Nonlinear outcome of gravitational instability in cooling, gaseous disks

Thin, Keplerian accretion disks genetically 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 τ_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 α = [(9/4)γ(γ - 1)Ωτ_c]^-1. Numerical experiments show that (1) if τ_c ≳ 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 τ_c ≲ 3Ω^-11, 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.