Discovery of Two Ultra-Diffuse Galaxies with Unusually Bright Globular Cluster Luminosity Functions via a Mark-Dependently Thinned Point Process (MATHPOP)

TL;DR

This paper introduces extsc{Mathpop}, a new statistical method for accurately inferring globular cluster counts and luminosity functions in ultra-diffuse galaxies, addressing uncertainties and revealing unusually bright GCLFs in some galaxies.

Contribution

extsc{Mathpop} is a novel mark-dependent thinned point process that jointly infers GC counts and GCLFs, improving over traditional methods by handling uncertainties and minimal assumptions.

Findings

Identified two galaxies with GCLF turnover points brighter than the canonical value.

Validated extsc{Mathpop} through simulations and comparison with standard methods.

Detected significant brightness deviations with high statistical confidence.

Abstract

We present \textsc{Mathpop}, a novel method to infer the globular cluster (GC) counts in ultra-diffuse galaxies (UDGs) and low-surface brightness galaxies (LSBGs). Many known UDGs have a surprisingly high ratio of GC number to surface brightness. However, standard methods to infer GC counts in UDGs face various challenges, such as photometric measurement uncertainties, GC membership uncertainties, and assumptions about the GC luminosity functions (GCLFs). \textsc{Mathpop} tackles these challenges using the mark-dependent thinned point process, enabling joint inference of the spatial and magnitude distributions of GCs. In doing so, \textsc{Mathpop} allows us to infer and quantify the uncertainties in both GC counts and GCLFs with minimal assumptions. As a precursor to \textsc{Mathpop}, we also address the data uncertainties coming from the selection process of GC candidates: we obtain probabilistic GC candidates instead of the traditional binary classification based on the color--magnitude diagram. We apply \textsc{Mathpop} to 40 LSBGs in the Perseus cluster using GC catalogs from a \textit{Hubble Space Telescope} imaging program. We then compare our results to those from an independent study using the standard method. We further calibrate and validate our approach through extensive simulations. Our approach reveals two LSBGs having GCLF turnover points much brighter than the canonical value with Bayes' factor being $\sim4.5$ and $\sim2.5$, respectively. An additional crude maximum-likelihood estimation shows that their GCLF TO points are approximately $0.9$~mag and $1.1$~mag brighter than the canonical value, with $p$-value $\sim 10^{-8}$ and $\sim 10^{-5}$, respectively.