Globular Cluster Giant Branch Luminosity Functions: “Extra Stars” and “Deep Mixing”

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Abstract
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 mixing has often been invoked to account for the abundance anomalies observed in many bright Galactic globular cluster giants. Here we assume that it also adds fuel to the hydrogen-burning shell of a typical giant in some clusters 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 shell of a typical red giant in M5 and M30 from the number of extra stars in the red giant branch (RGB) luminosity functions for these two clusters. Presumably, extra red giants are common in Galactic globular clusters. M5 and M30 were chosen solely because the available luminosity functions for both were derived from an exceptionally large sample of stars in two colors: the RGB 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 significantly enriched in helium (ΔY ≈ 0.07) by the time it 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 ΔY ≈ 0.07, we can account for part, but only a small part, of the very 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 of the helium indicator delta suggests that the helium abundance is enhanced (ΔY = 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 M30, Y will be about 0.05 higher in the envelope of a typical M30 HB star than 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 lack of a "bump" on the RGB or the presence of a small bump in the wrong place, (2) the surprisingly bright horizontal branch, and (3) the anomalous values of both Δ 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 in some clusters, there are many interesting ramifications. For example, all horizontal branches may not have been created equal; some might well be brighter 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 mysteries 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 HB stars), the observed range in the helium estimator Δ at a constant metallicity, and the variations observed in the RGB "bumps" among otherwise similar clusters.