Establishing a reliable determination of the final mass for rapidly accreting supermassive stars

Abstract

Context. The formation of supermassive black holes possibly takes place via direct collapse, with a supermassive star (SMS) as its progenitor. In this scenario, the SMS accretes at > 0.1 M⊙ yr−1 until it collapses into a massive black hole seed as a result of the general-relativistic (GR) instability. However, the exact mass at which the collapse occurs is not known, as existing numerical simulations give us a divergent range of results. Aims. Here, we address this problem analytically, which allows for reliable ab initio determination of the onset point of the GR instability, for given hydrostatic structures. Methods. We applied the relativistic equation of radial pulsations in its general form to the hydrostatic GENEC models already published in the literature. Results. We show that the mass of spherical SMSs forming in atomically cooled halos cannot exceed 500 000 M⊙, which stands in contrast to previous claims. On the other hand, masses in excess of this limit, possibly up to ∼106 M⊙, could be reached in alternative versions of direct collapse. Conclusions. Our method can be used to test the consistency of GR hydrodynamical stellar evolution codes.