Population of Binary Black Holes Inferred from One Hundred and Fifty Gravitational Wave Signals

TL;DR

The paper addresses how to infer the population properties of binary black holes from the LVK GWTC-4 catalog using the Vamana mixture-model framework. It jointly infers primary and secondary masses, aligned spins, and redshift evolution, revealing a low-mass excess and three chirp-mass peaks whose locations suggest hierarchical merger origins. The work connects mass correlations to distinct chirp-mass features and identifies a high-spin sub-population whose properties align with hierarchical expectations, while noting the limits imposed by selection effects and priors. These findings imply that hierarchical mergers could play a significant role in shaping the BBH mass distribution, and they set the stage for stronger tests with upcoming GW observations from the next observing runs.

Abstract

The LIGO-Virgo-KAGRA collaborations have reported gravitational wave signals from more than 150 binary black holes in the fourth catalog (GWTC-4). Here, we investigate the population properties of these binary black holes using the mixture-model framework Vamana. We present one-dimensional distributions of masses and spins, explore their correlations, and examine their evolution with redshift. These features may reflect astrophysical processes associated with binary black hole formation channels, although most remain poorly constrained. A notable feature is a peak near $10M_\odot$ in the primary mass and $8M_\odot$ in the chirp mass. Additionally, the primary and secondary masses correlate uniquely, producing pronounced peaks in the chirp mass around $14M_\odot$ and $27M_\odot$. The three peaks are roughly separated by a factor of two. A simple explanation for such well-placed peaks is a hierarchical merger scenario, in which the first peak arises from mergers of black holes of stellar origin, and higher-mass peaks arise from repeated mergers of black holes from lower-mass peaks. Although most binaries do not exhibit the high spins and characteristic mass ratios expected from hierarchical mergers, those that do are associated with the peaks observed in the chirp mass distribution.

Figures (12)

• Figure 1: The (a) chirp, (b) secondary, (c) primary, and (d) component mass distribution of BBH. Solid curves indicate the median, and shaded bands show the 90% credible intervals for the differential merger rate. All mass parameters show an over-density at the lower-mass end. The chirp mass distribution exhibits four distinct peaks, with the first three exceeding a 99% confidence level. The region between the first two peaks is labelled 'gap' due to a lack of observations. Subsequent peaks are separated by approximately a factor of 1.9, shown by brown lines $\mathfrak{L}$. Other mass parameters show local maxima at comparable locations, but with lower confidence. Primary and secondary masses uniquely correlate to produce the peaks in the chirp mass distribution (see sub-section \ref{['subsec:corrmass']}).
• Figure 2: Inferred mass-ratio (left) and aligned spin (right) distributions. Solid lines indicate the median, shaded bands the 90% credible interval. The mass ratio is mostly uniform from 0.6 to 0.9. Aligned spins are typically small, ranging from -0.30 to 0.37 at 90% credibility.
• Figure 3: Local merger rate (left) and redshift evolution (right). Solid lines indicate the mean, shaded bands the 90% credible interval. The local merger rate is $R_0 = 14.0^{+4.8}_{-5.9}\mathrm{Gpc}^{-3},\mathrm{yr}^{-1}$. Redshift evolution is confidently positive.
• Figure 4: Differential merger rate on the component mass plane (right plot is lower-left quadrant of the left). Three over-dense regions correspond to peaks in the chirp mass distribution. The dashed curve indicates a constant chirp mass track, $\mathcal{M} = 13.9M_\odot$, which requires the component masses to correlate uniquely. The over-density around 60--40$M_\odot$ has been interpreted as due to the presence of a gap in the secondary mass caused by pulsational instability supernova 1964ApJS....9..201F2017ApJ...836..244W and lack of it in the primary mass due to 2G--1G hierarchical mergers, where masses of 1G BHs in this interpretation extends up to around 45$M_\odot$2025PhRvD.112f3040A2025arXiv250904151T2025arXiv250904637A2025arXiv250909123A2025arXiv250909876G.
• Figure 5: Variation of mass ratio with mass parameters. The primary/total mass combines uniquely with the mass ratio to produce the second chirp mass peak at 14$M_\odot$. The jagged structure arises from a change in the sign of the correlation around $m_1 = 19M_\odot$. In contrast, the third peak mostly consists of binaries with comparable masses.