Radiation magnetohydrodynamics in global simulations of protoplanetary discs

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.

On the filtering and processing of dust by planetesimals

“…(We note that v th ∼ 1 km s −1 at 1 AU in the MMSN.) Flock et al (2013) also obtain similar values of α and slightly lower turbulent velocities in the range 10−100 m s −1 in the mid-plane, but an order of magnitude higher in the disk atmosphere heated both by stellar irradiation and MRI dissipation. These velocity fluctuations obtained in MRI-active regions are of the same order of magnitude as the mean headwind felt by planetesimals ηv K ∼ 50 m s −1 .…”

“…(We note that Youdin & Lithwick (2007) extend this relation to any eddy mixing timescale with a slightly more complex dependence on τ s which is minor and not taken into account here.) We will use a fiducial value α = 10 −2 broadly compatible with measured T-Tauri accretion rates and disk observations (e.g., Hartmann et al 1998;Hueso & Guillot 2005) and simulations of magneto-rotational instability in disks (e.g., Heinemann & Papaloizou 2009;Flock et al 2013). We will also use a lower value α = 10 −4 more relevant to the turbulence inside dead zones (e.g., Okuzumi & Hirose 2011).…”

Radiation Hydrodynamical Turbulence in Protoplanetary Disks: Numerical Models and Observational Constraints

“…The radiation hydrodynamic equations are solved using the hybrid flux limited diffusion and irradiation method developed by Flock et al (2013) as implemented in the current version 4.2 of the PLUTO code (Mignone et al 2007). For this work we choose the high-order piece-wise parabolic method (PPM), the Harten-Lax-Van Leer approximate Riemann Solver with the contact discontinuity (HLLC), the FARGO scheme (Masset 2000;Mignone et al 2012) and the Runge-Kutta time integrator.…”

Thermodynamics of the dead-zone inner edge in protoplanetary disks

“…As indicated by the discussion above, this shortcoming should be rectified in future. Note that radiative MHD simulations are challenging and Flock et al (2013) performed the first global radiative MHD simulations of protoplanetary disks only very recently. Previous studies had been confined to the shearing box approximation (Hirose et al 2006;Flaig et al 2010;Hirose & Turner 2011) because of the inherent numerical difficulties of radiative simulations.…”