Black hole spin-mass correlation and accretion disks at birth stage of dense star clusters

We review the accretion-driven channel of stellar black-hole growth and spin-up in gaseous star clusters, developed within the framework of our MSCA project “protoBH”. Our detailed calculations involving semi-analytic modelling, dynamical and hydrodynamic simulations suggest that the growth and spin-up of initially low-mass stellar black holes is an integral element of the formation process of dense massive star clusters, such as the proto-globular clusters observed at high redshift. The black holes accrete residual gas, remaining from the first star formation event, and form accretion disks generated by gas angular momentum induced by the black-holes’ own curved orbits. Assuming initial black hole masses below the pair-instability mass gap $\le 55{\mathrm{M}}_{\odot }$, the gap gets populated with black-hole masses growing to $\sim {10}^2{\mathrm{M}}_{\odot }$, and even reaching several hundred solar masses for sufficiently dense and massive proto-clusters. We predict a consistent spin-mass relation with low black hole spins $\lesssim 0.2$ for low black hole masses $\lesssim 20{\mathrm{M}}_{\odot }$, spanning all intermediate spins for higher masses and saturating to high spins $\gtrsim 0.8$ for high masses $\gtrsim 70{\mathrm{M}}_{\odot }$. We find evidence in favour of such an accretion-driven subpopulation of black holes in the GWTC-5.0 released by the LIGO-Virgo-KAGRA collaboration.