Clearing the hurdle: The mass of globular cluster systems as a function
  of host galaxy mass
  Current observational evidence suggests that all large galaxies contain
globular clusters (GCs), while the smallest galaxies do not. Over what galaxy
mass range does the transition from GCs to no GCs occur? We investigate this
question using galaxies in the Local Group, nearby dwarf galaxies, and galaxies
in the Virgo Cluster Survey. We consider four types of statistical models: (1)
logistic regression to model the probability that a galaxy of stellar mass
$M_{\star}$ has any number of GCs; (2) Poisson regression to model the number
of GCs versus $M_{\star}$, (3) linear regression to model the relation between
GC system mass ($\log{M_{gcs}}$) and host galaxy mass ($\log{M_{\star}}$), and
(4) a Bayesian lognormal hurdle model of the GC system mass as a function of
galaxy stellar mass for the entire data sample. From the logistic regression,
we find that the 50% probability point for a galaxy to contain GCs is
$M_{\star}=10^{6.8}M_{\odot}$. From post-fit diagnostics, we find that Poisson
regression is an inappropriate description of the data. Ultimately, we find
that the Bayesian lognormal hurdle model, which is able to describe how the
mass of the GC system varies with $M_{\star}$ even in the presence of many
galaxies with no GCs, is the most appropriate model over the range of our data.
In an Appendix, we also present photometry for the little-known GC in the Local
Group dwarf Ursa Major II.
