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

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$(\alpha, \gamma)^{16}$O and $^{16}$O+$^{16}$O reaction rates on the final fate. Varying the $^{12}$C$(\alpha, \gamma)^{16}$O reaction rate by $-3 \sigma$ to $+3\sigma$, we find that the predicted BH mass gap shifts from $\sim104 - 184$ M$_\odot$ to $\sim45 - 135$ 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$(\alpha, \gamma)^{16}$O reaction at 300 keV of $S_{300} \simeq$ 137.6 - 263.4 keV barn.