Maximum accretion rate of supermassive stars

Abstract

Context. 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. Aims. 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. Methods. We use the continuity equation and the assumption of spherical symmetry and free fall to derive the 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. Results. We find that, as long as the density of the accreted gas is smaller than or equal to the average density of the accretor, the maximum allowed rate, Ṁmax, is given uniquely by the compactness of the accretor. We argue that a density inversion between accreting matter and the accretor is inconsistent with gravitational collapse. For the compactness of rapidly accreting supermassive stars, Ṁmax is related to the stellar mass, M, by a power law, Ṁmax ∝ M3/4. The rates of atomically cooled halos (0.1−10 M⊙ yr−1) are allowed as soon as M ≳ 1 M⊙. The largest rates expected in galaxy mergers (104 − 105 M⊙ yr−1) become accessible once the accretor is supermassive (M ≳ 104 M⊙). Conclusions. These results suggest that supermassive stars can accrete up to masses > 106 M⊙ 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.

Direct collapse of exceptionally heavy black holes in the merger-driven scenario

“…The argument in Mayer et al (2010) and Mayer et al (2015) (hereafter MI and MII, respectively) is that SMDs represent an optimal environment for the rapid formation of an SMBH, either through an intermediate supermassive star (SMS) phase (see, e.g. Haemmerlé et al 2020Haemmerlé et al , 2021, or directly via the collapse of a general relativistic (GR)-unstable region. The advantages of the merger-driven scenario are that the formation of SMDs does not require any specific restrictions on thermodynamical conditions of the gas, nor any specific angular momentum loss mechanism other than the ones provided by the hydrodynamics of galaxy mergers.…”

Astrophysics with the Laser Interferometer Space Antenna

“…The resulting accumulation of billions of solar masses of gas in a nuclear region less than a parsec in size could either induce the formation of a very large SMS, and hence a massive BH seed by direct collapse, or even directly form a large MBH via the radial general-relativistic instability of a supermassive protostellar precursor. Recent models show that an accreting SMS, owing to the much higher accretion rates occurring in the merger-driven scenario, can grow in mass much more than in the atomic cooling halo case, namely to > 10 7 M in absence of rotation, before collapsing into an MBH seed (Haemmerlé et al, 2021).…”

In-situ extreme mass ratio inspirals via sub-parsec formation and migration of stars in thin, gravitationally unstable AGN discs

“…Conventional star formation involves the collapse of diffuse gas to dense, accreting cores, involving a vast range of temperatures and physical scales. Determining the stellar mass distribution from a collapsing cloud is a non-trivial problem given that complexities in opacity, radiative processes, rotation, and magnetic fields are all critical for determining the resulting stellar masses (Larson 1969;Penston 1969;Stahler & Palla 2004), particularly in regimes of high accretion rates that lead to supermassive stars (Haemmerlé et al 2021;Hosokawa 2019).…”

“…Such cores collapse rapidly due to the gas conditions, as we will show, experiencing high accretion rates. Certain conditions lead to the formation of supermassive stars (SMSs), for which there are greater uncertainties in the final stellar masses and structure (Hosokawa et al 2013) and subsequent evolution (Haemmerlé et al 2021). Critically, the formation and subsequent evolution of AGNstars does not occur in isolation: gas from the disc may feed the protostellar envelopes and exert torques.…”