The reliability of approximate radiation transport methods for irradiated disk studies

¹ Universität Tübingen, Institut für Astronomie und Astrophysik, Computational Physics, Auf der Morgenstelle 10, 72076 Tübingen, Germany
e-mail: rolf.kuiper@uni-tuebingen.de
² Max-Planck-Institut für Astronomie Heidelberg, Königstuhl 17, 69117 Heidelberg, Germany
³ Universität Heidelberg, Zentrum für Astronomie Heidelberg, Institut für theoretische Astrophysik, Albert-Überle-Strasse 2, 69120 Heidelberg, Germany

Received: 4 March 2013
Accepted: 23 April 2013

Abstract

Context. Dynamical studies of irradiated circumstellar disks require an accurate treatment of radiation transport to, for example, properly determine cooling and fragmentation properties. At the same time the radiation transport algorithm should be as fast as the (magneto-) hydrodynamics to allow for an efficient usage of computing resources. Such fast radiation transport methods imply the acceptance of far-reaching approximations.

Aims. We check the reliability of fast, approximate radiation transport methods for circumstellar disk studies by comparing their accuracy to previous standard radiation benchmark test results.

Methods. We use different approximate radiation transport methods and compute the equilibrium temperature distribution in a setup of a central star and a slightly flared circumstellar disk, which is embedded in an optically thin envelope. We perform simulations for a wide range of optical depths of the disk’s midplane from τ_550 nm = 0.1 up to τ_810 nm = 1.22 × 10⁺⁶. We check the accuracy of the gray flux-limited diffusion (FLD) approximation and the gray and frequency-dependent hybrid approximation. In the hybrid method, the stellar irradiation is computed via a gray or frequency-dependent ray-tracing (RT) step and the thermal (re-)emission by dust grains is shifted to a gray FLD solver.

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% in the optically thin and up to 280% 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.