Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks

Thin, Keplerian accretion disks generically become gravitationally unstable at large radius. I investigate the nonlinear outcome of such instability in cool disks using razorthin, 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 = ((9/4)γ(γ − 1)Ωτc) . Numerical experiments show that: (1) if τc & 3Ω−1 then the disk reaches a steady, gravito-turbulent 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, gravito-turbulent state, surface density structures have a characteristic physical scale ∼ 64GΣ/Ω that is independent of the size of the computational domain. Subject headings: accretion, accretion disks, solar system: formation, galaxies: nuclei