volume framework that ensures exact particle conservation and numerical stability. To manage the interplay between diverse physical processes, SAETASS employs a modular operator-splitting architecture. Radial advection and continuous momentum losses are treated using a second-order, shock-capturing MUSCL-Hancock scheme, while the diffusive operator is integrated via an implicit, batched Crank-Nicolson algorithm. This approach allows for the robust handling of steep gradients, spatial discontinuities and regularity conditions at the origin. We rigorously validate the code through a suite of tests for pure advection, diffusion and losses. Finally, we demonstrate the solver's capabilities by modelling cosmic-ray proton transport in a real astrophysical scenario. Our results successfully recover established steady-state limits while revealing relevant pre-equilibrium temporal dynamics across Kolmogorov, Kraichnan and Bohm diffusion regimes. SAETASS provides the community with a lightweight, flexible tool for investigating particle acceleration and propagation in complex, radially dependent astrophysical environments.