Gravitational instability and fragmentation of self-gravitating accretion disks

We know from observations that supermassive black holes (SMBH) of masses up to $10^{10} \msol$ existed in quasars when the universe was only about $10^9$ years old. The rapid formation of SMBHs can be understood as the outcome of the collision of two large gas-rich galaxies followed by disk accretion. This model relies on a large enough turbulent viscosity in the disk. We show in a linear stability analysis of thin self-gravitating viscous disks that the gravitational instability can drive a turbulence generating the $\beta$-viscosity. For simulating a self-gravitating accretion disk in polar coordinates the hydrodynamics code NIRVANA2.0 is adapted for our needs which includes cooling. The results are disk fragmentation, strong accretion at the inner radial boundary of the calculation domain and strong outflow at the outer boundary which both come about by interactions between clumps. The accretion time scale for a disk mass of $6\ex{8} \msol$ in a radial extent of $29 \pc$ to $126 \pc$ is about $1.2\ex{7} \yr$, corresponding to a viscosity parameter $\beta \approx 0.04$. We can confirm the $\beta$-viscosity interpretation by the turbulent velocity and length scale and by the scaling of the accretion time scale. All this supports the SMBH-formation model