Low-mass failed supernovae and the $10\,M_{\odot}$ peak in the merging black hole mass distribution

Abstract

Gravitational-wave observations reveal that the rate of merging black holes drops by $\sim2$ orders of magnitude from component masses $\sim 10\,M_{\odot}$ to $\sim 15\,M_{\odot}$. The increased compactness of the black hole progenitor cores may contribute to the $\sim 10\,M_{\odot}$ overdensity, but cannot fully explain the rate difference. In this paper, we consider the possibility that the overdensity is reinforced by supernova processes that result in efficient black hole formation from direct collapse in a narrow range around $10\, M_{\odot}$. We extend previous studies by considering a distinct subpopulation of failed-supernovae black holes, possibly separated by a gap in the primary mass distribution from the rest of the population. Using 153 observations from the latest GWTC-4.0 catalog, we confirm a strong peak in the primary mass distribution at $10\,M_{\odot}$, with a peak rate density of $7.36_{-3.11}^{+6.35}$ $M_{\odot}^{-1}\mathrm{yr}^{-1} \mathrm{Gpc}^{-3}$. The rate drops sharply and becomes consistent with zero at the 90 % level for primary mass $m_1\in (12.0, 16.1)\, M_{\odot}$, then rises again to confidently nonzero values above $\sim 16\,M_{\odot}$ before falling at higher masses. Our results reveal structure in the mass distribution in the $10-20\,M_{\odot}$ range, with rate changes of multiple orders of magnitude across a few solar masses, consistent with a distinct population of failed-supernova black holes.

Figures (13)

• Figure 1: Posterior predictive distribution for the differential rate for the primary (top) and secondary (bottom) binary component. Results for the failed-sn+broken powerlaw model are shown in red-orange and results for failed-sn + powerlaw + peak are shown in blue. The 90% symmetric credible region is shaded, while the median is marked with the corresponding color.
• Figure 2: The inferred differential rate at $m_1=13\,M_{\odot }$ (effectively a vertical cross-section of Fig. \ref{['fig:compare-bpl-plp-fsn']}) for the failed-sn+broken powerlaw and failed-sn + powerlaw + peak models in pink and blue respectively. We class all samples below $10^{-3}$$M_{\odot}^{-1}\mathrm{yr}^{-1} \mathrm{Gpc}^{-3}$ into a single histogram bin. The inset zooms in near the $y$-axis and vanishing rate.
• Figure 3: Marginalized posteriors on key masses related to the separations of the low- and high-mass components for the failed-sn + powerlaw + peak (blue) model and failed-sn+broken powerlaw (red-orange) models. We show $\mu^f$, the mean of the failed-sn peak, $m^f_{\max, \rm eff}$, the effective failed-sn maximum mass (see text), and $m^u_{\rm turn}$, the turnover mass for the high-mass component. The red dashed lines mark the "$x=y$" lines where the two quantities on each axis are equal. Contours mark $50\%$ and $90\%$ highest-probability credible regions.
• Figure 4: Marginalized posterior for the source-frame primary and secondary masses for the 153 BBHs used in this analysis under two different choices for a population prior. Left: the population prior is not consistent with a gap, $m^u_{\rm turn} < 10\, M_{\odot}$. Right: The population prior is consistent with a gap, $m^u_{\rm turn} > 15\,M_{\odot}$. Contours show the 90% posterior credible regions and stars correspond to the median. The shaded band denotes $(12, 16)\, M_{\odot}$, the approximate gap region under the failed-sn + powerlaw + peak model. Dashed lines denote constant mass ratio contours, $q=1.0, 0.7,$ and $0.5$. Most events are depicted in gray, with colors highlighting the $6$ events with the largest posterior support inside the gap. These events are, in order, GW190708_232457 LIGOScientific:2020iblLIGOScientific:2021usb, GW230605_065343, GW230706_104333, GW230723_101834, GW231110_040320, GW231118_090602 LIGOScientific:2025slb. Two BBHs with low masses (bottom left of each panel) do not appear by eye to belong to the $10\,M_{\odot}$ subpopulation; we discuss them in more detail in App. \ref{['app:low-mass-sources']}.
• Figure 5: Inferred distribution for the binary the mass ratio $q$ (left) and the effective inspiral spin $\chi_{\rm eff}$ (right) for the failed-sn and powerlaw + peak subpopulations of the failed-sn + powerlaw + peak model in light and dark blue respectively.