Constrain the Dark-matter Distribution of Ultra-diffuse Galaxies with Globular-cluster Mass Segregation: A Case Study with NGC5846-UDG1

The properties of globular clusters (GCs) contain valuable information of their host galaxies and dark-matter halos. In the remarkable example of ultra-diffuse galaxy, NGC5846-UDG1, the GC population exhibits strong radial mass segregation, indicative of dynamical-friction-driven orbital decay, which opens the possibility of using imaging data alone to constrain the dark-matter content of the galaxy. To explore this possibility, we develop a semianalytical model of GC evolution, which starts from the initial mass, structural, and spatial distributions of the GC progenitors, and follows the effects of dynamical friction, tidal evolution, and two-body relaxation. Using Markov Chain Monte Carlo, we forward-model the GCs in a UDG1-like potential to match the observed GC statistics, and to constrain the profile of the host halo and the origin of the GCs. We find that, with the assumptions of zero mass segregation when the star clusters were born, UDG1 is relatively dark-matter-poor compared to what is expected from stellar-to-halo-mass relations, and its halo concentration is lower than the cosmological average, irrespective of having a cuspy or a cored profile. Its GC population has an initial spatial distribution more extended than the smooth stellar distribution. We discuss the results in the context of scaling laws of galaxy-halo connections, and warn against naively using the GC-abundance-halo-mass relation to infer the halo mass of ultra-diffuse galaxies. Our model is generally applicable to GC-rich dwarf galaxies, and is publicly available.