Clearing the hurdle: The mass of globular cluster systems as a function of host galaxy mass

TL;DR

This study investigates how the presence and mass of globular cluster systems in galaxies depend on galaxy mass, identifying a transition point around 10^6.8 solar masses where galaxies start to host GCs.

Contribution

It introduces a Bayesian lognormal hurdle model to accurately describe the relationship between galaxy mass and globular cluster system mass, especially accounting for galaxies with no GCs.

Findings

50% probability of hosting GCs at galaxy mass of 10^6.8 M_sun

Poisson regression was found unsuitable for the data

Bayesian hurdle model best describes the data across galaxy masses

Abstract

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.