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

Context. The formation of supermassive black holes possibly takes place via direct collapse, with a star (SMS) as its progenitor. In this scenario, the SMS accretes at > 0.1 M ? yr ?1 until it collapses into massive hole seed result general-relativistic (GR) instability. However, exact mass which collapse occurs is not known, existing numerical simulations give us divergent range results. Aims. Here, we address problem analytically, allows for reliable ab initio determination onset point GR instability, given hydrostatic structures. Methods. We applied relativistic equation radial pulsations in general form to GENEC models already published literature. Results. show that spherical SMSs forming atomically cooled halos cannot exceed 500 000 , stands contrast previous claims. On other hand, masses excess limit, up ?10 6 could be reached alternative versions collapse. Conclusions. Our method can used test consistency hydrodynamical stellar evolution codes.