A Bayesian hierarchical model for the galaxy mass - globular cluster system mass scaling relation for low-mass galaxies

Oregon Convention Center 

Galaxy stellar mass is known to be monotonically related to the size of the galaxy's globular cluster (GC) population, but the relation becomes ambiguous for dwarf galaxies. Smaller dwarfs are increasingly likely to have no GCs, and these zeros cannot be easily incorporated into linear models. We introduce the hierarchical errors-in variables Bayesian lognormal hurdle (HERBAL) model to represent the relationship between dwarf galaxies and their GC populations. Our model thoroughly accounts for all uncertainties, including measurement uncertainty, uncertainty in luminosity to stellar mass conversions, and intrinsic scatter. The hierarchical nature of our Bayesian model also allows us to estimate galaxy masses and individual mass-to-light ratios from luminosity data. We find that 50% of galaxies are expected to host globular cluster populations at a stellar mass of log10(M∗) = 6.996, and that the expected mass of GC populations remains linear down to the smallest galaxies. Our hierarchical model recovers an accurate estimate of the Milky Way stellar mass. Under our assumed error model, we find a non-zero intrinsic scatter of 0.59 that should be accounted for in future models.