Globular cluster giant branch luminosity functions: "Extra stars" and "deep mixing"

We explore the possibility that "deep mixing" is the reason that there are "too many" red giants in the Galactic globular clusters M5 and M30. Deep mi xing has often been invoked to account for the abundance anomalies observed in many bright Galactic globular cluster giants. Here we assume that it al so adds fuel to the hydrogen-burning shell of a typical giant in some clust ers and returns helium to the envelope above. We use a simple mixing model to estimate how much extra fuel has been added to the hydrogen-burning shel l of a typical red giant in M5 and M30 from the number of extra stars in th e red giant branch (RGB) luminosity functions for these two clusters. Presu mably, extra red giants are common in Galactic globular clusters. M5 and M3 0 were chosen solely because the available luminosity functions for both we re derived from an exceptionally large sample of stars in two colors: the R GB luminosity functions are especially well defined and well normalized to unevolved main-sequence stars. If deep mixing is the reason that there are too many M5 giants, the number of extra giants suggests that the envelope of a typical M5 star should be s ignificantly enriched in helium (Delta Y approximate to 0.07) by the time i t reaches the tip of the giant branch. Hence, deep mixing may be (at least part of) the reason that M5 has a surprisingly blue horizontal branch (HB) for a moderately metal-rich cluster. If deep mixing occurs and Delta Y appr oximate to 0.07, we can account for part, but only a small part, of the ver y low value of R-and the surprisingly low estimate for Y-that Sandquist et al. found from their B-band luminosity function. Sandquist et al.'s value o f the helium indicator delta suggests that the helium abundance is enhanced (Delta Y = 0.04 +/- 0.02) in HB stars at the blue edge of the instability strip. If deep mixing accounts for the "extra" giants that have been observed in M 30, Y will be about 0.05 higher in the envelope of a typical M30 HE star th an it was when that star left the main sequence. In addition to accounting for the extra M30 giants, deep mixing can give a good account of (1) the la ck of a "bump" on the RGB or the presence of a small bump in the wrong plac e, (2) the surprisingly bright horizontal branch, and (3) the anomalous val ues of both Delta and R. The abundances of the light elements suggest that deep mixing is much more common in some clusters than in others and more extensive in some stars in a cluster than in others. If deep mixing does add fuel to evolving giants i n some clusters, there are many interesting ramifications. For example, all horizontal branches may not have been created equal; some might well be br ighter than others. Sweigart and Sweigart & Catelan have recently described how mixing helium out into the envelope of a red giant may solve a number of cluster blue star mysteries. We point out a number of additional mysteri es that might be solved by looking at the fuel that is mixed down into the hydrogen-burning shell: e.g., the large range in the values that have been observed for R (the ratio of bright giants to HE stars), the observed range in the helium estimator Delta at a constant metallicity, and the variation s observed in the RGB "bumps" among otherwise similar clusters.