| Abstract
| - We explore the cosmic evolution of massive black hole (MBH) seeds forming within ‘quasi-stars’ (QSs), accreting black holes embedded within massive hydrostatic gaseous envelopes. These structures could form if the infall of gas into the centre of a halo exceeds about 1 M⊙ yr−1. The collapsing gas traps its own radiation and forms a radiation pressure-supported supermassive star. When the core of the supermassive star collapses, the resulting system becomes a quasi-star. We use a merger-tree approach to estimate the rate at which supermassive stars might form as a function of redshift, and the statistical properties of the resulting QS and seed black hole populations. We relate the triggering of runaway infall to major mergers of gas-rich galaxies and to a threshold for global gravitational instability, which we link to the angular momentum of the host. This is the main parameter of our models. Once infall is triggered, its rate is determined by the halo potential; the properties of the resulting supermassive star, QS and seed black hole depend on this rate. After the epoch of QSs, we model the growth of MBHs within their hosts in a merger-driven accretion scenario. We compare MBH seeds grown inside quasi-stars to a seed model that derives from the remnants of the first metal-free stars, and also study the case in which both channels of MBH formation operate simultaneously. We find that a limited range of supermassive star/QS/MBH formation efficiencies exists that allows one to reproduce observational constraints. Our models match the density of z= 6 quasars, the cumulative mass density accreted on to MBHs (according to Sołtan’s argument) and the current mass density of MBHs. The mass function of QSs peaks at MQS≃ 106 M⊙, and we calculate the number counts for the James Webb Space Telescope (JWST) 2-10 μm band. We find that JWST could detect up to several QSs per field at z≃ 5-10.
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