Stability of rigidly rotating supermassive stars against gravitational collapse

Abstract

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 $n_p$ ($2.95 \alt n_p \alt 3$) for SMSs. This condition reconfirms that, while non-rotating SMSs with mass $\sim 10^5{M}_{\odot }$--$10^6{M}_{\odot }$ may undergo a general-relativistically induced quasi-radial collapse, rigidly rotating SMSs with a ratio of rotational to gravitational potential energy ($\beta$) of $\sim 10^{-2}$ are likely to be stable against collapse unless they are able to accrete $\sim 5$ times more mass during the (relatively brief) hydrogen-burning phase of their evolution. We discuss implications of our results.

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• Gravitational Collapse of Rotating Supermassive Stars including Nuclear Burning Effects
• Magnetorotational Collapse of Supermassive Stars: Black Hole Formation, Gravitational Waves and Jets
• Direct collapse of exceptionally heavy black holes in the merger-driven scenario
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• General-relativistic instability in rapidly accreting supermassive stars in the presence of dark matter
• Signatures of Exploding Supermassive PopIII Stars at High Redshift in JWST, EUCLID and Roman Space Telescope