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

Abstract

Pair-instability should prevent the direct formation of black holes above about $50M_\odot$ 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 catalog, with a lower edge at $44.3^{+5.9}_{-3.5}\,M_\odot$. We also obtain a measurement of the ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction rate, yielding an $S$-factor of $268^{+195}_{-116}\,\mathrm{keV\,b}$, a parameter critical for modeling 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.