Squeezing of toroidal accretion disks

Accretion disks around very compact objects such as very massive Black hole can grow according to thick toroidal models. We face the problem of defining how does change the thickness of a toroidal accretion disk spinning around a Schwarzschild Black hole under the influence of a toroidal magnetic field and by varying the fluid angular momentum. We consider both an hydrodynamic and a magnetohydrodynamic disk based on the Polish doughnut thick model. We show that the torus thickness remains basically unaffected but tends to increase or decrease slightly depending on the balance of the magnetic, gravitational and centrifugal effects which the disk is subjected to.