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, characteriz ed by a constant cooling time tau (c), drives the instability. I show analy tically that if the disk can reach a steady state in which heating by dissi pation of turbulence balances cooling, then the dimensionless angular momen tum flux density alpha = [(9/4)gamma(gamma - 1)Omega tau (c)](-1). Numerica l 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 simil ar 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 fragme nts, possibly forming planets or stars; (3) in a steady, gravitoturbulent s tate, surface density structures have a characteristic physical scale simil ar to 64G Sigma/Omega (2) that is independent of the size of the computatio nal domain.