Reexamining Evidence of a Pair-Instability Mass Gap in the Binary Black Hole Population

TL;DR

The paper reexamines the proposed pair-instability mass gap in the binary black hole population using GWTC-4 with flexible population models. Through Bayesian hierarchical inference that allows for smooth transitions in mass-ratio and spin distributions, the study finds no evidence for a sharp gap near $40-50\,M_{\\odot}$ and identifies a spin-transition around $\tilde{m}\approx43\,M_{\\odot}$ with a post-transition sub-population showing predominantly symmetric mass ratios. The results imply that the high-mass BBH sub-population is not dominantly explained by 2G+1G hierarchical mergers and that, within current uncertainties, a PISN cutoff would lie at $m_2\gtrsim57^{+17}_{-10}\,M_{\\odot}$, consistent with some stellar-evolution constraints but not requiring a sharp mass gap at $40-50\,M_{\\odot}$. The findings motivate considering alternative formation channels and caution against strong priors that artificially enforce gaps, while highlighting the role of future data to refine the PISN boundary and stellar-evolution physics.

Abstract

The fourth gravitational wave transient catalog~(GWTC-4) has enabled empirical probes of the theorized pair-instability gap in the higher end of the binary black hole~(BBH) mass-spectrum. In this letter, using flexibly parametrized models, we show that at present there is no evidence of a sharp drop-off in the spectrum of black hole masses near $~40-50M_{\odot}$. We simultaneously characterize the transition in the distribution of BBH mass-ratios, effective aligned and effective precessing spins using our flexible models. From the transitions in our inferred spin and mass-ratio distributions, we find that the high-mass broad-spin sub-population has a significant fraction~($52^{+18}_{-23}\%$) of systems with mass ratios in the range $0.6-1$. This suggests that alternatives to the hypothesis of 2G+1G hierarchical systems dominating BBH formation above $\sim 40-50 M_{\odot}$ are more consistent with the GWTC-4 detection sample. By comparing with the predictions of star cluster simulations, we further show that contributions from (2G+2G) systems are not abundant enough to alleviate this discrepancy. We also demonstrate the effects of strong model assumptions on this inference, which can lead to biased astrophysical interpretation from restricted priors. We note that our results do not exclude that a high-mass gap may be identified as our sample size increases. We constrain the lower bound on the location of a possible PISN cutoff still allowed within measurement uncertainties to be $(57^{+17}_{-10}M_{\odot})$ and discuss its implications on the S factor of $^{12}\mathrm{C}(α, γ)^{16}O$ at 300 kev.

Figures (12)

• Figure 1: Inferred mass distributions show no evidence for a sharp gap. The blue shaded region show demarcates the $90\%$ credible interval obtained from the posterior and the black dashed lines represent the lower edge of a sharp gap inferred by Tong:2025wpz.
• Figure 2: Secondary mass percentiles in the range $m_2 \in(m_{2,b1}, m_{2, b2})$ and the corresponding lower bounds on the Carbon-Oxygen reaction rate. Note that the bounds of Tong:2025wpz are nearly identical to that inferred by Antonini:2025ilj.
• Figure 3: Transition of mass-ratio, effective aligned and effective precision-spin distributions at $\tilde{m}=43_{-5}^{+11}M_{\odot}$. The CMC simulations were carried out for different values of the BBH birth spin which are indicated by the shade of orange. The faintest to brightest lines correspond to birth spins of $[0, 0.1, 0.2, 0.5]$.
• Figure 4: Metrics from the spin transition study: the transition mass compared to the break location in terms of secondary mass of the mass-ratio distribution (left), cumulative density function (center), and fraction of events with $q\geq 0.6$ (right), below and above the spin-transition mass. As in Figure \ref{['fig:trans']}, for the CMC simulations, different shades of orange indicate different values of the BH birth spin.
• Figure 5: Comparison of the gap enforced inference with the flexible one and non-parametric results. The top panel uses BPL2P for the primary mass model and the bottom one SPL2P. The non-parametric (binned Gaussian process) results for GWTC-4 were reported in LIGOScientific:2025pvj and are obtained from their public data release: ligo_scientific_collaboration_2025_16911563. The black dotted lines demarcate the lower and upper edge of the PISN mass-gap inferred by Tong:2025wpz using their gap-inclusive model.