Rigidly rotating, incompressible spheroid–ring systems: new bifurcations, critical rotations, and degenerate states

The equilibrium of incompressible spheroid-ring systems in rigid rotation is investigated by numerical means for a unity density contrast. A great diversity of binary configurations is obtained, with no limit neither in the mass ratio, nor in the orbital separation. We found only detached binaries, meaning that the end-point of the ɛ2-sequence is the single binary state in strict contact, easily prone to mass-exchange. The solutions show a remarkable confinement in the rotation frequency-angular momentum diagram, with a total absence of equilibrium for Ω2/πGρ ≳ 0.21. A short band of degeneracy is present next to the one-ring sequence. We unveil a continuum of bifurcations all along the ascending side of the Maclaurin sequence for eccentricities of the ellipsoid less than ≈0.612 and which involves a gradually expanding, initially massless loop.