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, local, numerical models. Cooling, characterized by a constant cooling time τc, 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 α = -1. Numerical experiments show that (1) if τc ≳ 3Ω-1 then the disk reaches a steady, gravitoturbulent state in which Q ~ 1 and cooling is balanced by heating due to dissipation of turbulence; (2) if τc ≲ 3Ω-1, then the disk fragments, possibly forming planets or stars; (3) in a steady, gravitoturbulent state, surface density structures have a characteristic physical scale ~64GΣ/Ω2 that is independent of the size of the computational domain.