Evidence of the pair instability gap from black hole masses

Abstract

Stellar theory predicts a forbidden range of black-hole masses between $\sim 50$--$130M_{\odot }$ due to pair-instability supernovae, but evidence for such a gap in the mass distribution from gravitational-wave astronomy has proved elusive. Early hints of a cutoff in black-hole masses at $\sim 45M_{\odot }$ disappeared with the subsequent discovery of more massive binary black holes. Here, we report evidence of the pair-instability gap in LIGO--Virgo--KAGRA's fourth gravitational wave transient catalog (GWTC-4), with a lower boundary of $44_{-4}^{+5}{M}_{\odot }$ (90\% credibility). While the gap is not present in the distribution of \textit{primary} masses $m_1$ (the bigger of the two black holes in a binary system), it appears unambiguously in the distribution of \textit{secondary} masses $m_2$, where $m_2\le m_1$. The location of the gap lines up well with a previously identified transition in the binary black-hole spin distribution; binaries with primary components in the gap tend to spin more rapidly than those below the gap. We interpret these findings as evidence for a subpopulation of hierarchical mergers: binaries where the primary component is the product of a previous black-hole merger and thus populates the gap. Our measurement of the location of the pair-instability gap constrains the $S$-factor for ${}^{12}\mathrm{C}(\hat{\mathrm{I}}\pm ,{\hat{\mathrm{I}}}^3{)}^{16}\mathrm{O}$ at 300keV to $260_{-108}^{+190}$ keV barns.

Nature (2026)