It is now widely accepted that globular cluster red giant branch (RGB) stars owe their strange abundance patterns to a combination of pollution from progenitor stars and in situ extra mixing. In this hybrid theory a first generation of stars imprints abundance patterns into the gas from which a second generation forms. The hybrid theory suggests that extra mixing is operating in both populations and we use the variation of [C/Fe] with luminosity to examine how efficient this mixing is. We investigate the observed RGBs ofM3, M13, M92, M15, and NGC 5466 as a means to test a theory of thermohaline mixing. The second parameter pair M3 and M13 are of intermediate metallicity and our models are able to account for the evolution of carbon along the RGB in both clusters, although in order to fit the most carbon-depleted main-sequence stars in M13 we require a model whose initial [C/Fe] abundance leads to a carbon abundance lower than is observed. Furthermore, our results suggest that stars in M13 formed with some primary nitrogen (higher C+N+O than stars in M3). In the metal-poor regime only NGC 5466 can be tentatively explained by thermohaline mixing operating in multiple populations. We find thermohaline mixing unable to model the depletion of [C/Fe] with magnitude in M92 and M15. It appears as if extra mixing is occurring before the luminosity function bump in these clusters. To reconcile the data with the models would require first dredge-up to be deeper than found in extant models.
Angelou, G. C., Stancliffe, R. J., Church, R. P., Lattanzio, J. C., & Smith, G. H. (2012). The role of thermohaline mixing in intermediate- and low-metallicity globular clusters. The Astrophysical Journal, 749(2), 1 - 12. https://doi.org/10.1088/0004-637X/749/2/128