Self-similar evolutionary solutions of self-gravitating, polytropic β-viscous disks

¹ Department of Physics, Damghan University of Basic Sciences, Damghan, Iran e-mail: sabbassi@dubs.ac.ir
² Department of Physics, School of Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
³ Department of Physics and Astronomy, San Francisco State University, 1600 Holloway, San Francisco, CA 94132, USA
⁴ Department of Physics, Khayam Institute of Higher Education, Mashhad, Iran

Received: 3 January 2006
Accepted: 20 June 2006

Abstract

Aims. We investigate the β-prescription for viscosity in standard self-gravitating thin disks and predict that in a self-gravitating thin disk the β-model will have a different dynamical behavior compared to the well-known α-prescription.

Methods. We used self-similar methods to solve the integrated equations that govern the dynamical behavior of the thin disk.

Results.We present the results of self-similar solutions of the time evolution of axisymmetric, polytropic, self-gravitating viscous disks around a new-born central object. We apply a β-viscosity prescription derived from rotating shear flow experiments (). Using reduced equations in a slow accretion limit, we demonstrate inside-out self-similar solutions after core formation in the center. Some physical quantities for β-disks are determined numerically. We compare our results with α-disks under the same initial conditions. The accretion rate onto the central object for β-disks is grater than for α-disks in the outer regions where β-disks are more efficient. Our results show that the Toomre instability parameter is less than one everywhere on the β-disk which means that in such disks gravitational instabilities can occur, so the β-disk model can be a good candidate for the origin of planetary systems. Our results show that the β-disks will decouple in the outer part of the disk where self-gravity plays an important role, in agreement with theoretical predictions.