Accretion disk dynamics alpha-viscosity in self-similar self-gravitating models

Abstract

Aims. We investigate the suitability of alpha-viscosity in self-similar models for self-gravitating disks with a focus on active galactic nuclei (AGN) disks. Methods. We use a self-similar approach to simplify the partial di ff erential equations arising from the evolution equation, which are then solved using numerical standard procedures. Results. We find a self-similar solution for the dynamical evolution of self-gravitating alpha-disks and derive the significant quantities. In the Keplerian part of the disk our model is consistent with standard stationary alpha-disk theory, and self-consistent throughout the self-gravitating regime. Positive accretion rates throughout the disk demand a high degree of self-gravitation. Combined with the temporal decline of the accretion rate and its low amount, the model prohibits the growth of large central masses. Conclusions. alpha-viscosity cannot account for the evolution of the whole mass spectrum of super-massive black holes (SMBH) in AGN. However, considering the involved scales it seems suitable for modelling protoplanetary disks.