Stability domain of the self-gravitating vortices as a function of q₀. Left: when estimated from numerical simulations and right, when deduced from Eq. (9). Vortices are stable above the surface and unstable below (blue and orange, respectively). Both surfaces were projected on the left-hand side and the right-hand side of the box. χ and δ are, respectively, the vortex aspect ratio and the radial extent at t = 50 t₀.