OXYGEN ABUNDANCES IN HALO GIANTS .4. THE OXYGEN-SODIUM ANTICORRELATION IN A SAMPLE OF 22 BRIGHT GIANTS IN M13

We have analyzed high resolution echelle spectra of nine bright M13 giants which, when added to those we have analyzed previously by similar techniques, bring our M13 sample size to 22. The sample is 88% complete from the red giant tip (at M(bol)0 = -3.6) to a point one bolometric magnitude fainter, and is presumably representative down to M(bol)0 = -2.1. We find that the brightest M13 giants are predominantly super oxygen poor ([O/Fe] approximately - 0.4 to - 0. 8) and correspondingly sodium rich ([Na/Fe] approximately +0.2 to +0.4). We argue that these super 0-poor stars are ''first ascent'' giants. The most straightforward way to understand (1) the decline in the average oxygen abundance as M13 stars approach the tip of the giant branch and (2) their anticorrelated oxygen and sodium abundances, is that they are the results of very deep mixing. In the case of the super 0-poor stars this idea requires that 90 percent of the oxygen atoms of the envelope be transformed into nitrogen. Since there are significant variations in the oxygen abundances of stars at the same point on the giant branch, such mixing must vary stochastically from star to star. Variable deep mixing is most likely to be the result of variable internal rotation. We have added Ni and the alpha elements Si, Ca, and Ti to our list of abundance determinations for all 22 M13 giants and seven giants in M3. We find: [Fe/H] is identical for the two clusters, the mean values of [Sc/Fe], [V/Fel, and [Ni/Fe] are close to zero for both clusters, and the alpha elements are overabundant by similar amounts ([el/Fe] approximately 0.2 to 0.3) in all stars. Despite the wide ranges in the observed 0 (greater-than-or-equal-to 1.0 dex) and Na (approximately 0. 8 dex) abundances, we find no correlation between the abundances of 0 or Na and the abundances of any of these other elements.