Time dependence of advection-dominated accretion flow with a toroidal magnetic field

The present study examines the self-similar evolution of advection-dominated accretion flow (ADAF) in the presence of a toroidal magnetic field. In this research, it was assumed that angular momentum transport is due to viscous turbulence and the α-prescription was used for the kinematic coefficient of viscosity. The flow does not have a good cooling efficiency and so a fraction of energy accretes along with matter on to the central object. The effect of a toroidal magnetic field on such a system with regard to the dynamical behaviour was investigated. In order to solve the integrated equations that govern the dynamical behaviour of the accretion flow, a self-similar solution was used. The solution provides some insights into the dynamics of quasi-spherical accretion flow, and avoids many of the strictures of steady self-similar solutions. The solutions show that the behaviour of the physical quantities in a dynamical ADAF is different from that for a steady accretion flow or a disc using a polytropic approach. The effect of the toroidal magnetic field is considered using additional variable β (=p_mag/p_gas, where p_mag and p_gas are the magnetic and gas pressure, respectively). Also, to consider the effect of advection in such systems, the advection parameter f, which stands for the fraction of energy that accretes by matter on to the central object, was introduced. The solution indicates a transonic point in the accretion flow for all selected values of f and β. Also, by increasing the strength of the magnetic field and the degree of advection, the radial thickness of the disc decreases and the disc compresses. The model implies that the flow has differential rotation and is sub-Keplerian at small radii and super-Keplerian at large radii, and that different results were obtained using a polytropic accretion flow. The β parameter obtained was a function of position, and increases with increasing radii. Also, the behaviour of ADAF in a large toroidal magnetic field implies that different results are obtained using steady self-similar models in large magnetic fields.