Nonlinear outcome of gravitational instability in cooling, gaseous disks

Thin, Keplerian accretion disks generically become gravitationally unstable at large radii. I investigate the nonlinear outcome of such instability in cool disks using razor-thin, focal, numerical models. Cooling, characterized by a constant cooling time tau (c), drives the instability. I show analytically that if the disk can reach a steady state in which heating by dissipation of turbulence balances cooling, then the dimensionless angular momentum flux density alpha = [(9/4)gamma(gamma - 1)Omega tau (c)](-1). Numerical experiments show that (1) if tau (c) greater than or similar to 3 Omega (-1) then the disk reaches a steady, gravitoturbulent state in which Q similar to 1 and cooling is balanced by heating due to dissipation of turbulence; (2) if tau (c) less than or similar to 3 Omega (-1), then the disk fragments, possibly forming planets or stars; (3) in a steady, gravitoturbulent state, surface density structures have a characteristic physical scale similar to 64G Sigma/Omega (2) that is independent of the size of the computational domain.