Jeremy J. Webb

The Influence of Orbital Eccentricity on Tidal Radii of Star Clusters

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 recaptures 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.

The state of globular clusters at birth II: primordial binaries

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 Kroupa (1995). 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 radius only 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 state of globular clusters at birth: emergence from the gas-embedded phase

In this paper, we discuss the origin of the observed correlation between cluster concentration c and present-day mass function (PDMF) slope α reported by De Marchi, Paresce & Pulone. This relation can either be reproduced from universal initial conditions combined with some dynamical mechanism(s) that alter(s) the cluster structure and mass function over time, or it must arise early on in the cluster lifetime, such as during the gas-embedded phase of cluster formation. Using a combination of Monte Carlo and N-body models for globular cluster evolution performed with the MOCCA and NBODY6 codes, respectively, we explore a number of dynamical mechanisms that could affect the observed relation. For the range of initial conditions considered here, our results are consistent with an universal initial binary fraction � 10% (which does not, however, preclude 100%) and an universal initial stellar mass function resembling the standard Kroupa distribution. Most of the dispersion observed in the c-α relation can be attributed to twobody relaxation and Galactic tides. However, dynamical processes alone could not have reproduced the dispersion in concentration, and we require at least some correlation between the initial concentration and the total cluster mass. We argue that the origin of this trend could be connected to the gas-embedded phase of cluster evolution.

The effect of orbital eccentricity on the dynamical evolution of star clusters

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.

Back to the Future: Estimating Initial Globular Cluster Masses from their Present Day Stellar Mass Functions

We use N-body simulations to model the 12 Gyr evolution of a suite of star clusters with identical initial stellar mass functions over a range of initial cluster masses, sizes, and orbits. Our models reproduce the distribution of present-day global stellar mass functions that is observed in the Milky Way globular cluster population. We find that the slope of a star cluster’s stellar mass function is strongly correlated with the fraction of mass that the cluster has lost, independent of the cluster’s initial mass, and nearly independent of its orbit and initial size. Thus, the mass function - initial mass relation can be used to determine a Galactic cluster’s initial total stellar mass, if the initial stellar mass function is known. We apply the mass function - initial mass relation presented here to determine the initial stellar masses of 33 Galactic globular clusters, assuming an universal Kroupa initial mass function. Our study suggests that globular clusters had initial masses that were on average a factor of 10 times larger than their present day mass, with seven clusters showing evidence for initial total stellar masses > 10 7 M⊙.

The size of star clusters accreted by the Milky Way

We perform N-body simulations of a cluster that forms in a dwarf galaxy and is then accreted by the Milky Way to investigate how a clusters structure is affected by a galaxy merger. We find that the clusters half-mass radius will respond quickly to this change in potential. When the cluster is placed on an orbit in the Milky Way with a stronger tidal field the cluster experiences a sharp decrease in size in response to increased tidal forces. Conversely, when placed on an orbit with a weaker tidal field, the cluster expands since tidal forces decrease and no longer limit the expansion due to internal effects. In all cases, we find that the clusters half-mass radius will eventually be indistinguishable from a cluster that has always lived in the Milky Way on that orbit. These adjustments occur within 1–2 half-mass relaxation times of the cluster in the dwarf galaxy. We also find this effect to be qualitatively independent of the time that the cluster is taken from the dwarf galaxy. In contrast to the half-mass radius, we show the core radius of the cluster is not affected by the potential the cluster lives in. Our work suggests that structural properties of accreted clusters are not distinct from clusters born in the Milky Way. Other cluster properties, such as metallicity and horizontal branch morphology, may be the only way to identify accreted star clusters in the Milky Way.

The effects of orbital inclination on the scale size and evolution of tidally filling star clusters

We have performed N-body simulations of tidally filling star clusters with a range of orbits in a Milky Way-like potential to study the effects of orbital inclination and eccentricity on their structure and evolution. At small galactocentric distances Rgc, a non-zero inclination results in increased mass loss rates. Tidal heating and disk shocking, the latter sometimes consisting of two shocking events as the cluster moves towards and away from the disk, help remove stars from the cluster. Clusters with inclined orbits at large Rgc have decreased mass loss rates than the non-inclined case, since the strength the disk potential decreases with Rgc. Clusters with inclined and eccentric orbits experience increased tidal heating due to a constantly changing potential, weaker disk shocks since passages occur at higher Rgc, and an additional tidal shock at perigalacticon. The effects of orbital inclination decrease with orbital eccentricity, as a highly eccentric cluster spends the majority of its lifetime at a large Rgc. The limiting radii of clusters with inclined orbits are best represented by the rt of the cluster when at its maximum height above the disk, where the cluster spends the majority of its lifetime and the rate of change in rt is a minimum. Conversely, the effective radius is independent of inclination in all cases.

Radial variation in the stellar mass functions of star clusters

A number of recent observational studies of Galactic globular clusters have measured the variation in the slope of a clusters stellar mass function

Globular Cluster Scale Sizes in Giant Galaxies: The Case of M87 and the Role of Orbital Anisotropy and Tidal Filling

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THE SIZE DIFFERENCE BETWEEN RED AND BLUE GLOBULAR CLUSTERS IS NOT DUE TO PROJECTION EFFECTS

with clustercentric distance