The assembly of intermediate black holes with complementary approaches: Dragon II and BPop

Intermediate-mass black holes (IMBHs) occupy the ${10}^2-{10}^5{M}_{\odot }$ range, but their existence remains poorly constrained. Only a few candidates have been suggested in dwarf galaxies, globular clusters, and LIGO-Virgo-Kagra detections. To investigate their formation and demographics, we adopt two complementary approaches. We first analyze the $\text{textsc}dragonii$ direct $N$-body simulations, which follow clusters with up to ${10}^6$ stars, capture IMBHs growth. We then employ the semi-analytic code $\text{textsc}bpop$, calibrated on $\text{textsc}dragonii$, to explore a broad range of cluster and cosmological conditions. Our models reproduce merger rates consistent with GWTC-3, with $\sim 30-60\mathrm{\%}$ of BBHs forming dynamically, mainly in globular and nuclear clusters. About 2-3% of mergers involve an IMBH, producing intermediate-mass ratio inspirals. The IMBH mass distribution spans $2.5\times {10}^2-4\times {10}^4{M}_{\odot }$, with rare growth beyond ${10}^6{M}_{\odot }$. Formation efficiency rises with initial binary fraction but declines in metal-rich environments. IMBHs thus emerge as a distinct population bridging stellar and supermassive black holes.