Abstract:

In this paper, we investigate the time evolution of quasi-spherical polytropic accretion flow with a toroidal magnetic field. We focus in particular on the astrophysically important case in which the adiabatic exponent γ= 5/3. In this scenario, we have assumed that the angular momentum transport is a result of viscous turbulence and we have used the α-prescription for the kinematic coefficient of viscosity. The equations of accretion flow are solved in a simplified one-dimensional model that neglects the latitudinal dependence of the flow. In order to solve the integrated equations that govern the dynamical behaviour of the accretion flow, we have used a self-similar solution. The solution provides some insight into the dynamics of quasi-spherical accretion flow and avoids many of the strictures of the steady self-similar solution. The effect of the toroidal magnetic field is considered with an additional variable β[=p_mag/p_gas], where p_mag and p_gas are the magnetic pressure and gas pressure, respectively. The solution indicates a transonic point in the accretion flow, that this point approaches the central object by adding the strength of the magnetic field. Also, by adding the strength of the magnetic field, the radial thickness of the disc decreases and the disc compresses. We indicate analytically that the radial velocity is only a function of Alfvén velocity. The model implies that the flow has differential rotation and is sub-Keplerian at all radii.