A&A 460, 357-363 (2006)
DOI: 10.1051/0004-6361:20064805

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

S. Abbassi¹, J. Ghanbari^{2, 3}, and F. Salehi<sup>2, 4

1</sup>  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 -prescription for viscosity in standard self-gravitating thin disks and predict that in a self-gravitating thin disk the -model will have a different dynamical behavior compared to the well-known -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 -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 -disks are determined numerically. We compare our results with -disks under the same initial conditions. The accretion rate onto the central object for -disks is grater than for -disks in the outer regions where -disks are more efficient. Our results show that the Toomre instability parameter is less than one everywhere on the -disk which means that in such disks gravitational instabilities can occur, so the -disk model can be a good candidate for the origin of planetary systems. Our results show that the -disks will decouple in the outer part of the disk where self-gravity plays an important role, in agreement with theoretical predictions.

Key words: accretion, accretion disks -- stars: formation -- planets and satellites: formation

© ESO 2006

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