ProtoBH · Black hole spin and mass function in gaseous proto-clusters

Gravitational-wave (GW) Astronomy opened a new window to the Universe from its infant state to the present. The key physical systems which allow probing the Universe through these vast time and length scales are Black Holes (BH). Low metallicity clouds, composed primarily of atomic hydrogen, before and during the epoch of reionization, are a natural environment for BHs to be born and form Binary Black Holes (BBH) which can merge via GW emission. Stellar BHs, being the remnants of the death of very massive stars, are generated early when a huge gas reservoir is available for accretion. Mass segregation leads the BHs close to the center of the system and a dense BH-subcluster, supported by gravitational fluctuations, is formed. The low metallicity of the gas suppresses cooling, while turbulence of the gas and the BHs’ motion further favor quasi-spherical accretion, surpassing the Eddington limit. For sufficiently compact configurations, the BHs shall grow in mass before the gas is depleted by stellar evolution and formation feedback processes. This rapid mass growth through turbulent hot accretion shall leave a distinct spin signature on the BHs. The BBH that accrete gas quasi-spherically may harden if there is not significant angular momentum loss from the system. Furthermore, these are also ideal conditions for high-redshift Intermediate Mass Black Holes (IMBH) to form. We shall calculate the spin distribution of stellar BHs accreting gas in proto-clusters, calculate the BH mass function following such accretion events, investigate the evolution of separation in accreting BBH in low-metallicity hot turbulent gas, develop theoretical models for the evolution of a BH-subcluster inside proto-clusters and investigate the formation of IMBH. Finally, we shall develop methods for identifying the origin of GW observations, confront our results with LIGO-Virgo-KAGRA data, and investigate synergetically the implications for the GW mission LISA and the X-ray mission Athena.