  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.
