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

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.

21 pages, 18 figures, 4 tables. Accepted for publication in ApJ

References in corpus (25)

• A comprehensive set of simulations studying the influence of gas expulsion on star cluster evolution
• An excess of massive stars in the local 30 Doradus starburst
• N-body modeling of globular clusters: Masses, mass-to-light ratios and intermediate-mass black holes
• Globular Cluster Streams as Galactic High-Precision Scales - The Poster Child Palomar 5
• The Initial Mass Function of the Massive Star-forming Region NGC 3603 from Near-Infrared Adaptive Optics observations
• From star clusters to dwarf galaxies: The properties of dynamically hot stellar systems
• Evidence for a Long-Standing Top-Heavy IMF in the Central Parsec of the Galaxy
• The secrets of the nearest starburst cluster: II. The present-day mass function in NGC 3603
• Very high redshift quasars and the rapid emergence of super-massive black holes
• Evidence for primordial mass segregation in globular clusters
• Why haven't loose globular clusters collapsed yet?
• Dependency of dynamical ejections of O stars on the masses of very young star clusters
• The Origin of the Arches Stellar Cluster Mass Function
• Whiting 1: the youngest globular cluster associated with the Sgr dSph
• The formation of NGC 3603 young starburst cluster: "prompt" hierarchical assembly or monolithic starburst?
• The bound fraction of young star clusters
• Testing the universal stellar IMF on the metallicity distribution in the bulges of the Milky Way and M31
• A perfect starburst cluster made in one go: the NGC 3603 young cluster
• The formation of UCDs and massive GCs: Quasar-like objects for testing for a variable stellar initial mass function (IMF)
• Do star clusters form in a completely mass-segregated way?
• Direct $N$-body simulations of globular clusters - II. Palomar 4
• A dynamical gravitational wave source in a dense cluster
• Neutron star natal kicks and the long-term survival of star clusters
• The effect of primordial mass segregation on the size scale of globular clusters
• Milky Way Subsystems from Globular Clusters Kinematics Using Gaia DR2 and HST Data

Cited by in corpus (6)

• Black Hole Mergers from Star Clusters with Top-Heavy Initial Mass Functions
• Do ultra compact dwarf galaxies form monolithically or as merged star cluster complexes?
• Impact of initial mass functions on the dynamical channel of gravitational wave sources
• Are the host galaxies of Long Gamma-Ray Bursts more compact than star-forming galaxies of the field?
• The giants that were born swiftly -- Implications of the top-heavy stellar initial mass function on the birth conditions of globular clusters
• Dynamical double black holes and their host cluster properties