Time Dependent Radiative Transfer for Multi-Level Atoms using Accelerated Lambda Iteration

TL;DR

This paper introduces a comprehensive numerical method for solving the time-dependent radiative transfer equation in multi-level ions, using Accelerated Lambda Iteration to achieve efficient and accurate results in astrophysical contexts.

Contribution

The authors develop a fully time-dependent formalism and numerical solution for radiative transfer and atomic rate equations in low velocity media, advancing beyond previous static or simplified models.

Findings

Efficient convergence achieved with Accelerated Lambda Iteration

Demonstrated importance of time-dependent effects in astrophysical scenarios

Validated method with a three-level atomic model

Abstract

We present a general formalism for computing self-consistent, numerical solutions to the time-dependent radiative transfer equation in low velocity, multi-level ions undergoing radiative interactions. Recent studies of time-dependent radiative transfer have focused on radiation hydrodynamic and magnetohydrodynamic effects without lines, or have solved time-independent equations for the radiation field simultaneously with time-dependent equations for the state of the medium. In this paper, we provide a fully time-dependent numerical solution to the radiative transfer and atomic rate equations for a medium irradiated by an external source of photons. We use Accelerated Lambda Iteration to achieve convergence of the radiation field and atomic states. We perform calculations for a three-level atomic model that illustrates important time-dependent effects. We demonstrate that our method provides an efficient, accurate solution to the time-dependent radiative transfer problem. Finally, we characterize astrophysical scenarios in which we expect our solutions to be important.