Population synthesis of black hole mergers with B-POP: the impact of dynamics, natal spins, and intermediate-mass black holes on the population of gravitational wave sources

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 multiples structures and is likely truncated beyond $M_1 > 100$ M$_\odot$, while spins are relatively low. Theoretical models of BBH formation in different environments can provide a key to interpret the population of observed mergers, but they require the simultaneous treatment of stellar evolution and dynamics, galaxy evolution, and general relativity. Here, we present B-POP, a tool enabling population synthesis of BBH mergers originating either via isolated binary stellar evolution or dynamical interactions in young, globular, and nuclear clusters. Using B-POP, we show that observed BBHs can be interpreted as members of a mixed population comprised of $\sim 34\% \,{}(66\%)$ isolated (dynamical) BBHs. Our models suggest that the overall primary mass distribution of merging BBHs extends beyond $M_1 \simeq 200$ M$_\odot$. We explore the impact of BH natal spins, showing that the effective spin parameter distribution might hint at different natal spins for single and binary black holes. Hierarchical mergers represent $4.6-7.9\%$ of mock mergers in our reference model and dominate the primary mass distribution beyond $M_1 > 65$ M$_\odot$. Taking into account observational biases, we found that around $2.7-7.5\%$ of BBH mergers might involve intermediate-mass black hole (IMBH) seeds formed via stellar collisions and accretion in dense clusters. Comparing this percentage with the observed value might help us to constrain the impact of IMBHs on the formation of BBH mergers.