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

Abstract

The effect of toroidal magnetic fields 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 coefficient of viscosity. Moreover, the general relativistic effects are neglected. The degree of advection which 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 flows, 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 field strength. The ratio of the angular velocities of the central body and the accretion flow is indicated by the rotating parameter a. The possible combined effects of magnetic field, spin of central object and degree of advection is investigated. We also show the effect of rotating parameter a on the physical quantities of disc is different for co and counter rotating flows. Moreover, by increasing the degree of advection and strength of magnetic field, the behavior 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 depends on rotation parameter and strength of magnetic field.