Radiative transfer in a spherical, emitting, absorbing and anisotropically scattering medium

TL;DR

This paper presents an exact solution for radiative transfer in spherical media with anisotropic scattering, improving accuracy over traditional plane-parallel models and applicable to astrophysics, climate science, and nuclear engineering.

Contribution

It introduces a novel spherical numerical method for solving radiative transfer with anisotropic scattering, providing exact solutions and efficient computation.

Findings

Excellent agreement with established isotropic benchmarks

Method effectively handles arbitrary phase scattering functions

Applicable to diverse fields like astrophysics and climate modeling

Abstract

The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an exact solution of the radiative transfer specific intensity at all points and directions in a finite spherical medium having arbitrary radial spectral distribution of: source (temperature), absorption, emission and anisotropic scattering. The power and efficiency of the method stems from the spherical numerical gridding used to discretize the transfer equations prior to matrix solution: the wanted ray and the rays which scatter into it both have the same physico-geometric structure. Very good agreement is found with an isotropic astrophysical benchmark (Avrett & Loeser, 1984). We introduce a specimen arbitrary forward-back-side phase scattering function for future comparisons. Our method directly and exactly addresses spherical symmetry with anisotropic scattering, and could be used to study the Earth's climate, nuclear power (neutron diffusion) and the astrophysics of stars and planets.