We conduct a series of comparisons between spectroscopic and photometric observations of globular clusters and stellar models to examine their predictive power. Data from medium-to-high resolution spectroscopic surveys of lithium allow us to investig
ate first dredge-up and extra mixing in two clusters well separated in metallicity. Abundances at first dredge-up are satisfactorily reproduced but there is preliminary evidence to suggest that the models overestimate the luminosity at which the surface composition first changes in the lowest-metallicity system. Our models also begin extra mixing at luminosities that are too high, demonstrating a significant discrepancy with observations at low metallicity. We model the abundance changes during extra mixing as a thermohaline process and determine that the usual diffusive form of this mechanism cannot simultaneously reproduce both the carbon and lithium observations. Hubble Space Telescope photometry provides turnoff and bump magnitudes in a large number of globular clusters and offers the opportunity to better test stellar modelling as function of metallicity. We directly compare the predicted main-sequence turn-off and bump magnitudes as well as the distance-independent parameter $Delta M_V ~^{rm{MSTO}}_{rm{bump}}$. We require 15 Gyr isochrones to match the main-sequence turn-off magnitude in some clusters and cannot match the bump in low-metallicity systems. Changes to the distance modulus, metallicity scale and bolometric corrections may impact on the direct comparisons but $Delta M_V ~^{rm{MSTO}}_{rm{bump}}$, which is also underestimated from the models, can only be improved through changes to the input physics. Overshooting at the base of the convective envelope with an efficiency that is metallicity dependent is required to reproduce the empirically determined value of $Delta M_V ~^{rm{MSTO}}_{rm{bump}}$.
It is now widely accepted that globular cluster red giant branch 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 imprint abunda
nce 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 red giant branches of M3, 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.
We provide a brief review of thermohaline physics and why it is a candidate extra mixing mechanism during the red giant branch (RGB). We discuss how thermohaline mixing (also called $delta$ $mu$ mixing) during the RGB due to helium-3 burning, is more
complicated than the operation of thermohaline mixing in other stellar contexts (such as following accretion from a binary companion). We try to use observations of carbon depletion in globular clusters to help constrain the formalism and the diffusion coefficient or mixing velocity that should be used in stellar models. We are able to match the spread of carbon depletion for metal poor field giants but are unable to do so for cluster giants, which may show evidence of mixing prior to even the first dredge-up event.
Recent work has proposed that a merger event between a red-giant and a He white dwarf may be responsible for the production of R-stars (Izzard et al, 2007). We investigate the proposed evolution and nucleosynthesis of such a model. We simulate the hy
pothesized late ignition of the core flash by increasing the neutrino losses until the ignition occurs sufficiently far from the centre that the subsequent evolution produces dredge-up of carbon to the extent that the post-flash object is a carbon star. Detailed nucleosynthesis is performed within this approximation, and we show that the overall properties are broadly consistent with the observations. Details will depend on the dynamics of the merger event.
