Equilibria of a self-gravitating, rotating disc around a magnetized compact object

We examine the effect of self-gravity in a rotating thick-disc equilibrium in the presence of a dipolar magnetic field. First, we find a self-similar solution for non-self-gravitating discs. The solution that we have found shows that the pressure and density equilibrium profiles are strongly modified by a self-consistent toroidal magnetic field. We introduce three dimensionless variables, CB, Cc and Ct, which indicate the relative importance of toroidal component of the magnetic field (CB), and centrifugal (Cc) and thermal (Ct) energy with respect to the gravitational potential energy of the central object. We study the effect of each of these on the structure of the disc. Secondly, we investigate the effect of self-gravity on the discs; thus, we introduce another dimensionless variable (Cg) which shows the importance of self-gravity. We find a self-similar solution for the equations of the system. Our solution shows that the structure of the disc is modified by the self-gravitation of the disc, the magnetic field of the central object and the azimuthal velocity of the gas disc. We find that self-gravity and magnetism from the central object can change the thickness and the shape of the disc. We show that as the effect of self-gravity increases the disc becomes thinner. We also show that, for different values of the star’s magnetic field and of the disc’s azimuthal velocity, the disc’s shape and its density and pressure profiles are strongly modified.