The impact of a top-heavy IMF on the formation and evolution of dark star clusters

TL;DR

This study uses N-body simulations to show that a top-heavy initial mass function in star clusters can lead to the formation of dark star clusters through black hole sub-systems, especially in the Milky Way.

Contribution

It provides the first detailed analysis of how a top-heavy IMF influences dark star cluster formation and evolution using comprehensive direct N-body simulations.

Findings

Top-heavy IMFs cause rapid evaporation of luminous stars and formation of dark star clusters.

A minimum initial black hole mass fraction of 0.05 is needed for Milky Way globular clusters to transition into DSC phase.

Higher initial black hole fractions (>0.08) lead to DSC formation regardless of initial density and galactocentric distance.

Abstract

The Spitzer instability leads to the formation of a black hole sub-system (BHSub) at the center of a star cluster providing energy to luminous stars (LSs) and increasing their rate of evaporation. When the self-depletion time of the BHSub exceeds the evaporation time of the LSs, a dark star cluster (DSC) will appear. Using the NBODY7 code, we performed a comprehensive set of direct \Nbody simulations over a wide range of initial conditions to study the pure effect of the top-heaviness of the IMF on the formation of the DSC phase. In the Galactic tidal field, top-heavy IMFs lead to the fast evaporation of LSs and the formation of DSCs. Therefore, DSCs can be present even in the outer region of the Milky Way (MW). To successfully transition to the DSC phase, the MW Globular Clusters (GCs) must possess an initial BH mass fraction of $\widetilde{\mathit{M}}_\mathrm{BH}(0)>0.05$. For star clusters with $\widetilde{\mathit{M}}_\mathrm{BH}(0)>0.08$, the DSC phase will be created for any given initial density of the cluster and Galactocentric distance. The duration of the cluster's lifetime spent in the DSC phase shows a negative (positive) correlation with the initial density, and Galactocentric distance of the star cluster if $\widetilde{\mathit{M}}_\mathrm{BH}(0)\leq 0.12$ ($\widetilde{\mathit{M}}_\mathrm{BH}(0)\geq 0.15$). Considering the canonical IMF, it is unlikely for any MW GCs to enter the DSC phase. We discuss the BH retention fraction in view of the observed properties of the GCs of the MW.