Similarity solutions for a magnetized supercritical accretion disc around a rotating object

Abstract

The effect of toroidal magnetic elds on a supercritical accretion disc (slim disc) around a rotating object is examined. In this research, it is supposed that angular momentum transport is due to viscous turbulence and the α-prescription is used for the kinematic coefcient of viscosity. Moreover, the general relativistic effects are neglected. The degree of advection that demonstrates the fraction of energy that accretes by matter on to the central object is considered by f parameter. For the steady-state structure of such accretion ows, a set of self-similar solution is presented. Our solutions will include two important non-dimensional parameters β and a. β is the ratio of the magnetic pressure to the gas pressure, the so-called friction of magnetic pressure, which shows the magnetic eld strength. The ratio of the angular velocities of the central body and the accretion ow is indicated by the rotating parameter a. The possible combined effects of magnetic eld, spin of central object, and degree of advection are investigated. We also show the effect of rotating parameter a on the physical quantities of disc is different for co-rotating and counter-rotating ows. Moreover, by increasing the degree of advection and strength of magnetic eld, the behaviour of the radial and angular velocities becomes reversed with respect to a. The model implies that the surface temperature, thickness, and luminosity of disc strongly depend on rotation parameter and strength of magnetic eld.