Pair-instability should prevent the direct formation of black holes above about 50M⊙ 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 44.3−3.5+5.9M⊙. We also obtain a measurement of the 12C(α,γ)16O reaction rate, yielding an S-factor of 268−116+195keVb, 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.
@article{arxiv.2509.04637,
title = {Gravitational-wave constraints on the pair-instability mass gap and nuclear burning in massive stars},
author = {Fabio Antonini and Isobel Romero-Shaw and Thomas Callister and Fani Dosopoulou and Debatri Chattopadhyay and Yonadav Barry Ginat and Mark Gieles and Michela Mapelli},
journal= {arXiv preprint arXiv:2509.04637},
year = {2026}
}