Constraints on the ${}^{12}$C$(\hat{I}\pm ,{\hat{I}}^3{)}^{16}$O and ${}^{16}$O+${}^{16}$O Reaction Rates from Binary Black Holes Detected via Gravitational Wave Signals

Abstract

Gravitational-wave observations of binary black hole (BH) mergers provide a novel avenue for testing massive-star evolution and the resulting BH mass spectrum. Recent population analyses under the hierarchical-merger hypothesis have offered evidence for the BH mass gap and inferred its lower edge to $\sim 44-68$ M${}_{\odot }$. Motivated by these findings, we compute low-metallicity ($Z=10^{-5}$) helium star models with MESA and systematically explore the effect of uncertainties in the ${}^{12}$C$(\hat{I}\pm ,{\hat{I}}^3{)}^{16}$O and ${}^{16}$O+${}^{16}$O reaction rates on the final fate. Varying the ${}^{12}$C$(\hat{I}\pm ,{\hat{I}}^3{)}^{16}$O reaction rate by $-3\ddot{I}ƒ$ to $+3\ddot{I}ƒ$, we find that the predicted BH mass gap shifts from $\sim 104-184$ M${}_{\odot }$ to $\sim 45-135$ M${}_{\odot }$. In contrast, scaling the ${}^{16}$O+${}^{16}$O reaction rate by global factors of 0.1, 1, and 10 has only a modest effect on the lower edge of the BH mass gap (less than 5 M${}_{\odot }$), and shifts the upper edge by more than 10 M${}_{\odot }$. Using the predictions of our models together with the literature estimates for the lower edge of the BH mass gap, we constrain the astrophysical S factor of ${}^{12}$C$(\hat{I}\pm ,{\hat{I}}^3{)}^{16}$O reaction at 300 keV of $S_{300}\simeq$ 137.6 - 263.4 keV barn.