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

TL;DR

The paper addresses the existence and demographics of intermediate-mass black holes in dense star clusters and their imprint on BBH mergers. It combines Dragon-II direct N-body simulations with B-pop, a semi-analytic model calibrated on Dragon-II, to produce large BBH catalogs across cosmic history. Key findings include a local BBH merger rate around 27 per year per cubic gigaparsec and that about 30-60% of mergers are dynamical, with IMBH-involved mergers around 2-3% of all events, and an IMBH mass spectrum spanning roughly 2.5e2 to 4e4 solar masses. IMBH demographics are strongly shaped by cluster environment and metallicity, with low-metallicity clusters sustaining higher IMRI fractions and metal-rich environments suppressing them. The hybrid Dragon-II plus B-pop framework provides a versatile platform to interpret LVK gravitational-wave observations and to constrain IMBH demographics through cosmic time.

Abstract

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 \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 \textsc{bpop}, calibrated on \textsc{dragonii}, to explore a broad range of cluster and cosmological conditions. Our models reproduce merger rates consistent with GWTC-3, with $\sim30 - 60\%$ 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.

Figures (2)

• Figure 1: Merger rates as a function of redshift for the fiducial model with $f_{\rm mix} = 0.5$, $f_{\rm YC}=0.005$, and $f_{\rm IB}=1$. Different colors and line styles correspond to different formation channels: isolated binaries (IB, straight purple line), young clusters (YC, dashed blue line), globular clusters (GC, dotted green line), and nuclear clusters (NC, dot-dashed light green line). The thick red line represents the total merger rate, while the light blue line and shaded region represent the BBH merger rate inferred from the GWTC-3.
• Figure 2: IMBH mass distribution for all models. The number in the model name indicates the binary fraction at birth, with 0, 1, 2, 3, and 4 corresponding to $f_{\rm mix} = 0, 0.25, 0.5, 0.75,$ and $1$, respectively. The letter (a or b) indicates the different GCs/NCs star formation histories (see Arcasedda_BPOP for details). The stellar BH distribution is obtained from our catalogs, while the SMBH distribution is based on low-$z$ observations 2009ApJ...690...20S. Areas are normalized to unity for comparison.