Radiation magnetohydrodynamics in global simulations of protoplanetary discs

¹ CEA, Irfu, SAp Centre de Saclay 91191 Gif-sur-Yvette France
e-mail: Mario.Flock@cea.fr
² UMR AIM, CEA-CNRS-Univ. Paris Diderot, Centre de Saclay, 91191 Gif-sur-Yvette, France
³ Université Paris Diderot, Sorbonne Paris Cité, AIM, UMR 7158, CEA, CNRS, 91191 Gif-sur-Yvette, France
⁴ Laboratoire de radioastronomie, UMR 8112 du CNRS, École normale supérieure et Observatoire de Paris, 24 rue Lhomond, 75231 Paris Cedex 05, France

Received: 6 August 2013
Accepted: 18 October 2013

Abstract

Aims. Our aim is to study the thermal and dynamical evolution of protoplanetary discs in global simulations, including the physics of radiation transfer and magneto-hydrodynamic turbulence caused by the magneto-rotational instability.

Methods. We have developed a radiative transfer method based on the flux-limited diffusion approximation that includes frequency dependent irradiation by the central star. This hybrid scheme is implemented in the PLUTO code. The focus of our implementation is on the performance of the radiative transfer method. Using an optimized Jacobi preconditioned BiCGSTAB solver, the radiative module is three times faster than the magneto-hydrodynamic step for the disc set-up we consider. We obtain weak scaling efficiencies of 70% up to 1024 cores.

Results. We present the first global 3D radiation magneto-hydrodynamic simulations of a stratified protoplanetary disc. The disc model parameters were chosen to approximate those of the system AS 209 in the star-forming region Ophiuchus. Starting the simulation from a disc in radiative and hydrostatic equilibrium, the magneto-rotational instability quickly causes magneto-hydrodynamic turbulence and heating in the disc. We find that the turbulent properties are similar to that of recent locally isothermal global simulations of protoplanetary discs. For example, the rate of angular momentum transport α is a few times 10^-3. For the disc parameters we use, turbulent dissipation heats the disc midplane and raises the temperature by about 15% compared to passive disc models. The vertical temperature profile shows no temperature peak at the midplane as in classical viscous disc models. A roughly flat vertical temperature profile establishes in the optically thick region of the disc close to the midplane. We reproduce the vertical temperature profile with viscous disc models for which the stress tensor vertical profile is flat in the bulk of the disc and vanishes in the disc corona.

Conclusions. The present paper demonstrates for the first time that global radiation magneto-hydrodynamic simulations of turbulent protoplanetary discs are feasible with current computational facilities. This opens up the window to a wide range of studies of the dynamics of the inner parts of protoplanetary discs, for which there are significant observational constraints.