Evolution of star clusters on eccentric orbits
  We study the evolution of star clusters on circular and eccentric orbits
using direct $N$-body simulations. We model clusters with initially $N=8{\rm
k}$ and $N=16{\rm k}$ single stars of the same mass, orbiting around a
point-mass galaxy. For each orbital eccentricity that we consider, we find the
apogalactic radius at which the cluster has the same lifetime as the cluster
with the same $N$ on a circular orbit. We show that then, the evolution of
bound particle number and half-mass radius is approximately independent of
eccentricity. Secondly, when we scale our results to orbits with the same
semi-major axis, we find that the lifetimes are, to first order, independent of
eccentricity. When the results of Baumgardt and Makino for a singular
isothermal halo are scaled in the same way, the lifetime is again independent
of eccentricity to first order, suggesting that this result is independent of
the Galactic mass profile. From both sets of simulations we empirically derive
the higher order dependence of the lifetime on eccentricity. Our results serve
as benchmark for theoretical studies of the escape rate from clusters on
eccentric orbits. Finally, our results can be useful for generative models for
cold streams and cluster evolution models that are confined to spherical
symmetry and/or time-independent tides, such as Fokker-Planck models, Monte
Carlo models, and (fast) semi-analytic models.
