Maximally rotating supermassive stars at the onset of collapse: Effects of gas pressure

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/M² 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 ~ 10⁶ 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 >~ 10⁴ MO.