Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks

Abstract

Thin, Keplerian accretion disks generically become gravitationally unstable at large radius. I investigate the nonlinear outcome of such instability in cool disks using razor-thin, local, numerical models. Cooling, characterized by a constant cooling time t_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) Ωt_c)^{-1}. Numerical experiments show that: (1) if t_c \gtrsim 3Ω^{-1} then the disk reaches a steady, gravito-turbulent state in which Q \sim 1 and cooling is balanced by heating due to dissipation of turbulence; (2) if t_c \lesssim 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 \sim 64 G Σ/Ω^2 that is independent of the size of the computational domain.