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 $44.3_{-3.5}^{+5.9}{M}_{\odot }$ . We also obtain a measurement of the ¹²C(α, γ)¹⁶O reaction rate, yielding an S-factor of $268_{-116}^{+195}\mathrm{keV\; b}$ , 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.