Time Evolution of Accreting Magnetofluid Around a Compact Object-Newtonian Analysis

Abstract

Time evolution of a magneto fluid with finite conductivity around a non-rotating compact object is presented. Along with the Maxwell equations and the Ohm law, the Newtonian limit of the relativistic fluid equations governing the motion of a finitely conducting plasma is derived. The magnetofluid is considered to possess only the colloidal components of the electromagnetic field. Moreover, the shear viscous stress is neglected, as well as the self-gravity of the disc. In order to solve the equations, we have used a self-similar solution. The main features of this solution are as follows. The azimuthal velocity is somewhat increased from the keplerian value in the equator plane to the super-keplerian values at the surface of disc. Moreover, the radial velocity is obtained proportional to the meridional velocity. Magneto fluid does not have any non-zero component of the current density. Subsequently, the electromagnetic force is vanished and does not play any role in the force balance. The pressure gradient maintains the disc structure in latitudinal direction, but this force does not have appreciable role in the radial force balance. Analogously to the parameter α in the standard model, our calculations contain one parameter η0 which specifies the size of the electrical resistivity.