Equilibria of a Self-Gravitating, Rotating Disk Around a Magnetized   Compact Object
  We examine the effect of self-gravity in a rotating thick-disk equilibrium in the presence of a dipolar magnetic field. In the first part, we find a self-similar solution for non-self-gravitating disks. 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 3 dimensionless variables $C_B$, $C_c$, $C_t$ that indicate the relative importance of toroidal component of magnetic field ($C_B$), centrifugal ($C_c$) and thermal ($C_t$) energy with respect to the gravitational potential energy of the central object. We study the effect of each of them on the structure of the disk. In the second part, we investigate the effect of self-gravity on the these disks; thus we introduce another dimensionless variable ($C_g$) that 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 disk is modified by the self-gravitation of the disk, the magnetic field of the central object, and the azimuthal velocity of the gas disk. We find that self-gravity and magnetism from the central object can change the thickness and the shape of the disk. We show that as the effect of self-gravity increases the disk becomes thinner. We also show that for different values of the star's magnetic field and of the disk's azimuthal velocity, the disk's shape and its density and pressure profiles are strongly modified. 
J. Ghanbari and S. Abbassi