New boundary conditions for the approximate flux-limited diffusion radiative transfer in circumstellar environments: test case study for spherically symmetric envelopes

TL;DR

This paper introduces new boundary conditions for the flux-limited diffusion approximation in radiative transfer models of circumstellar environments, improving accuracy and computational efficiency in spherically symmetric envelope simulations.

Contribution

The authors develop and implement novel boundary conditions for FLD in circumstellar environments, validated against benchmarks and Monte Carlo simulations, enhancing modeling precision.

Findings

Average relative difference below 2% for temperature profiles

Spectral energy distribution accuracy within 6%

New boundary conditions improve flux approximation

Abstract

In order to constrain the models describing circumstellar environments, it is necessary to solve the radiative transfer equation in the presence of absorption and scattering, coupled with the equation for radiative equilibrium. However, solving this problem requires much CPU time, which makes the use of automatic minimisation procedures to characterise these environments challenging. The use of approximate methods is then of primary interest. One promising candidate method is the flux-limited diffusion (FLD), which recasts the radiative transfer problem into a non-linear diffusion equation. One important aspect for the accuracy of the method lies in the implementation of appropriate boundary conditions (BCs). We present new BCs for the FLD approximation in circumstellar environments that we apply here to spherically symmetric envelopes. At the inner boundary, the entering flux (coming from the star and from the envelope itself) may be written in the FLD formalism and provides us with an adequate BC. At the free outer boundary, we used the FLD formalism to constrain the ratio of the mean radiation intensity over the emerging flux. In both cases we derived non-linear mixed BCs relating the surface values of the mean specific intensity and its gradient. We implemented these conditions and compared the results with previous benchmarks and the results of a Monte Carlo radiative transfer code. A comparison with results derived from BCs that were previously proposed in other contexts is presented as well. For all the tested cases, the average relative difference with the benchmark results is below 2\% for the temperature profile and below 6\% for the corresponding spectral energy distribution or the emerging flux. We point out that the FLD method together with the new outer BC also allows us to derive an approximation for the emerging flux.