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

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(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 ξ. We adopt two α-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 1.0 Mₛun) protostars. We find that the effective viscosity can, in principle, simulate the effect of GI in stellar systems with ξ<= 0.2-0.3, thus corroborating a similar conclusion by Lodato & Rice (2004) that was based on a different α-parameterization. In particular, the Kratter et al's α-parameterization has proven superior to that of Lin & Pringle's, because the success of the latter depends crucially on the proper choice of the α-parameter. However, the α-parameterization generally fails in stellar systems with ξ>= 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 α-parameterization in the case of large ξis caused by a growing strength of low-order spiral modes in massive disks.