Vertical structure and turbulent saturation level in fully radiative protoplanetary disc models

Abstract

We investigate a massive ( g cm−2 at 1 au) protoplanetary disc model by means of 3D radiation magnetohydrodynamic simulations. The vertical structure of the disc is determined self‐consistently by a balance between turbulent heating caused by the magnetorotational turbulence and radiative cooling. Concerning the vertical structure, two different regions can be distinguished: a gas‐pressure‐dominated, optically thick mid‐plane region where most of the dissipation takes place, and a magnetically dominated, optically thin corona which is dominated by strong shocks. At the location of the photosphere, the turbulence is supersonic (), which is consistent with previous results obtained from the fitting of spectra of young stellar objects. It is known that the turbulent saturation level in simulations of MRI‐induced turbulence does depend on numerical factors such as the numerical resolution and the box size. However, by performing a suite of runs at different resolutions (using up to grid cells) and with varying box sizes (with up to 16 pressure scaleheights in the vertical direction), we find that both the saturation levels and the heating rates show a clear trend to converge once a sufficient resolution in the vertical direction has been achieved.

Local outflows from turbulent accretion disks

“…We found the vertically averaged value to be α SS = 6.2 × 10 −2 when Pm = 1 and α SS = 4.8 × 10 −2 when Pm = 0.5. The vertical profile of the stress we obtained in each case is comparable to that reported in the literature by many authors using local or global simulations (Miller & Stone 2000;Hirose et al 2006;Fromang & Nelson 2006;Flaig et al 2010;Dzyurkevich et al 2010;Sorathia et al 2010;Fromang et al 2011;Simon et al 2011b). It is rather flat in the bulk of the disk, with possible local maxima at z ∼ 2H before dropping to low values in the corona.…”

“…Yet the natural and simple configuration of an initially uniform vertical magnetic field threading an isothermal vertically stratified disk has been relatively neglected compared to the large number of papers that have been published reporting studies of other configurations, such as unstratified disks, or stratified disks with a toroidal magnetic field or without any net flux (Stone et al 1996;Brandenburg et al 1995;Miller & Stone 2000;Ziegler & Rüdiger 2000;Fleming & Stone 2003;Hirose et al 2006;Johansen & Levin 2008;Oishi & Mac Low 2009;Shi et al 2010;Davis et al 2010;Flaig et al 2010;Simon et al 2011b,a;Flaig et al 2012). This is largely the result of computational difficulties.…”

Radiation magnetohydrodynamics in global simulations of protoplanetary discs

“…It decreases from 4.6 × 10 −3 to 2.5 × 10 −3 . This trend of increased turbulence in radiative models was also suggested by Flaig et al (2010). Nevertheless, as shown in Fig.…”

Thermodynamics of the dead-zone inner edge in protoplanetary disks

“…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.…”