Light or heavy supermassive black hole seeds: the role of internal rotation in the fate of supermassive stars

Supermassive black holes are a key ingredient of galaxy evolution. However, their origin is still highly debated. In one of the leading formation scenarios, a black hole of ∼100 M_⊙ results from the collapse of the inner core of a supermassive star (≳10^4-5 M_⊙), created by the rapid accumulation (≳0.1 M_⊙ yr^-1) of pristine gas at the centre of newly formed galaxies at z ∼ 15. The subsequent evolution is still speculative: the remaining gas in the supermassive star can either directly plunge into the nascent black hole or part of it can form a central accretion disc, whose luminosity sustains a surrounding, massive, and nearly hydrostatic envelope (a system called a `quasi-star'). To address this point, we consider the effect of rotation on a quasi-star, as angular momentum is inevitably transported towards the galactic nucleus by the accumulating gas. Using a model for the internal redistribution of angular momentum that qualitatively matches results from simulations of rotating convective stellar envelopes, we show that quasi-stars with an envelope mass greater than a few 10⁵ M_{⊙} × (black hole mass/100 M_{⊙})^{0.82} have highly sub-Keplerian gas motion in their core, preventing gas circularization outside the black hole's horizon. Less massive quasi-stars could form but last for only ≲10⁴ yr before the accretion luminosity unbinds the envelope, suppressing the black hole growth. We speculate that this might eventually lead to a dual black hole seed population: (I) massive (>10⁴ M_⊙) seeds formed in the most massive (>10⁸ M_⊙) and rare haloes; (II) lighter (∼10² M_⊙) seeds to be found in less massive and therefore more common haloes.