Abundance Anomalies and Rotational Evolution of Low Mass Red Giants: A Maximal Mixing Approach

(ABRIDGED) We use a fully self-consistent evolutionary code to follow the rotational evolution of red giants, making a comprehensive attempt to assess the role of rotationally induced mixing in the development of abundance anomalies in giants with a range of masses and metallicities in stellar clusters and the field. Unlike most previous work, we do not focus on the determination of combinations of mixing rate and depth that reproduce the data on a particular stellar type. Instead, we concentrate on the more fundamental problem of the simultaneous reproduction of the CNO surface patterns in both Population I and Population II giants using the same physics and models. A general result of all our models is that rotational mixing, although present in small amounts, is inefficient on the lower RGB independently of any inhibiting effect of composition barriers. Models with differentially rotating envelopes are able to reproduce the carbon isotope data on M67 giants with initial rotation rates adequate to their progenitors, but fail to do so for open clusters of larger turnoff mass as well as for metal-poor giants in the field and globular clusters. Possible solutions are discussed. Our favored scenario is one in which the overall strength of canonical extra mixing has been underestimated by existent derivations, but which additionally needs to be coupled with a much lower efficiency for rotational mixing among the rapidly rotating open cluster giants than in the slowly rotating ones in the field and globular clusters. We hypothesize that this last requirement is provided by the interaction between convection and rotation in the envelopes of giants, in the sense that rapidly rotating stars would develop much shallower angular velocity profiles in their envelopes than do slowly rotating stars.