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.
