Multidimensional half-moment multigroup radiative transfer

Improving moment-based thermal models of circumstellar disks

Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany

^★ Corresponding author: fuksman@mpia.de

Received: 1 April 2025
Accepted: 23 July 2025

Abstract

Context. Common moment-based radiative transfer methods, such as flux-limited diffusion (FLD) and the M1 closure, suffer from artificial interactions between crossing beams. In protoplanetary disks, this leads to an overestimation of the midplane temperature due to the merging of vertical inward and outward fluxes. Methods that avoid these artifacts typically require angular discretization, which can be computationally expensive.

Aims. In the spirit of the two-stream approximation, we aim to remove the interaction between beams in a fixed spatial direction by introducing a half-moment (HM) closure, which integrates the radiative intensity over hemispheres.

Methods. We derived a multidimensional HM closure via entropy maximization and replaced this closure with an approximate expression that closely matches it, coinciding in the diffusion and free-streaming regimes while remaining expressible through simple operations. We implemented the HM and M1 closures via implicit-explicit (IMEX) schemes, including multiple frequency groups. We tested these methods in numerical benchmarks, such as computing the temperature in an irradiated disk around a T Tauri star, comparing the results with Monte Carlo (MC) radiative transfer simulations.

Results. The resulting HM closure tends to the correct limit in the diffusion regime and prevents interactions between crossing fluxes in a chosen spatial direction. Using multiple frequency groups, our new method closely reproduces the midplane temperature distributions obtained with classical MC methods in disk simulations. With the M1 closure and a single frequency group, the midplane temperature is around 44% higher compared to MC. With 22 frequency groups, the M1 closure agrees with MC by up to 21%, while HM reduces this discrepancy to 6%. Even with just three frequency groups, HM significantly outperforms M1, with maximum departures of 8% compared to M1’s 23%. Our results show that combining HM with a multigroup treatment yields more realistic disk temperatures than M1, particularly in optically thick regions.