Carbon-Reaction Constraints on Stellar Evolution: White-Dwarf Heating, Carbon-Burning Products, and Black-Hole Masses

Abstract

The effects of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion and ${}^{12}\mathrm{C}(α,γ){}^{16}\mathrm{O}$ capture on stellar heating, composition, and black-hole masses are examined. Rates from a published Bayesian analysis of carbon fusion are used in calculations with MESA. In an accreting carbon--oxygen white dwarf, the Bayesian rates move the point at which nuclear heating equals combined neutrino and surface photon losses to slightly larger stellar masses and higher central temperatures and densities. At an accretion rate of $10^{-7}\,M_\odot\,\mathrm{yr}^{-1}$, the Bayesian median gives a central temperature approximately $2.57\%$ higher and a central density $18.9\%$ higher than the calculation using the standard CF88 rate. A separate calculation follows carbon burning in an initially $20\,M_\odot$, $Z=0.0142$ star. Relative to the CF88 rate with MESA's standard division between proton and alpha channels, the Bayesian-median rate with the proton-to-alpha ratio of Yang et al. increases the neon-20 mass remaining at central carbon depletion by $10.8\%$ and decreases the sodium-23 mass by $28.7\%$. For helium capture on carbon, the nuclear constraint $S_{\rm tot}(300\,\mathrm{keV})=118\pm17\,\mathrm{keV\,b}$ is applied to the published $Z=10^{-5}$ stellar models of Farag et al. Linear interpolation gives a maximum black-hole mass below the pair-instability gap of approximately $61.5$--$77.4\,M_\odot$ within the assumptions of those models. New MESA calculations at $Z=0.00142$ give smaller bound masses before collapse. Differences in the stellar assumptions prevent attributing the difference between the two curves to metallicity alone.