Signatures of a subpopulation of hierarchical mergers in the GWTC-4 gravitational-wave dataset

TL;DR

The paper addresses how to identify hierarchical black-hole mergers within GWTC-4 by moving beyond one-dimensional spin diagnostics to a joint spin space. It develops an astrophysically-motivated two-component model in the space of $\chi_{eff}$ and $\chi_{p}$, comprising a Gaussian 1G+1G component and an ellipse-boundary 1G+2G component with a mass-dependent mixing fraction. The analysis finds strong evidence for a population transition near $m_1\sim 46 M_\odot$—consistent with the onset of the pair-instability gap—and a secondary peak in hierarchical mergers around $m_1\sim 15.7 M_\odot$, yielding a total hierarchical fraction $\xi\approx 0.14$. These results imply contributions from both solar-metallicity and metal-poor clusters and demonstrate that mass-dependent, multi-dimensional spin structure provides robust signatures of hierarchical assembly beyond what $\chi_{eff}$ alone can reveal. The approach highlights the power of joint spin-mass population modeling for constraining stellar-evolutionary processes and the origin of black holes in the PISN gap.

Abstract

Repeated black-hole mergers in dense stellar clusters are a plausible mechanism to populate the predicted gap in black hole masses due to the pair-instability process. These hierarchical mergers carry distinct spin and tilt features relative to first-generation black holes, for which previous studies have found evidence at a population level by interpreting features in the effective inspiral spin domain. We introduce an astrophysically-motivated model in the joint space of effective inspiral and precessing spins, which captures the dominant spin dynamics expected for hierarchical mergers. We find decisive evidence both for a population transition above $\sim 45M_\odot$, consistent with the anticipated onset of the pair-instability gap, as well as a peak at $\sim 15 M_\odot$, which we interpret as the global peak in the hierarchical merger rate. The existence of low- and high-mass subpopulations of higher-generation black holes suggests the contribution of both near-solar-metallicity and metal-poor star clusters to the hierarchical merger population. Our results reinforce the growing evidence for detailed, mass-dependent substructure in the spin distribution of the binary black hole population.

Figures (6)

• Figure 1: Schematic of our two-component model in $\chi_\mathrm{eff}\xspace$--$\chi_\mathrm{p}\xspace$ space. The truncated Gaussian describes 1G+1G mergers and is defined by its means ($\mu_\mathrm{eff,p}$) and standard deviations ($\sigma_\mathrm{eff,p}$) in both dimensions. The ellipse-boundary component, ascribed to 1G+2G mergers, is determined by a characteristic spin $\chi_c$, characteristic mass ratio $q_c$, and Gaussian width perpendicular to the curve $\sigma$.
• Figure 2: Posterior on the ellipse-boundary component in $\chi_\mathrm{eff}\xspace$--$\chi_\mathrm{p}\xspace$ space. The joint distribution plots the median inference, with 50%, 90%, and 99% percentile contours; side panels plot the 90% credible regions of the marginals, including those for prior draws that pass the likelihood variance threshold.
• Figure 3: The inferred fraction of hierarchical mergers $\xi(m_1)$. We plot the median and 90% symmetric credible interval. Gray squares mark the locations of the spline nodes.
• Figure 4: The 90% credible bounds on the marginal mass ratio distributions for the first-generation component (solid teal), modeled by a truncated power law, and the hierarchical component (dashed pink), modeled with a truncated normal.
• Figure 5: Marginal and two-dimensional joint posteriors on the characteristic spin $\chi_c$, characteristic mass ratio $q_c$, and width $\ln\sigma$ of the ellipse component. The dashed gray histograms in the marginals consist of draws from the prior that pass the likelihood variance cut.