Evidence of the pair-instability gap from black-hole masses

Stellar theory predicts a forbidden range of black-hole masses between approximately 50 M_⊙ and 130 M_⊙ owing to pair-instability supernovae^1-7, but evidence for such a gap in the mass distribution from gravitational-wave astronomy has proved elusive. Early hints of a cut-off in black-hole masses at about 45 M_⊙ disappeared with the subsequent discovery of more massive binary black holes^8,9. 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). Although the gap is not present in the distribution of primary masses m₁ (the bigger of the two black holes in a binary system), it appears unambiguously in the distribution of secondary masses m₂, in which m₂ ≤ m₁. 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 in which 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 ¹²C(α, γ)¹⁶O at 300 keV to $260_{-108}^{+190}\mathrm{keV}\mathrm{barns}$ .