Dynamical evolution of star clusters in tidal fields

Abstract

We report the results of a large set of N-body calculations aimed at studying the evolution of multimass star clusters in external tidal fields. Our clusters start with the same initial mass functions, but varying particle numbers, orbital types and density profiles. Our main focus is to study how the stellar mass function and other cluster parameters change under the combined influence of stellar evolution, two-body relaxation and the external tidal field. We find that the lifetimes of star clusters moving on similar orbits scale as T∼Txrh, where Trh is the relaxation time, and the exponent x depends on the initial concentration of the cluster and is around x≈ 0.75. The scaling law does not change significantly if one goes from circular orbits to eccentric ones. From the results for the lifetimes, we predict that between 53 and 67 per cent of all Galactic globular clusters will be destroyed within the next Hubble time. Low-mass stars are preferentially lost and the depletion is strong enough to turn initially increasing mass functions into mass functions that decrease towards the low-mass end. The details of this depletion are insensitive to the starting condition of the cluster and can be characterized as a function of a single variable, such as, for example, the fraction of time spent until total cluster dissolution. The preferential depletion of low-mass stars from star clusters leads to a decrease of their mass-to-light ratios except for a short period close to final dissolution, when the mass fraction in the form of compact remnants starts to dominate. The fraction of compact remnants increases throughout the evolution. They are more strongly concentrated towards the cluster cores than main-sequence stars and their mass fraction in the centre can reach 95 per cent or more around and after core collapse. For a sample of Galactic globular clusters with well-observed parameters, we find a correlation between the observed slope of the mass function and the lifetimes predicted by us. It seems possible that Galactic globular clusters started with a mass function similar to what one observes for the average mass function of the Galactic disc and bulge.