Isolated and dynamical black hole mergers with \texttt{B-POP}: the role of star formation and dynamics, star cluster evolution, natal kicks, mass and spins, and hierarchical mergers

The current interpretation of LIGO--Virgo--KAGRA data suggests that the primary mass function of merging binary black holes (BBHs) at redshift $z\lesssim 1$ contains multiple structures, while spins are relatively low. Theoretical models of BBH formation in different environments can provide a key to interpreting the population of observed mergers, but they require the simultaneous treatment of stellar evolution and dynamics, galaxy evolution, and general relativity. We present \texttt{B-POP}, a population synthesis tool to model BBH mergers formed in the field or via dynamical interactions in young, globular, and nuclear clusters. Using \texttt{B-POP}, we explore how BH formation channels, star cluster evolution, hierarchical mergers, and natal BH properties affect the population of BBH mergers. We find that the primary mass distribution of BBH mergers extends beyond $M_1 \simeq 200\,{}$ M$_\odot$, and the effective spin parameter distribution hints at different natal spins for single and binary BHs. Observed BBHs can be interpreted as members of a mixed population comprised of $\sim 34\% \,{}(66\%)$ isolated (dynamical) BBHs, with the latter likely dominating at redshift $z>1$. Hierarchical mergers constitute the $4.6-7.9\%$ of all mergers in the reference model, dominating the primary mass distribution beyond $M_1 > 65\,{}$ M$_\odot$. The inclusion of cluster mass-loss and expansion causes an abrupt decrease in the probability for mergers beyond the third generation to occur. Considering observational biases, we find that $2.7-7.5\%$ of mock mergers involve intermediate-mass black hole (IMBH) seeds formed via stellar collisions. Comparing this percentage to observed values will possibly help us to constrain IMBH formation mechanisms.
26 Pages, 20 Figures, 1 Table. We significantly improved B-POP since the first submission, this led to a major restructuring of the previous version of the manuscript. Accepted for publication in MNRAS