The Lifetimes of Star Clusters Born with a Top-heavy IMF

TL;DR

This study uses advanced N-body simulations to explore how a top-heavy initial mass function influences the long-term evolution and survival of star clusters, especially globular clusters, considering early gas expulsion effects.

Contribution

It provides the first comprehensive analysis of star cluster evolution starting with a top-heavy IMF using direct N-body simulations, linking IMF variations to cluster longevity and properties.

Findings

Cluster lifetimes scale with relaxation time to the power of 0.8-1.

Top-heavy IMFs can explain observed properties of Galactic GCs.

Early gas expulsion significantly impacts cluster survival and characteristics.

Abstract

Several observational and theoretical indications suggest that the initial mass function (IMF) becomes increasingly top-heavy (i.e., overabundant in high-mass stars with mass $m > 1M_{\odot}$) with decreasing metallicity and increasing gas density of the forming object. This affects the evolution of globular clusters (GCs) owing to the different mass-loss rates and the number of black holes formed. Previous numerical modeling of GCs usually assumed an invariant canonical IMF. Using the state-of-the-art $NBODY6$ code, we perform a comprehensive series of direct $N$-body simulations to study the evolution of star clusters, starting with a top-heavy IMF and undergoing early gas expulsion. Utilizing the embedded cluster mass-radius relation of Marks & Kroupa (2012) for initializing the models, and by varying the degree of top-heaviness, we calculate the minimum cluster mass needed for the cluster to survive longer than 12 Gyr. We document how the evolution of different characteristics of star clusters such as the total mass, the final size, the density, the mass-to-light ratio, the population of stellar remnants, and the survival of GCs is influenced by the degree of top-heaviness. We find that the lifetimes of clusters with different IMFs moving on the same orbit are proportional to the relaxation time to a power of $x$ that is in the range of 0.8 to 1. The observed correlation between concentration and the mass function slope in Galactic GCs can be accounted for excellently in models starting with a top-heavy IMF and undergoing an early phase of rapid gas expulsion.