We propose a viscosity prescription based on the assumption that the effective Reynolds number of the turbulence does not fall below the critical Reynolds number. In this parameterization the viscosity is proportional to the azimuthal velocity and the radius (-disks). This prescription yields physically consistent models of both Keplerian and fully selfgravitating accretion disks. Moreover, for the case of thin disks with sufficiently small mass, we recover the -disk solution as a limiting case.
Such -disk models may be relevant to protoplanetary accretion disks as well as to galactic and galactic center disks. In the case of protoplanetary disks they yield spectra that are considerably flatter than those due to non-selfgravitating disks, in better agreement with observed spectra of these objects. In galactic disks, they result in viscous evolution on time scales shorter than the Hubble time and thus offer a natural explanation for an inward flow that could account for the observed chemical abundance gradients. In galactic centers, -disks may be the supply for powering AGN and for forming supermassive black holes within time scales short compared to the Hubble time.
Finally, -disks yield a natural solution to an inconsistency in the -disk models if the disk's mass is large enough for selfgravity to play a role. This problem arises even in Keplerian selfgravitating disks in which only the vertical structure is dominated by selfgravity while the azimuthal motion remains Keplerian.
© European Southern Observatory (ESO) 2000
Online publication: June 5, 2000