# The HERBAL model: A hierarchical errors-in-variables Bayesian lognormal hurdle model for galactic globular cluster populations

**Authors:** Samantha C. Berek, Gwendolyn M. Eadie, Joshua S. Speagle, William E. Harris  
**arXiv:** [2306.14945](https://arxiv.org/abs/2306.14945)  
**Date:** 2023-06-26  
**Summary page:** https://www.summarizepaper.com/en/paper/2306.14945v1/

## Key points

- Relationship between galaxy stellar mass and size of globular cluster (GC) populations
- Well-established relationship for Milky Way-sized and larger galaxies
- Ambiguity for dwarf galaxies, evidence suggesting a downturn in GC population size at low galaxy masses
- Introduce new model called HERBAL to accurately represent relationship for dwarf galaxies
- HERBAL model considers two distinct populations: those with GCs and those without
- Takes into account various uncertainties, including measurement uncertainty, conversions, and scatter
- Applied HERBAL model to Local Group galaxies with maximal coverage of luminosity range
- At stellar mass $\log_{10}(M_*)=6.996$, approximately 50% of galaxies expected to host GC populations
- Expected mass of GC populations remains linear even for smallest galaxies
- Hierarchical nature of Bayesian HERBAL model allows estimation of galaxy masses and individual mass-to-light ratios using luminosity data within the framework
- Used model to recover accurate estimate of Milky Way's stellar mass
- Non-zero intrinsic scatter found with value of $0.59_{-0.21}^{+0.30}$ (95% credible interval)
- Importance of accounting for intrinsic scatter in future models emphasized

## Summary

The study focuses on the relationship between galaxy stellar mass and the size of their globular cluster (GC) populations. While this relationship is well-established for Milky Way-sized and larger galaxies, it becomes less clear for dwarf galaxies. In fact, there is evidence suggesting a downturn in GC population size at low galaxy masses for dwarf galaxies. To address this ambiguity, the authors introduce a new model called the Hierarchical ERrors-in-variables Bayesian lognormAL hurdle (HERBAL) model. This model aims to accurately represent the relationship between dwarf galaxies and their GC populations by considering two distinct populations: those that have GCs and those that do not. The HERBAL model takes into account various uncertainties, including measurement uncertainty, uncertainty in luminosity to stellar mass conversions, and intrinsic scatter. The researchers apply the HERBAL model to a sample of Local Group galaxies with maximal coverage of luminosity range. They find that at a stellar mass of $\log_{10}(M_*)=6.996$, approximately 50% of galaxies are expected to host globular cluster populations. Furthermore, they observe that the expected mass of GC populations remains linear even for the smallest galaxies. One notable advantage of the hierarchical nature of the Bayesian HERBAL model is its ability to estimate galaxy masses and individual mass-to-light ratios using luminosity data within the model framework. Additionally, the authors use their model to recover an accurate estimate of the Milky Way's stellar mass. Considering their assumed error model, they find a non-zero intrinsic scatter with a value of $0.59_{-0.21}^{+0.30}$ (95% credible interval). This finding highlights the importance of accounting for intrinsic scatter in future models. In conclusion, this study presents a refined understanding of the relationship between galaxy stellar mass and their globular cluster populations, particularly focusing on dwarf galaxies.