2000AJ....120.1364C

We analyze high-resolution, high signal-to-noise ratio spectra of six red giant branch (RGB) stars in the globular cluster M3 (NGC 5272) and three in M13 (NGC 6205) that were obtained with the 4 m Mayall Telescope and echelle spectrometer on Kitt Peak. The spectra include lines of O, Na, Mg, Al, Si, Ca, Ti, V, Mn, Fe, and Ni. We also analyze the [Al/Fe] values of 96 RGB stars in M13 covering the brightest 3.5 mag, which include 66 measurements that were derived from moderate-resolution, low signal-to-noise ratio spectra obtained with the WIYN 3.5 m telescope and Hydra multiobject spectro graph, also on Kitt Peak. In addition, we compile from the literature and inspect the [Na/Fe] values of 119 RGB stars in M13. We test for bimodality in the [Al/Fe] and [Na/Fe] distributions using the KMM algorithm and find that the [Al/Fe] values in M13 are distributed bimodally at all points along the RGB that were observed, while the [Na/Fe] values are bimodal only over the brightest 2 mag. The ratios of Al-enhanced to Al-normal and Na-enhanced to Na-normal giants increase toward the tip of the RGB in M13, which is suggestive of deep mixing in this cluster. The limited M3 data exhibit a bimodal distribution of [Al/Fe] values and are suggestive of no deep mixing; however, they are too few to be conclusive. We further test for a relationship between deep mixing on the RGB and a second parameter that can create the extended blue tail seen along the horizontal branches of some clusters by using an ``instantaneous'' mixing algorithm, which we develop here. We conclude that the data for both clusters are consistent with deep mixing as a ``blue-tail second parameter'', and we suggest future observations to further constrain the results. Finally, we offer a solution to the problem of overproducing sodium during deep mixing that is based on the depletion of ²²Ne in asymptotic giant branch stars and suggest that pollution might best be traced by s-process elements in the Sr-Y-Zr peak.