Accretion disk dynamics

α-viscosity in self-similar self-gravitating models

¹ Institut für Theoretische Physik und Astrophysik, Chrisitan-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24118 Kiel, Germany
e-mail: mmeissner@astrophysik.uni-kiel.de; tillense@astrophysik.uni-kiel.de; wjd@astrophysik.uni-kiel.de
² Steward Observatory, The University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721, USA

Received: 30 July 2015
Accepted: 25 January 2016

Abstract

Aims. We investigate the suitability of α-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 differential 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 α-disks and derive the significant quantities. In the Keplerian part of the disk our model is consistent with standard stationary α-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. α-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.