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