Oxygen isotopic ratios in first dredge‐up red giant stars and nuclear reaction rate uncertainties revisited

We describe a general yet simple method to analyse the propagation of nuclear reaction rate uncertainties in a stellar nucleosynthesis and mixing context. The method combines post‐processing nucleosynthesis and mixing calculations with a Monte Carlo scheme. With this approach we reanalyse the dependence of theoretical oxygen isotopic ratio predictions in first dredge‐up red giant branch stars in a systematic way. Such predictions are important to the interpretation of pre‐solar Al 2 O 3 grains from meteorites. The reaction rates with uncertainties were taken from the NACRE compilation of Angulo et al. We include seven reaction rates in our systematic analysis of stellar models with initial masses from 1 to 3 M ⊙ . We find that the uncertainty of the 18 O(p, α) 15 N reaction rate typically causes an error in the theoretical 16 O/ 18 O ratio of ≃+20/− 5 per cent. The error of the 16 O/ 17 O prediction is 10–40 per cent depending on the stellar mass, and is persistently dominated by the comparatively small uncertainty of the 16 O(p, γ) 17 F reaction. With the new estimates on reaction rate uncertainties by the NACRE compilation, the p‐capture reactions 17 O(p, α) 14 N and 17 O(p, γ) 18 F have virtually no impact on theoretical predictions for stellar mass ≤1.5 M ⊙ . However, the uncertainty in 17 O(p, α) 14 N has an effect comparable to or greater than that of 16 O(p, γ) 17 F for masses >1.5 M ⊙ , where core mixing and subsequent envelope mixing interact. In these cases where core mixing complicates post‐dredge‐up surface abundances, uncertainty in other reactions have a secondary but noticeable effect on surface abundances.