We investigate the epicyclic motion of stars escaping from star clusters. Using streaklines, we visualise the path of escaping stars and show how epicyclic motion leads to over- and underdensities in tidal tails of star clusters moving on circular an
d eccentric orbits about a galaxy. Additionally, we investigate the effect of the cluster mass on the tidal tails, by showing that their structure is better matched when the perturbing effect of the cluster mass is included. By adjusting streaklines to results of N-body computations we can accurately and quickly reproduce all observed substructure, especially the streaky features often found in simulations which may be interpreted in observations as multiple tidal tails. Hence, we can rule out tidal shocks as the origin of such substructures. Finally, from the adjusted streakline parameters we can verify that for the star clusters we studied escape mainly happens from the tidal radius of the cluster, given by x_L = (GM/(Omega^2-partial^2Phi/partial R^2))^{1/3}. We find, however, that there is another limiting radius, the edge radius, which gives the smallest radius from which a star can escape during one cluster orbit about the galaxy. For eccentric cluster orbits the edge radius shrinks with increasing orbital eccentricity (for fixed apocentric distance) but is always significantly larger than the respective perigalactic tidal radius. In fact, the edge radii of the clusters we investigated, which are extended and tidally filling, agree well with their (fitted) King radii, which may indicate a fundamental connection between these two quantities.
By analysing models of the young massive cluster R136 in 30 Doradus, set-up using the herewith introduced and publicly made available code McLuster, we investigate and compare different methods for detecting and quantifying mass segregation and subst
ructure in non-seeing limited N-body data. For this purpose we generate star cluster models with different degrees of mass segregation and fractal substructure and analyse them. We quantify mass segregation by measuring, from the projected 2d model data, the mass function slope in radial annuli, by looking for colour gradients in radial colour profiles, by measuring Allisons Lambda parameter, and by determining the local stellar surface density around each star. We find that these methods for quantifying mass segregation often produce ambiguous results. Most reliable for detecting mass segregation is the mass function slope method, whereas the colour gradient method is the least practical in an R136-like configuration. The other two methods are more sensitive to low degrees of mass segregation but are computationally much more demanding. We also discuss the effect of binaries on these measures. Moreover, we quantify substructure by looking at the projected radial stellar density profile, by comparing projected azimuthal stellar density profiles, and by determining Cartwright & Whitworths Q parameter. We find that only high degrees of substructure affect the projected radial density profile, whereas the projected azimuthal density profile is very sensitive to substructure. The Q parameter is also sensitive to substructure but its absolute value shows a dependence on the radial density gradient of the cluster and is strongly influenced by binaries. (abridged)
Based on our recent work on tidal tails of star clusters (Kuepper et al. 2009) we investigate star clusters of a few 10^4 Msun by means of velocity dispersion profiles and surface density profiles. We use a comprehensive set of $N$-body computations
of star clusters on various orbits within a realistic tidal field to study the evolution of these profiles with time, and ongoing cluster dissolution From the velocity dispersion profiles we find that the population of potential escapers, i.e. energetically unbound stars inside the Jacobi radius, dominates clusters at radii above about 50% of the Jacobi radius. Beyond 70% of the Jacobi radius nearly all stars are energetically unbound. The velocity dispersion therefore significantly deviates from the predictions of simple equilibrium models in this regime. We furthermore argue that for this reason this part of a cluster cannot be used to detect a dark matter halo or deviations from Newtonian gravity. By fitting templates to the about 10^4 computed surface density profiles we estimate the accuracy which can be achieved in reconstructing the Jacobi radius of a cluster in this way. We find that the template of King (1962) works well for extended clusters on nearly circular orbits, but shows significant flaws in the case of eccentric cluster orbits. This we fix by extending this template with 3 more free parameters. Our template can reconstruct the tidal radius over all fitted ranges with an accuracy of about 10%, and is especially useful in the case of cluster data with a wide radial coverage and for clusters showing significant extra-tidal stellar populations. No other template that we have tried can yield comparable results over this range of cluster conditions. All templates fail to reconstruct tidal parameters of concentrated clusters, however. (abridged)
