Evidence for a bottom-light initial mass function in massive star clusters

Abstract

We have determined stellar mass functions of 120 Milky Way globular clusters and massive LMC/SMC star clusters based on a comparison of archival Hubble Space Telescope photometry with a large grid of direct N-body simulations. We find a strong correlation of the global mass function slopes of star clusters with both their internal relaxation times as well as their lifetimes. Once dynamical effects are being accounted for, the mass functions of most star clusters are compatible with an initial mass function described by a broken power-law distribution $N(m)\sim m^{\alpha }$ with break masses at 0.4 M${}_{\odot }$ and 1.0 M${}_{\odot }$ and mass function slopes of ${\alpha }_{Low}=-0.3$ for stars with masses $m<0.4$ M${}_{\odot }$, ${\alpha }_{High}=-2.30$ for stars with $m>1.0$ M${}_{\odot }$ and ${\alpha }_{Med}=-1.65$ for intermediate-mass stars. Alternatively, a log-normal mass function with a characteristic mass $\log M_C=-0.36$ and width ${\sigma }_C=0.28$ for low-mass stars and a power-law mass function for stars with $m>1$ M${}_{\odot }$ also fits our data. We do not find a significant environmental dependency of the initial mass function with either cluster mass, density, global velocity dispersion or metallicity. Our results lead to a larger fraction of high-mass stars in globular clusters compared to canonical Kroupa/Chabrier mass functions, increasing the efficiency of self-enrichment in clusters and helping to alleviate the mass budget problem of multiple stellar populations in globular clusters. By comparing our results with direct N-body simulations we finally find that only simulations in which most black holes are ejected by natal birth kicks correctly reproduce the observed correlations.

20 pages, 9 figures, accepted for publication in MNRAS, data is available from http://people.smp.uq.edu.au/HolgerBaumgardt/globular/index.html

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