Back to the Future: Estimating Initial Globular Cluster Masses from their Present Day Stellar Mass Functions

TL;DR

This study uses N-body simulations to link the present-day stellar mass functions of globular clusters to their initial masses, revealing a method to estimate their original sizes based on current observations.

Contribution

It introduces a new relation between stellar mass function slope and initial cluster mass, enabling estimation of initial masses from present data.

Findings

Globular clusters were on average 4.5 times more massive initially.

The mass function slope correlates strongly with mass loss fraction.

Three clusters may have been ten times more massive at birth.

Abstract

We use N-body simulations to model the 12 Gyr evolution of a suite of star clusters with identical initial stellar mass functions over a range of initial cluster masses, sizes, and orbits. Our models reproduce the distribution of present-day global stellar mass functions that is observed in the Milky Way globular cluster population. We find that the slope of a star cluster's stellar mass function is strongly correlated with the fraction of mass that the cluster has lost, independent of the cluster's initial mass, and nearly independent of its orbit and initial size. Thus, the mass function - initial mass relation can be used to determine a Galactic cluster's initial total stellar mass, if the initial stellar mass function is known. We apply the mass function - initial mass relation presented here to determine the initial stellar masses of 33 Galactic globular clusters, assuming an universal Kroupa initial mass function. Our study suggests that globular clusters had initial masses that were on average a factor of 4.5 times larger than their present day mass, with three clusters showing evidence for being 10 times more massive at birth.