We compute statistical equilibrium states of rotating self-gravitating fermions by maximizing the Fermi-Dirac entropy at fixed mass , energy and angular momentum .
We describe the phase transition from a gaseous phase to a condensed phase ( corresponding to white dwarfs , neutron stars or fermion balls in dark matter models ) as we vary energy and temperature .
We increase the rotation up to the Keplerian limit and describe the flattening of the configuration until mass shedding occurs .
At the maximum rotation , the system develops a cusp at the equator .
We draw the equilibrium phase diagram of the rotating self-gravitating Fermi gas and discuss the structure of the caloric curve as a function of degeneracy parameter ( or system size ) and angular velocity .
We argue that systems described by the Fermi-Dirac distribution in phase space do not bifurcate to non-axisymmetric structures when rotation is increased , in continuity with the case of polytropes with index n > 0.808 ( the Fermi gas at T = 0 corresponds to n = 3 / 2 ) .
This differs from the study of Votyakov et al .
( 2002 ) who consider a Fermi-Dirac distribution in configuration space appropriate to stellar formation and find “ double star ” structures ( their model at T = 0 corresponds to n = 0 ) .
We also consider the case of classical objects described by the Boltzmann entropy and discuss the influence of rotation on the onset of gravothermal catastrophe ( for globular clusters ) and isothermal collapse ( for molecular clouds ) .
On general grounds , we complete previous investigations concerning the nature of phase transitions in self-gravitating systems .
We emphasize the inequivalence of statistical ensembles regarding the formation of binaries ( or low-mass condensates ) in the microcanonical ensemble ( MCE ) and Dirac peaks ( or massive condensates ) in the canonical ensemble ( CE ) .
We also describe an hysteretic cycle between the gaseous phase and the condensed phase that are connected by a “ collapse ” or an “ explosion ” .