Nuclear reaction rate uncertainties and astrophysical modeling: Carbon yields from low-mass giants

Abstract

Calculations that demonstrate the influence of three key nuclear reaction rates on the evolution of asymptotic giant branch stars have been carried out. We study the case of a star with an initial mass of $2\phantom{\rule{0.3em}{0ex}}{M}_{\ensuremath{\bigodot}}$ and a metallicity of $Z=0.01$, somewhat less than the solar metallicity. The dredge-up of nuclear processed material from the interior of the star and the yield predictions for carbon are sensitive to the rate of the $^{14}\mathrm{N}$$(p,\ensuremath{\gamma})$$^{15}\mathrm{O}$ and triple-\ensuremath{\alpha} reactions. These reactions dominate the H- and He-burning shells of stars in this late evolutionary phase. Published uncertainty estimates for each of these two rates propagated through stellar evolution calculations cause uncertainties in carbon enrichment and yield predictions of about a factor of 2. The other important He-burning reaction, $^{12}\mathrm{C}$$(\ensuremath{\alpha},\ensuremath{\gamma})$$^{16}\mathrm{O}$, although associated with the largest uncertainty in our study, does not have a significant influence on the abundance evolution compared with other modeling uncertainties. This finding remains valid when the entire evolution from the main sequence to the tip of the asymptotic giant branch is considered. We discuss the experimental sources of the rate uncertainties addressed here and give some outlooks for future work.