Accretion disk dynamics: {\alpha}-viscosity in self-similar self-gravitating models

TL;DR

This paper develops a self-similar model of self-gravitating accretion disks using {\

Contribution

It introduces a self-similar solution for {\

Findings

The model aligns with standard {\

The model suggests high self-gravity is necessary for positive accretion rates.

{\

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 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 {\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. Keywords: accretion, accretion disks, turbulence, hydrodynamics, methods: analytical