Gravitational waves reveal the pair-instability mass gap and constrain nuclear burning in massive stars (2509.04637v1)

Abstract: Stellar evolution theory predicts that electron--positron pair production in the cores of massive stars triggers unstable thermonuclear explosions that prevent the direct formation of black holes above about $50\,M_\odot$, creating a ``pair-instability gap''. Yet black holes have been detected above this mass with gravitational waves; such objects might be explained with uncertainties in the physics of massive stars and stellar collapse or with hierarchical mergers of black holes in stellar clusters. Hierarchical mergers are associated with large spins as predicted by general relativity, and isotropic spin orientations. Here we present strong evidence for the pair-instability mass gap in the LIGO--Virgo--KAGRA fourth transient catalog, with a lower edge at $45.3^{+6.5}{-4.8}\,M\odot$. We also obtain a measurement of the ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction rate, yielding an $S$-factor of $242.5^{+310.4}_{-101.5}\,\mathrm{keV\,b}$, a parameter critical for modeling helium burning and stellar evolution. The new data reveal two populations: a low-spin group with no black holes above the gap, consistent with direct stellar collapse, and a high-spin, isotropic group that extends across the full mass range and occupies the gap, consistent with hierarchical mergers. These findings confirm the role of pair-instability in shaping the black hole spectrum, establish a new link between gravitational-wave astronomy and nuclear astrophysics, and highlight hierarchical mergers and star cluster dynamics as key channels in the growth of black holes.