Isolated or Dynamical? Tracing Black Hole Binary Formation through the Population of Gravitational-Wave Sources

Abstract

The population of binary black hole (BBH) mergers observed by the LIGO-Virgo-KAGRA (LVK) collaboration offers a window into the cosmic evolution of compact binaries and their formation. We employ the semi-analytic population-synthesis code B-POP to model BBHs assembled through isolated binary evolution and dynamical interactions in young, globular, and nuclear star clusters. Our framework incorporates star formation history, metallicity evolution, and single and binary stellar evolution to quantify their impact on the observable properties of the BBH population and on the relative contribution of distinct formation channels. Our models are characterized by a merger rate, $\mathcal{R} = 17.5-24.1\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$, broadly consistent with LVK constraints. Moreover, the predicted distributions of primary mass, mass ratio, and effective inspiral spin parameter are compatible with those inferred from current LVK observations. Our primary-mass distribution is dominated by isolated binaries at $m_1 < 20$ M$_\odot$, while dynamically assembled first- and higher-generation mergers dominate at larger masses. As a consequence, the sub-population of mergers with $m_1 > 45$ M$_\odot$ exhibits a nearly flat mass-ratio distribution and distinctive spin properties. We leverage our models to explore how: (i) the fraction of stars in isolated binaries and the fraction of stellar mass bound in clusters regulate the merger rate; (ii) common-envelope physics shapes the primary-mass distribution and its redshift evolution; (iii) the inclusion of stellar-collision products enhances the formation of higher-generation mergers; and (iv) the natal spin distribution influences the effective spin. Using our models to assess possible origins of selected GW events, we illustrate how the complexity of the underlying astrophysical processes can hinder the possibility to draw definitive conclusions.

Figures (24)

• Figure 1: Primary mass distribution of merging BBHs in different environments. From left to right and from top to bottom: isolated binaries (IB), young (YC), globular (GC), and nuclear clusters (NC). Diffrent colors correspond to different metallicity bins.
• Figure 2: Merger rate density of all BBH mergers for different models. The straight blue and orange lines, as well as the shaded regions, correspond to the inferred rate from GWTC-4 according to a strongly modelled approach (Power-law, blue) and a weakly modelled approach (B-SPLINE, orange) 2025arXiv250818083T, and their $90\%$ confidence interval. In all panels, the red straight line identifies the total simulated merger rate density, while the other lines highlight the contributions from BBHs in isolated binaries (purple straight line, IB), young clusters (blue dashed line, YC), globular clusters (green dotted line, GC), and nuclear clusters (light green dash-dotted line, NC). From left to right, top row panels display the rate for the fiducial model (F) and its variations assuming a primordial binary fraction $f_{\rm mix} = 0$ (Fb0), and $1$ (Fb1). Similarly, bottom row panels display the rate for a model with $\alpha_{\rm CE}=5$ (F5), with a GC formation history as described in 2020ApJ...898..152S (Fe), and excluding dynamically formed upper-mass gap BHs and VMS remnants.
• Figure 3: Merger rate density at redshift $z=0.2$ as a function of the fraction of isolated binaries ($f_{\rm IB}$) and the fraction of stars in YCs ($f_{\rm YC}$). The red star identifies the considered model. White dashed lines denote the loci of $f_{\rm IB}-f_{\rm YC}$ values required to reproduce the upper and lower bounds of the LVK-inferred rate. The horizontal, white, dotted lines mark the observational constraints on $f_{\rm YC}$.
• Figure 4: Top row panels: mass distribution of black hole binary mergers in different redshift bins extracted from the overall population (filled red steps) and mergers from isolated binaries (purple steps), young (blue steps), globular (green steps), and nuclear clusters (light green steps). Central row panels: same as above, but for the binary effective spin parameter. Bottom row panels: same as in top panels, but for the binary precession spin parameter.
• Figure 5: Differential merger rate density as a function of the primary mass for our fiducial model (red straight line), considering only mergers occurring at $z<2$ (top panel) or $z>2$ (bottom panel), compared against the rate inferred from GWTC-4 within the B-Spline (straight orange line) and the Broken Power Law + 2 Peaks (dashed blue line) fit models 2025arXiv250818083T.