2003MNRAS.340..763S

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 Al₂O₃ 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 ¹⁸O(p,α)¹⁵N reaction rate typically causes an error in the theoretical ¹⁶O/¹⁸O ratio of ≃+20/- 5 per cent. The error of the ¹⁶O/¹⁷O prediction is 10-40 per cent depending on the stellar mass, and is persistently dominated by the comparatively small uncertainty of the ¹⁶O(p,γ)¹⁷F reaction. With the new estimates on reaction rate uncertainties by the NACRE compilation, the p-capture reactions ¹⁷O(p,α)¹⁴N and ¹⁷O(p,γ)¹⁸F have virtually no impact on theoretical predictions for stellar mass ≤1.5 M_☉. However, the uncertainty in ¹⁷O(p,α)¹⁴N has an effect comparable to or greater than that of ¹⁶O(p,γ)¹⁷F 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.