Vertically Self-Gravitating ADAFs in the Presence of Toroidal Magnetic   Field
  Force due to the self-gravity of the disc in the vertical direction is considered to study its possible effects on the structure of a magnetized advection-dominated accretion disc. We present steady-sate self similar solutions for the dynamical structure of such a type of the accretion flows. Our solutions imply reduced thickness of the disc because of the self-gravity. It also imply that the thickness of the disc will increase by adding the magnetic field strength. 
A. Mosallanezhad, S. Abbassi, M. Shadmehri, J. Ghanbari
astro-ph.HE