Evolution of self-gravitating magnetized disks. II- Interaction between   MHD turbulence and gravitational instabilities
  We present 3D magnetohydrodynamic (MHD) numerical simulations of the evolution of self--gravitating and weakly magnetized disks with an adiabatic equation of state. Such disks are subject to the development of both the magnetorotational and gravitational instabilities, which transport angular momentum outward. As in previous studies, our hydrodynamical simulations show the growth of strong m=2 spiral structure. This spiral disturbance drives matter toward the central object and disappears when the Toomre parameter Q has increased well above unity. When a weak magnetic field is present as well, the magnetorotational instability grows and leads to turbulence. In that case, the strength of the gravitational stress tensor is lowered by a factor of about~2 compared to the hydrodynamical run and oscillates periodically, reaching very small values at its minimum. We attribute this behavior to the presence of a second spiral mode with higher pattern speed than the one which dominates in the hydrodynamical simulations. It is apparently excited by the high frequency motions associated with MHD turbulence. The nonlinear coupling between these two spiral modes gives rise to a stress tensor that oscillates with a frequency which is a combination of the frequencies of each of the modes. This interaction between MHD turbulence and gravitational instabilities therefore results in a smaller mass accretion rate onto the central object. 
Sebastien Fromang, Steven A. Balbus, Caroline Terquem, Jean-Pierre De   Villiers