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)
We investigate the dynamical status of the low-mass globular cluster Palomar 13 by means of N-body computations to test whether its unusually high mass-to-light ratio of about 40 and its peculiarly shallow surface density profile can be caused by tid
al shocking. Alternatively, we test - by varying the assumed proper motion - if the orbital phase of Palomar 13 within its orbit about the Milky Way can influence its appearance and thus may be the origin of these peculiarities, as has been suggested by Kuepper et al. (2010). We find that, of these two scenarios, only the latter can explain the observed mass-to-light ratio and surface density profile. We note, however, that the particular orbit that best reproduces those observed parameters has a proper motion inconsistent with the available literature value. We discuss this discrepancy and suggest that it may be caused by an underestimation of the observational uncertainties in the proper motion determination. We demonstrate that Palomar 13 is most likely near apogalacticon, which makes the cluster appear supervirial and blown-up due to orbital compression of its tidal debris. Since the satellites of the Milky Way are on average closer to apo- than perigalacticon, their internal dynamics may be influenced by the same effect, and we advocate that this needs to be taken into account when interpreting their kinematical data. Moreover, we briefly discuss the influence of a possible binary population on such measurements.
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)
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.
