Time evolution of a thick disc with finite conductivity around a nonrotating compact object is presented. Along with the Maxwell equations and the Ohm's 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 poloidal 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. Magnetofluid does not have any nonzero component of the current density. Subsequently, the electromagnetic force is vanished and does not play any role in the force balance. While the pressure gradient maintains the disc structure in latitudinal direction, magnetofluid has no accretion on the central compact object. Analogously to the parameter α in the standard model, our calculations contain one parameter η0 which specifies the size of the electrical resistivity.
Self-similar dynamic converging shocks – I. An isothermal gas sphere with self-gravity