Stability of Rigidly Rotating Supermassive Stars Against Gravitational Collapse

We revisit secular stability against quasi-radial collapse for rigidly rotating supermassive stars (SMSs) in general relativity. We suppose that the SMSs are in a nuclear-burning phase and can be modeled by polytropic equations of state with the polytropic index n p slightly smaller than 3. The stability is determined in terms of the turning point method. We find a fitting formula of the stability condition for the plausible range of n p ( ) for SMSs. This condition reconfirms that while non-rotating SMSs with a mass of – may undergo a general relativistically induced quasi-radial collapse, rigidly rotating SMSs with a ratio of rotational to gravitational potential energy (β) of are likely to be stable against collapse unless they are able to accrete ∼5 times more mass during the (relatively brief) hydrogen-burning phase of their evolution. We discuss the implications of our results.