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

Wenyu Xin, Xiaokun Hou, Xianfei Zhang, Shaolan Bi, Gang Zhao

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$(α, γ)^{16}$O and $^{16}$O+$^{16}$O reaction rates on the final fate. Varying the $^{12}$C$(α, γ)^{16}$O reaction rate by $-3 σ$ to $+3σ$, 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$(α, γ)^{16}$O reaction at 300 keV of $S_{300} \simeq$ 137.6 - 263.4 keV barn.

Constraints on the $^{12}$C$(α, γ)^{16}$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 M. Motivated by these findings, we compute low-metallicity () helium star models with MESA and systematically explore the effect of uncertainties in the CO and O+O reaction rates on the final fate. Varying the CO reaction rate by to , we find that the predicted BH mass gap shifts from M to M. In contrast, scaling the O+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), and shifts the upper edge by more than 10 M. 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 CO reaction at 300 keV of 137.6 - 263.4 keV barn.
Paper Structure (10 sections, 7 equations, 5 figures, 3 tables)

This paper contains 10 sections, 7 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Models and Input Physics
  3. Evolution of PPISN and the BH mass gap
  4. Maximum BHs
  5. BH Mass Gap and the Effect of $^{16}$O+$^{16}$O Reaction Rate
  6. Constraints the $^{12}$C$(\alpha, \gamma)^{16}$O and $^{16}$O+$^{16}$O reaction rates
  7. RBF model
  8. Constrain reaction rates with Bayesian model
  9. Discussion
  10. Conclusion

Figures (5)

  • Figure 1: The $\sigma_{12C\alpha}$ and $f_{\rm 16O}$ computed in the stellar models. The red points show the parameter grid computed in Farmer_2020 and the black crosses show those computed in this work.
  • Figure 2: The BH masses as a function of initial He core mass. Green points, blue stars, and red diamonds denote the results from Farmer_20202022ApJ...937..112F and 2023RAA....23a5014X. It should be noted that 2023RAA....23a5014X adopted $Z=10^{-3}$ while other studies employ $Z=10^{-5}$. These studies also adopt different reaction rate tables. Farmer_2020 used STARLIB tables for both 3$\alpha$ and $^{12}$C$(\alpha, \gamma)^{16}$O reaction rates. 2022ApJ...937..112F employs NACRE tables for the 3$\alpha$ reaction but also uses a high-resolution table refined in 2022ApJ...924...39M. In 2023RAA....23a5014X, the 3$\alpha$ reaction rate is from JINA REACLIB, while the $^{12}$C$(\alpha, \gamma)^{16}$O reaction rate is from 2002ApJ...567..643K.
  • Figure 3: The PISN BH mass gap as a function of $\sigma_{12C\alpha}$. The orange region indicates that the BHs are formed from CCSNe below the mass gap or PPISNe, while the light blue region represents that the BHs are formed by the CCSNe above the mass gap. The white region indicates the mass gap formed due to the PISNe explosion. Left: The red, blue, and green lines represent PPISN/PISN and PISN/CC boundaries from this work, Farmer_2020, and 2022ApJ...924...39M, respectively. The gray region represents an interval that is excluded for all considered $\sigma_{12C\alpha}$s. Right: The red, blue, and green lines represent the results for $f_{\rm 16O}$ = 0.1, 1, and 10, respectively.
  • Figure 4: Performance of the RBF model as a computational substitute for the discrete MESA calculations in determining the lower edge of the mass gap. Left panel: Color map of the RBF-predicted $m$ over the $\sigma_{12C\alpha}-\sigma_{16O}$ space. Black contour lines denote iso-$m$ levels. Right panel: One-dimensional slices of the RBF surface at fixed values of $\sigma_{16O}=-1,\,0,$ and $1$. Solid curves represent the RBF predictions, while symbols show the corresponding MESA grid results.
  • Figure 5: Posterior distribution of the $^{12}$C$(\alpha, \gamma)^{16}$O and $^{16}$O+$^{16}$O reaction rates, inferred using the lower edge of mass gap from 2025arXiv250904637A ($m_0 = 45.3^{+6.5}_{-6.8}$). The top and right panels show the marginalized posterior distributions of $\sigma_{12C\alpha}$ and $\sigma_{16O}$, respectively, while the lower-left panel displays their joint posterior distribution. The blue dashed lines indicate the posterior medians, and the red dashed lines mark the 16th and 84th percentiles.