Equilibrium solutions for a rotating isothermal spheroid, mass vs. shape and mass vs. size. Solutions are in units of the Jeans mass Mj, plotted versus axes ratio X = a3/a1 and versus equatorial radius a1 in units of the Jeans radius Rj. For each curve, the ratio J/M^(5/3) is held fixed as the mass M is varied, where J is the angular momentum. Curve (e) (dashed line) is the equilibrium solution for a non-rotating sphere.

Curve (c) has a triple equilibria region for a range of masses. Of the three equilibria states, the free energy is minimized by two: one compact (and flattened) and one diffuse (and rounded). This region is bounded by a maxium allowed diffuse mass Mmax and a minimum allowed compact mass Mmin, where Mmax is analogous to the Jeans collapse mass Mj. However, because the compact state has the lowest free energy for masses greater than a critical mass Mpt, where Mmin < Mpt < Mmax, the body may undergo a phase transition-type collapse before Mmax is reached.

Figures are from Praton & Traschen 1994.