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

We investigate a massive (Sigma similar to 10000g 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 (M similar to 2), 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 64 x 128 x 512 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.