### Abstract

The ‘direct collapse’ scenario has emerged as a promising evolutionary track for the formation of supermassive black holes early in the Universe. In an idealized version of such a scenario, a uniformly rotating supermassive star spinning at the mass-shedding (Keplerian) limit collapses gravitationally after it reaches a critical configuration. Under the assumption that the gas is dominated by radiation pressure, this critical configuration is characterized by unique values of the dimensionless parameters J/M^{2} and R_{p}/M, where J is the angular momentum, R_{p} the polar radius, and M the mass. Motivated by a previous perturbative treatment, we adopt a fully non-linear approach to evaluate the effects of gas pressure on these dimensionless parameters for a large range of masses. We find that gas pressure has a significant effect on the critical configuration even for stellar masses as large as M ~ 10^{6} MO. We also calibrate two approximate treatments of the gas pressure perturbation in a comparison with the exact treatment, and find that one commonly used approximation in particular results in increasing deviations from the exact treatment as the mass decreases, and the effects of gas pressure increase. The other approximation, however, proves to be quite robust for all masses M >~ 10^{4} MO.

Original language | English (US) |
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Pages (from-to) | 4195-4206 |

Number of pages | 12 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 488 |

Issue number | 3 |

DOIs | |

State | Published - 2019 |

### Keywords

- Black hole physics
- Equation of state
- Stars: Population III

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Monthly Notices of the Royal Astronomical Society*,

*488*(3), 4195-4206. https://doi.org/10.1093/mnras/stz1961