The reliability of approximate radiation transport methods for irradiated disk studies

TL;DR

This study evaluates the accuracy of different radiation transport methods in modeling irradiated circumstellar disks, finding that a frequency-dependent RT combined with gray FLD provides high accuracy across various optical depths.

Contribution

It demonstrates that a hybrid radiation transport method combining frequency-dependent RT with gray FLD is highly accurate for diverse optical depths in disk simulations.

Findings

Gray FLD fails in all optical depth regimes, with deviations up to 280%.

Gray approximation of stellar irradiation is slightly inaccurate but generally acceptable.

Frequency-dependent RT + gray FLD yields high accuracy across all tested optical depths.

Abstract

Context: Dynamical studies of irradiated circumstellar disks require an accurate treatment of radiation transport to, for example, properly determine cooling and fragmentation properties. The radiation transport algorithm should be as fast as the (magneto-) hydrodynamics to allow for an efficient usage of computing resources. Methods: We use a setup of a central star and a slightly flared circumstellar disk. We perform simulations for a wide range of optical depths of the disk's midplane from tau(550nm) = 0.1 up to tau(810nm) = 1 million. We check the accuracy of the gray flux-limited diffusion (FLD) approximation and a gray and frequency-dependent ray-tracing plus FLD approximation. Results: 1. For moderate optical depths, a gray approximation of the stellar irradiation yields a slightly hotter inner rim and a slightly cooler midplane of the disk at larger radii, but is otherwise in agreement with the frequency-dependent treatment. 2. The gray FLD approximation fails to compute an appropriate temperature profile in all regimes of optical depth; the maximum deviations to the comparison runs are 50 percent in the optically thin and up to 280 percent in the optically thick limit. For low optical depth, the isotropic assumption within the FLD method yields a too steep decrease of the radial temperature slope. For higher optical depths, the FLD approximation does not reproduce the shadow behind the optically thick inner rim of the circumstellar disk, yielding artificial heating at larger disk radii. 3. The frequency-dependent RT + gray FLD approximation yields remarkable accuracy for the whole range of optical depths. Conclusions: The high accuracy of the frequency-dependent hybrid radiation transport algorithm makes this method ideally suited for (magneto-) hydrodynamical studies of irradiated circumstellar disks.