We investigate the velocity dispersion of Pal 14, an outer Milky-Way globular cluster at Galactocentric distance of 71 kpc with a very low stellar density (central density 0.1-0.2 Msun/pc^3). Due to this low stellar density the binary population of P
al 14 is likely to be close to the primordial binary population. Artificial clusters are generated with the observed properties of Pal 14 and the velocity dispersion within these clusters is measured as Jordi et al. (2009) have done with 17 observed stars of Pal 14. We discuss the effect of the binary population on these measurements and find that the small velocity dispersion of 0.38 km/s which has been found by Jordi et al. (2009) would imply a binary fraction of less than 0.1, even though from the stellar density of Pal 14 we would expect a binary fraction of more than 0.5. We also discuss the effect of mass segregation on the velocity dispersion as possible explanation for this discrepancy, but find that it would increase the velocity dispersion further. Thus, either Pal 14 has a very unusual stellar population and its birth process was significantly different than we see in todays star forming regions, or the binary population is regular and we would have to correct the observed 0.38 km/s for binarity. In this case the true velocity dispersion of Pal 14 would be much smaller than this value and the cluster would have to be considered as kinematically frigid, thereby possibly posing a challenge for Newtonian dynamics but in the opposite sense to MOND.
Based on recent findings of a formation mechanism of substructure in tidal tails by Kuepper, Macleod & Heggie (2008) we investigate a more comprehensive set of N-body models of star clusters on orbits about a Milky-Way-like potential. We find that th
e predicted epicyclic overdensities arise in any tidal tail no matter which orbit the cluster follows as long as the cluster lives long enough for the overdensities to build up. The distance of the overdensities along the tidal tail from the cluster centre depends for circular orbits only on the mass of the cluster and the strength of the tidal field, and therefore decreases monotonically with time, while for eccentric orbits the orbital motion influences the distance, causing a periodic compression and stretching of the tails and making the distance oscillate with time. We provide an approximation for estimating the distance of the overdensities in this case. We describe an additional type of overdensity which arises in extended tidal tails of clusters on eccentric orbits, when the acceleration of the tidal field on the stellar stream is no longer homogeneous. Moreover, we conclude that a pericentre passage or a disk shock is not the direct origin of an overdensity within a tidal tail. Escape due to such tidal perturbations does not take place immediately after the perturbation but is rather delayed and spread over the orbit of the cluster. All observable overdensities are therefore of the mentioned two types. In particular, we note that substructured tidal tails do not imply the existence of dark-matter sub-structures in the haloes of galaxies.
A novel way of looking at the evolution of star clusters is presented. With a dynamical temperature, given by the mean kinetic energy of the cluster stars, and a dynamical luminosity, which is defined as the kinetic energy of the stars leaving the cl
uster in analogy to the energy of photons emitted by a star, the dissolution of star clusters is studied using a new dynamical temperature-luminosity diagram for star clusters. The investigation contains a parameter-space study of open clusters of up to N = 32768 single-mass stars with different initial density distributions, half-mass radii, tidal conditions and binary fractions. The clusters show a strong correlation between dynamical temperature and dynamical luminosity and most of the investigated cluster families share a common sequence in such a dynamical temperature-luminosity diagram. Deviations from this sequence are analyzed and discussed. After core collapse, the position of a cluster within this diagram can be defined by three parameters: the mass, the tidal conditions and the binary fraction. Due to core collapse all initial conditions are lost and the remaining stars adjust to the given tidal conditions. Binaries as internal energy sources influence this adjustment. A further finding concerns the Lagrange radii of star clusters: Throughout the investigated parameter space nearly all clusters show a constant half-mass radius for the time after core collapse until dissolution. Furthermore, the ratio of half-mass radius to tidal radius evolves onto a common sequence which only depends on the mass left in the cluster.
We examine the longitudinal distribution of the stars escaping from a cluster along tidal tails. Using both theory and simulations, we show that, even in the case of a star cluster in a circular galactic orbit, when the tide is steady, the distributi
on exhibits maxima at a distance of many tidal radii from the cluster.
