On the maximum accretion rate of supermassive stars

Abstract

The formation of the most massive quasars observed at high redshifts requires extreme inflows of gas down to the length scales of the central compact object. Here, we estimate the maximum inflow rate allowed by gravity down to the surface of supermassive stars, the possible progenitors of these supermassive black holes. We use the continuity equation and the assumption of free-fall to derive maximum allowed inflow rates for various density profiles. We apply our approach to the mass-radius relation of rapidly accreting supermassive stars to estimate an upper limit to the accretion rates allowed during the formation of these objects. We find that the maximum allowed rate ${\dot{M}}_{\max }$ is given uniquely by the compactness of the accretor. For the compactness of rapidly accreting supermassive stars, ${\dot{M}}_{\max }$ is related to the stellar mass $M$ by a power-law ${\dot{M}}_{\max }\propto M^{3/4}$. The rates of atomically cooled halos (0.1 -- 10 M${}_{\odot }$ yr${}^{-1}$) are allowed as soon as $M\gtrsim 1$ M${}_{\odot }$. The largest rates expected in galaxy mergers ($10^4-10^5$ M${}_{\odot }$ yr${}^{-1}$) become accessible once the accretor is supermassive ($M\gtrsim 10^4$ M${}_{\odot }$). These results suggest that supermassive stars can accrete up to masses $>10^6$ M${}_{\odot }$ before they collapse via the general-relativistic instability. At such masses, the collapse is expected to lead to the direct formation of a supermassive black hole even within metal-rich gas, resulting in a black hole seed that is significantly heavier than in conventional direct collapse models for atomic cooling halos.

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• The physical origin of super-competitive accretion during the formation of the first supermassive black holes
• The Evolution of Accreting Population III Stars at 10${}^{-6}$-10${}^3$ M${}_{\odot }$/yr
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