General-relativistic instability in rapidly accreting supermassive stars: The impact of rotation

Supermassive stars (SMSs) collapsing via the general-relativistic (GR) instability are invoked as the possible progenitors of supermassive black holes. Their mass and angular momentum at the onset of the instability are key in many respects, in particular regarding the possibility for observational signatures of direct collapse. Here, we study the stability of rotating, rapidly accreting SMSs against GR and derive the properties of these stars at death. On the basis of hylotropic structures, relevant for rapidly accreting SMSs, we define rotation profiles under the assumption of local angular momentum conservation in radiative regions, which allows for differential rotation. We find that rotation favours the stability of rapidly accreting SMSs as soon as the accreted angular momentum represents a fraction f > 0.1% of the Keplerian angular momentum. For f = 0.3%-0.5% the maximum masses consistent with GR stability are increased by an order of magnitude compared to the non-rotating case. For f = 1%, the GR instability cannot be reached if the stellar mass does not exceed 10^7-10^8 Msun. These results imply that, like in the non-rotating case, the final masses of the progenitors of direct collapse black holes range in distinct intervals depending on the scenario considered: 10^5 Msun < M < 10^6 Msun for primordial atomically cooled haloes; 10^6 Msun < M < 10^9 Msun for metal-rich galaxy mergers. The models suggest that the centrifugal barrier is inefficient to prevent the direct formation of a supermassive black hole at the collapse of a SMS. Moreover, the conditions of galaxy mergers appear as more favorable than those of atomically cooled haloes for detectable gravitational wave emission and ultra-long gamma-ray bursts at black hole formation.