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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.16169 |
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| _version_ | 1866915684346232832 |
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| author | Mukhamedzhanov, A. M. |
| author_facet | Mukhamedzhanov, A. M. |
| contents | A Bayesian analysis of the astrophysical $S$ factor for the $^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion reaction is presented, based on available experimental information at carbon--carbon relative energies $E \gtrsim 2~\mathrm{MeV}$, including direct measurements, indirect Coulomb-renormalized Trojan Horse Method (THM) results, and recent inverse-kinematics data. The Bayesian inference is performed on the quantity $\log_{10}S^{*}(E)$ rather than on $S^{*}(E)$ itself, which naturally accommodates the wide dynamic range of the data and leads to approximately Gaussian uncertainties. The logarithm of the astrophysical factor is parametrized by a quadratic polynomial in energy, and the posterior distribution of the fit coefficients is determined using a weighted Bayesian regression. From this posterior, a global median $S^{*}(E)$ curve is constructed, and the associated covariance matrix is used to define a low/medium/high (LO/MED/HI) band corresponding to a $68\%$ credible interval.
Particular emphasis is placed on the extrapolation below $E_{\mathrm{cm}}=2~\mathrm{MeV}$, where the fusion reaction rate is most relevant for stellar carbon burning. At $E_{\mathrm{cm}}=1.5~\mathrm{MeV}$, the posterior distribution yields $S_{\mathrm{global}}^{*}(1.5~\mathrm{MeV})= \left(2.13^{+0.01}_{-0.01}\right)\times10^{16}\,\mathrm{keV\,b}, $ corresponding to a $68\%$ credible interval. The extracted result is consistent with recent inverse-kinematics measurements and with Coulomb-corrected Trojan Horse Method constraints, providing a tightly constrained estimate of the $^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion $S$ factor in the energy region relevant for stellar carbon burning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16169 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian Smooth-Fit Extrapolation of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ Astrophysical $S$ Factor Mukhamedzhanov, A. M. Solar and Stellar Astrophysics A Bayesian analysis of the astrophysical $S$ factor for the $^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion reaction is presented, based on available experimental information at carbon--carbon relative energies $E \gtrsim 2~\mathrm{MeV}$, including direct measurements, indirect Coulomb-renormalized Trojan Horse Method (THM) results, and recent inverse-kinematics data. The Bayesian inference is performed on the quantity $\log_{10}S^{*}(E)$ rather than on $S^{*}(E)$ itself, which naturally accommodates the wide dynamic range of the data and leads to approximately Gaussian uncertainties. The logarithm of the astrophysical factor is parametrized by a quadratic polynomial in energy, and the posterior distribution of the fit coefficients is determined using a weighted Bayesian regression. From this posterior, a global median $S^{*}(E)$ curve is constructed, and the associated covariance matrix is used to define a low/medium/high (LO/MED/HI) band corresponding to a $68\%$ credible interval. Particular emphasis is placed on the extrapolation below $E_{\mathrm{cm}}=2~\mathrm{MeV}$, where the fusion reaction rate is most relevant for stellar carbon burning. At $E_{\mathrm{cm}}=1.5~\mathrm{MeV}$, the posterior distribution yields $S_{\mathrm{global}}^{*}(1.5~\mathrm{MeV})= \left(2.13^{+0.01}_{-0.01}\right)\times10^{16}\,\mathrm{keV\,b}, $ corresponding to a $68\%$ credible interval. The extracted result is consistent with recent inverse-kinematics measurements and with Coulomb-corrected Trojan Horse Method constraints, providing a tightly constrained estimate of the $^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion $S$ factor in the energy region relevant for stellar carbon burning. |
| title | Bayesian Smooth-Fit Extrapolation of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ Astrophysical $S$ Factor |
| topic | Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2512.16169 |