The two vortex families. Top: relative density and streamlines of a vortex of the incompressible family. We note the closed structure of the streamlines in the vortex. Bottom: relative density and streamlines of a vortex of the compressible family. The streamlines are now open curves spiraling from the vortex centre. In the core, the density shows a peculiar structure, with a peanut shape. Such vortices are also characterized by exciting strong spiral waves and possibly shocks. The compressible vortex has a Rossby number ~ 3 larger than the incompressible while its amplitude is smaller by a factor of ~ 2/3.