Gravitational Collapse and Equilibrium Conditions of a Toroidal Vortex   with Thermal Pressure
  We found equilibrium conditions for a self-gravitating toroidal vortex by taking into account thermal pressure. These conditions are shown to significantly differ from those for a disk and a sphere. The evolution of a thin vortex turns it into a compact vortex that loses mechanical stability for low masses at a polytropic index $\gamma < 4/3$ but retains stability for sufficiently high masses and densities determined by the velocity circulation in the vortex. 
K.Yu. Bliokh and V.M. Kontorovich