Maximally Rotating Supermassive Stars at the Onset of Collapse: The Perturbative Effects of Gas Pressure, Magnetic Fields, Dark Matter and Dark Energy

TL;DR

This paper investigates how various physical effects like gas pressure, magnetic fields, dark matter, and dark energy influence the critical conditions of supermassive stars at collapse, refining the understanding of their universality and stability.

Contribution

It provides leading-order corrections to the universal collapse parameters of rotating supermassive stars considering multiple perturbative effects, extending previous models.

Findings

Gas pressure significantly affects collapse parameters.

Two approximation methods yield consistent results.

Results agree with recent numerical simulations.

Abstract

The discovery of quasars at increasingly large cosmological redshifts may favor "direct collapse" as the most promising evolutionary route to the formation of supermassive black holes. In this scenario, supermassive black holes form when their progenitors - supermassive stars - become unstable to gravitational collapse. For uniformly rotating stars supported by pure radiation pressure and spinning at the mass-shedding limit, the critical configuration at the onset of collapse is characterized by universal values of the dimensionless spin and radius parameters $J/M^2$ and $R/M$, independent of mass $M$. We consider perturbative effects of gas pressure, magnetic fields, dark matter and dark energy on these parameters, and thereby determine the domain of validity of this universality. We obtain leading-order corrections for the critical parameters and establish their scaling with the relevant physical parameters. We compare two different approaches to approximate the effects of gas pressure, which plays the most important role, find identical results for the above dimensionless parameters, and also find good agreement with recent numerical results.