Quantifying the Universality of the Stellar Initial Mass Function in Old Star Clusters

TL;DR

This study introduces a new method to analyze and compare the stellar mass functions of old star clusters, demonstrating that their current differences can be explained by a universal initial mass function and dynamical evolution.

Contribution

The paper presents a novel technique for quantifying cluster-to-cluster variations in stellar mass functions that is insensitive to the functional form of the mass function.

Findings

Mass functions of clusters are consistent with a universal initial mass function.

Cluster differences align with expectations from two-body relaxation.

Method applied successfully to a large sample of globular clusters.

Abstract

We present a new technique to quantify cluster-to-cluster variations in the observed present-day stellar mass functions of a large sample of star clusters. Our method quantifies these differences as a function of both the stellar mass and the total cluster mass, and offers the advantage that it is insensitive to the precise functional form of the mass function. We applied our technique to data taken from the ACS Survey for Globular Clusters, from which we obtained completeness-corrected stellar mass functions in the mass range 0.25-0.75 M$_{\odot}$ for a sample of 27 clusters. The results of our observational analysis were then compared to Monte Carlo simulations for globular cluster evolution spanning a range of initial mass functions, total numbers of stars, concentrations, and virial radii. We show that the present-day mass functions of the clusters in our sample can be reproduced by assuming an universal initial mass function for all clusters, and that the cluster-to-cluster differences are consistent with what is expected from two-body relaxation. A more complete exploration of the initial cluster conditions will be needed in future studies to better constrain the precise functional form of the initial mass function. This study is a first step toward using our technique to constrain the dynamical histories of a large sample of old Galactic star clusters and, by extension, star formation in the early Universe.