A two-dimensional study for cooling and self-gravitating accretion discs

Abstract

The importance of cooling for the structure and evolution of self-gravitating accretion discs has been confirmed through the use of direct numerical simulations. In this paper, we present a two-dimensional study for self-gravitating accretion discs, to investigate the influence of the cooling rate on the latitudinal structure of such accretion discs. The disc is cooled using a simple parametrization for the cooling function, (de/dt)_cool=−e/t_cool with e as the internal energy and t_cool as the cooling timescale. The cooling timescale is in units of the dynamical timescale, t_dyn[=Ω⁻¹], is Ωt_cool=β, where β is a free parameter. The mechanism of energy dissipation is assumed to be turbulent viscosity in the disc and an α-prescription is applied for the kinematic coefficient of viscosity. To study the gravitational stability of the self-gravitating disc, we use the Toomre parameter. We obtain the radial dependence of the physical variables through the use of a self-similar method and we numerically solve the equations to obtain the latitudinal dependence of the physical variables. The solutions show that the radial velocity is smaller than the Keplerian rotational velocity; however, the disc, dependent on the values of parameters α and β and only near the zone close to the equatorial plane, can rotate in a super-Keplerian manner. With the magnitude of both parameters α and β, the disc thickness increases due to the increase of the vertical pressure gradient. The dependence of the gas density on the parameters α and β indicates two zones in the accretion disc. In the first zone near the equatorial plane, the mass density decreases by increasing these parameters. However, in the second zone, the regions with higher latitude, the mass density increases with the magnitude of parameters α and β.