We have performed N -body simulations of star clusters orbiting in a spherically symmetric smooth galactic potential. The model clusters cover a range of initial half-mass radii and orbital eccentricities in order to test the historical assumption that the tidal radius of a cluster is imposed at perigalacticon. The traditional assumption for globular clusters is that since the internal relaxation time is larger than its orbital period, the cluster is tidally stripped at perigalacticon. Instead, our simulations show that a cluster with an eccentric orbit does not need to fully relax in order to expand. After a perigalactic pass, a cluster re-captures previously unbound stars, and the tidal shock at perigalacticon has the effect of energizing inner region stars to larger orbits. Therefore, instead of the limiting radius being imposed at perigalacticon, it more nearly traces the instantaneous tidal radius of the cluster at any point in the orbit. We present a numerical correction factor to theoretical tidal radii calculated at perigalacticon which takes into consideration both the orbital eccentricity and current orbital phase of the cluster.

In this paper, we constrain the properties of primordial binary populations in Galactic globular clusters. Using the MOCCA Monte Carlo code for cluster evolution, our simulations cover three decades in present-day total cluster mass. Our results are compared to the observations of Milone et al. (2012) using the photometric binary populations as proxies for the true underlying distributions, in order to test the hypothesis that the data are consistent with an universal initial binary fraction near unity and the binary orbital parameter distributions of . With the exception of a few possible outliers, we find that the data are to first-order consistent with the universality hypothesis. Specifically, the present-day binary fractions inside the half-mass radius can be reproduced assuming either high initial binary fractions near unity with a dominant soft binary component as in the Kroupa distribution combined with high initial densities (10 4 -10 6 M ⊙ pc −3 ), or low initial binary fractions (∼ 5-10%) with a dominant hard binary component combined with moderate initial densities near their present-day values (10 2 -10 3 M ⊙ pc −3 ). This apparent degeneracy can potentially be broken using the binary fractions outside the half-mass radiusonly high initial binary fractions with a significant soft component combined with high initial densities can contribute to reproducing the observed anti-correlation between the binary fractions outside the half-mass radius and the total cluster mass. We further illustrate using the simulated present-day binary orbital parameter distributions and the technique first introduced in Leigh et al. (2012) that the relative fractions of hard and soft binaries can be used to further constrain both the initial cluster density and the initial mass-density relation. Our results favour an initial mass-density relation of the form r h ∝ M α clus with α < 1/3, corresponding to an initial correlation between cluster mass and density.

We present a detailed analysis of the radial distribution of light-element multiple populations (LE-MPs) in the massive and dense globular cluster M 80 based on the combination of UV and optical Hubble Space Telescope data. Surprisingly, we find that first generation stars (FG) are significantly more centrally concentrated than extreme second generation ones (SG) out to ∼ 2.5r h from the cluster center. To understand the origin of such a peculiar behavior, we used a set of N-body simulations following the long-term dynamical evolution of LE-MPs. We find that, given the advanced dynamical state of the cluster, the observed difference does not depend on the primordial relative distributions of FG and SG stars. On the contrary, a difference of ∼ 0.05 − 0.10M between the average masses of the two sub-populations is needed to account for the observed radial distributions. We argue that such a mass difference might be the result of the higher He abundance of SG stars (of the order of ∆Y ∼ 0.05 − 0.06) with respect to FG. Interestingly, we find that a similar He variation is necessary to reproduce the horizontal branch morphology of M 80. These results demonstrate that differences in mass among LE-MPs, due to different He content, should be properly taken into account for a correct interpretation of their radial distribution, at least in dynamically evolved systems.

We use N -body simulations to explore the influence of orbital eccentricity on the dynamical evolution of star clusters. Specifically we compare the mass loss rate, velocity dispersion, relaxation time, and the mass function of star clusters on circular and eccentric orbits. For a given perigalactic distance, increasing orbital eccentricity slows the dynamical evolution of a cluster due to a weaker mean tidal field. However, we find that perigalactic passes and tidal heating due to an eccentric orbit can partially compensate for the decreased mean tidal field by energizing stars to higher velocities and stripping additional stars from the cluster, accelerating the relaxation process. We find that the corresponding circular orbit which best describes the evolution of a cluster on an eccentric orbit is much less than its semi-major axis or time averaged galactocentric distance. Since clusters spend the majority of their lifetimes near apogalacticon, the properties of clusters which appear very dynamically evolved for a given galactocentric distance can be explained by an eccentric orbit. Additionally we find that the evolution of the slope of the mass function within the core radius is roughly orbit-independent, so it could place additional constraints on the initial mass and initial size of globular clusters with solved orbits. We use our results to demonstrate how the orbit of Milky Way globular clusters can be constrained given standard observable parameters like galactocentric distance and the slope of the mass function. We then place constraints on the unsolved orbits of NGC 1261,NGC 6352, NGC 6496, and NGC 6304 based on their positions and mass functions.