Proton-capture nucleosynthesis in globular cluster red giant stars

Observational evidence suggests that many of the variations of the surface abundances of light- to intermediate-mass elements (A < 28) in globular cluster red giant branch (RGB) stars can be attributed to noncanonical mixing between the surface and the deep stellar interior during the RGB phase. As a first step to studying this mixing in more detail, we have combined a large nuclear reaction network with four detailed stellar evolutionary sequences of different metallicities in order to follow the production and destruction of the C, N, O, Ne, Na, Mg, and Al isotopes around the hydrogen-burning shell (H shell) of globular cluster RGB stars. The abundance distributions determined:by this method allow for the variation in the temperature and density around the H shell as well as for the dependence on both the stellar luminosity and cluster metallicity. Because our nuclear reaction network operates separately from the stellar evolution code, we are able to more readily explore the effects of the uncertainties in the reaction rates on the calculated abundances. We discuss implications of our results for mixing in the context of the observational data. Our results are qualitatively consistent with the observed C versus N, O versus N, Na versus O, and Al versus O anticorrelations and their variations with both luminosity and metallicity. We see evidence for variations in Na without requiring changes in O, independent of metallicity, as observed by Norris and Da Costa in 1995 and Briley and coworkers in 1997. Also, we derive C-12/C-13 ratios near the observed equilibrium value of 4 for all sequences and predict the temperature-dependent O-16/O-17 equilibrium ratio based on new data for the O-17(p, alpha)N-14 reaction rate. Additionally, we discuss the Mg isotopic abundances in light of the recent observations by Shetrone of M13 and NGC 6752.