# A model for the minimum mass of bound stellar clusters and its dependence on the galactic environment

## TL;DR

This paper introduces a physical model linking the minimum mass of bound stellar clusters to galactic environment, predicting initial cluster mass functions that align with observations and depend on star formation physics.

## Contribution

The model provides a novel, environment-dependent prediction of the minimum cluster mass and initial cluster mass functions, validated against local and extragalactic data.

## Key findings

- Minimum cluster mass of ~10^2 solar masses in local galaxies due to sampling statistics.
- High-density regions like the Galactic Center produce narrow ICMFs with higher characteristic masses.
- Predicted narrow ICMFs for dwarf galaxy progenitors at high redshift explain observed globular cluster frequencies.

## Abstract

We present a simple physical model for the minimum mass of bound stellar clusters as a function of the galactic environment. The model evaluates which parts of a hierarchically-clustered star-forming region remain bound given the time-scales for gravitational collapse, star formation, and stellar feedback. We predict the initial cluster mass functions (ICMFs) for a variety of galaxies and we show that these predictions are consistent with observations of the solar neighbourhood and nearby galaxies, including the Large Magellanic Cloud and M31. In these galaxies, the low minimum cluster mass of $\sim10^2~\rm{M}_{\odot}$ is caused by sampling statistics, representing the lowest mass at which massive (feedback-generating) stars are expected to form. At the high gas density and shear found in the Milky Way's Central Molecular Zone and the nucleus of M82, the model predicts that a mass $>10^2~\rm{M}_{\odot}$ must collapse into a single cluster prior to feedback-driven dispersal, resulting in narrow ICMFs with elevated characteristic masses. We find that the minimum cluster mass is a sensitive probe of star formation physics due to its steep dependence on the star formation efficiency per free-fall time. Finally, we provide predictions for globular cluster (GC) populations, finding a narrow ICMF for dwarf galaxy progenitors at high redshift, which can explain the high specific frequency of GCs at low metallicities observed in Local Group dwarfs like Fornax and WLM. The predicted ICMFs in high-redshift galaxies constitute a critical test of the model, ideally-suited for the upcoming generation of telescopes.