Gravitational-wave constraints on the pair-instability mass gap and nuclear burning in massive stars

Pair instability should prevent the direct formation of black holes above about 50 M ⊙ , creating a ‘pair-instability’ mass gap. Yet gravitational-wave observations have detected black holes in this mass range. These systems can be explained with uncertainties in massive-star evolution, or hierarchical mergers in stellar clusters, which are expected to produce large spins with isotropic orientations. Here we present evidence for the pair-instability mass gap in the LIGO–Virgo–KAGRA fourth transient catalogue, with a lower edge at 44.3-3.5+5.9\,M 44 . 3 − 3.5 + 5.9 M ⊙ . We also obtain a measurement of the 12 C(α, γ) 16 O reaction rate, yielding an S -factor of 268₋₁₁₆⁺¹⁹⁵\,keV\; b 26 8 − 116 + 195 keV b , a parameter critical for modelling helium burning and stellar evolution. The data reveal two populations: a low-spin group with no black holes above the gap, and a high-spin, isotropic group that extends across the full mass range and occupies the gap, consistent with hierarchical mergers. These findings are consistent with pair instability playing a role in shaping the black hole mass spectrum, point to a connection between gravitational-wave astronomy and nuclear astrophysics, and highlight dense stellar clusters as key environments in the growth of black holes.