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

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 the mass profile of the parent galaxy. Previous studies were done with simplification, where the parent galaxy was expressed by the point mass. We express different mass profiles of the parent galaxy by the tidal fields in which the ratios of the epicyclic frequency, $\kappa$, to the angular velocity, $\omega$, are different. We compare the mass-loss timescale of star clusters whose tidal radii are identical, but in parent galaxies with different mass profiles, 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, since the parent galaxy has a shallower mass profile. We found that the mass-loss timescale increase by 20% and 50% for the cases that the mass-density profiles 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 a moderately strong tidal field. Counterintuitively, a cluster that rotates around the parent galaxy more rapidly has a longer lifetime. The increase of the lifetime is due to the fact that the fraction occupied by a regular-like orbit increases in a 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.