Pathways to massive black holes and compact star clusters in pre-galactic dark matter haloes with virial temperatures ≳10 000 K

Abstract

Large dynamic range numerical simulations of atomic cooling driven collapse of gas in pre-galactic dark matter haloes with Tvir∼ 10 000 K show that the gas loses 90 per cent and more of its angular momentum before rotational support sets in. In a fraction of these haloes where the metallicity is low and ultraviolet (UV) radiation suppresses H2 cooling, conditions are thus very favourable for the rapid build-up of massive black holes. Depending on the progression of metal enrichment, the continued suppression of H2 cooling by external and internal UV radiation and the ability to trap the entropy produced by the release of gravitational energy, the gas at the centre of the halo is expected to form a supermassive star, a stellar-mass black hole accreting at super-Eddington accretion rates or a compact star-cluster undergoing collisional run-away of massive stars at its centre. In all three cases, a massive black hole of initially modest mass finds itself at the centre of a rapid inflow of gas with inflow rates of ≳1 M⊙ yr−1. The massive black hole will thus grow quickly to a mass of 105– 106 M⊙ until further inflow is halted either by consumption of gas by star formation or by the increasing energy and momentum feedback from the growing massive black hole. Conditions for the formation of massive seed black holes in this way are most favourable in haloes with Tvir∼ 15 000 K and Vvir∼ 20 km s−1 with less massive haloes not allowing collapse of gas by atomic cooling and more massive haloes being more prone to fragmentation. This should imprint a characteristic mass on the mass spectrum of an early population of massive black hole seeds in pre-galactic haloes which will later grow into the observed population of supermassive black holes in galactic bulges.