Rapidly accreting supermassive stars: reliable determination of the final mass

TL;DR

This paper presents an analytical method to determine the final mass at which supermassive stars become unstable and collapse into black holes, providing more reliable estimates than previous simulations.

Contribution

It introduces an analytical approach using relativistic pulsation equations to accurately predict the collapse point of supermassive stars, resolving discrepancies in prior numerical results.

Findings

Supermassive stars in atomically cooled haloes cannot exceed 500,000 solar masses.

Masses up to 1 million solar masses are possible in alternative collapse scenarios.

The method can validate the consistency of GR hydrodynamical stellar evolution codes.

Abstract

Supermassive black holes might form by direct collapse, with a supermassive star (SMS) as progenitor. In this scenario, the SMS accretes at > 0.1 Msun/yr until it collapses into a massive black hole seed due to the general-relativistic (GR) instability. However, the exact mass at which the collapse occurs is not known, as existing numerical simulations give divergent results. Here, this problem is addressed analytically, which allows for ab initio, reliable determination of the onset point of the GR instability, for given hydrostatic structures. We apply the relativistic equation of radial pulsations in its general form to the hydrostatic GENEC models already published. We show that the mass of spherical SMSs forming in atomically cooled haloes cannot exceed 500 000 Msun, in contrast to previous claims. On the other hand, masses in excess of this limit, up to 10^6 Msun, could be reached in alternative versions of direct collapse. Our method can be used to test the consistency of GR hydrodynamical stellar evolution codes.