Mass-Loss Timescale of Star Clusters in an External Tidal Field. II. Effect of Mass Profile of Parent Galaxy

TL;DR

This study examines how different mass profiles of parent galaxies affect the long-term mass-loss timescale of star clusters, revealing that shallower profiles extend cluster lifetimes and providing a formula to predict mass-loss timescales.

Contribution

It introduces a new analysis of the impact of galaxy mass profiles on star cluster evolution, extending previous point-mass models with more realistic profiles and deriving an evaluation formula.

Findings

Mass-loss timescale increases by 20-50% with shallower galaxy profiles.

Clusters in shallower profiles rotate faster and have longer lifetimes.

Derived formula explains observed size-distance relation of galactic globular clusters.

Abstract

We investigate the long-term dynamical evolution of star clusters in a steady tidal field produced by its parent galaxy. In this paper, we focus on the influence of mass profile of the parent galaxy. The previous studies were done with the simplification where the parent galaxy was expressed by point mass. We express different mass profiles of the parent galaxy by the tidal fields in which the ratios of the epicyclic frequency to the angular velocity are different. We compare the mass-loss timescale of star clusters whose tidal radii are identical but in parent galaxies with different mass profile, by means of orbits calculations in fixed cluster potential and N-body simulations. In this situation, a cluster rotates around the parent galaxy more rapidly as the parent galaxy has shallower mass profile. We found that the mass-loss timescale increase 20% and 50% for the cases that the mass density profile of the parent galaxies are proportional to R^-2 and R^-1.5 where R is the distance from the galaxy center, compared to the point-mass case, in moderately strong tidal field. Counterintuitively, a cluster which rotates around the parent galaxy more rapidly has a longer lifetime. The increase of lifetime is due to the fact that the fraction occupied by regular-like orbit increases in shallower profile. Finally, we derive an evaluation formula for the mass-loss timescale of clusters. Our formula can explain a property of the population of the observed galactic globular clusters that their half-mass radii become smaller as their distances from the galactic center become smaller.