The applicability of the viscous \alpha-parameterization of gravitational instability in circumstellar disks

Abstract

(Abridged) We study numerically the applicability of the effective-viscosity approach for simulating the effect of gravitational instability (GI) in disks of young stellar objects with different disk-to-star mass ratios \xi. We adopt two \alpha$-parameterizations for the effective viscosity based on Lin & Pringle (1990) and Kratter et al (2008) and compare the resultant disk structure, disk and stellar masses, and mass accretion rates with those obtained directly from numerical simulations of self-gravitating disks around low-mass (M_\ast ~ 1.0 M_sun) protostars. We find that the effective viscosity can, in principle, simulate the effect of GI in stellar systems with \xi <= 0.2-0.3, thus corroborating a similar conclusion by Lodato & Rice (2004) that was based on a different \alpha-parameterization. In particular, the Kratter et al's \alpha-parameterization has proven superior to that of Lin & Pringle's, because the success of the latter depends crucially on the proper choice of the \alpha-parameter. However, the \alpha-parameterization generally fails in stellar systems with \xi >= 0.3, particularly in the Class 0 and Class I phases of stellar evolution, yielding too small stellar masses and too large disk-to-star mass ratios. The failure of the \alpha-parameterization in the case of large \xi is caused by a growing strength of low-order spiral modes in massive disks.