Aluminum Abundances, Deep Mixing and the Blue-Tail Second-Parameter Effect in the Globular Clusters M 3 and M 13

We explore the relatiohsip between deep mixing on the red-giant branch and the second parameter that gives rise to the extended blue tail seen on the horizontal branch of the globular cluster M 13. We use the [Al/Fe] values of 96 RGB stars and the [Na/Fe] values of 119 RGB stars in M 13 to follow the evolution of mixing in this cluster. The data are compared to an "instantaneous" mixing algorithm to predict the effects of deep mixing on the HB morphology. In addition, we present new data for six giants in the cluster M 3 and three in M 13. Our final results are consistent with deep mixing as a blue-tail second parameter. We also examine the question of overproducing sodium during deep mixing and suggest ways around this problem and observational tests that center around the s-process elements Sr, Y and Zr.