Evidence of the pair instability gap in the distribution of black hole masses

Abstract Stellar theory predicts a forbidden range of black-hole masses between ~50--130\,M_ 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 ~ 45\,M_ 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 45₋₄⁺⁵ M_ (90% credibility). While 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, where 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 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 ¹²C(α,γ)¹⁶O at 300keV to 256₋₁₀₄⁺¹⁹⁷ keV barns.