Peculiarities in velocity dispersion and surface density profiles of star clusters

Based on our recent work on tidal tails of star clusters we investigate star clusters of a few 104 M(circle dot) 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 per cent of the Jacobi radius. Beyond 70 per cent 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 the Newtonian gravity. By fitting templates to about 104 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 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 three more free parameters. Our template can reconstruct the tidal radius over all fitted ranges with an accuracy of about 10 per cent, 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. Moreover, we find that the bulk of a cluster adjusts to the mean tidal field which it experiences and not to the tidal field at perigalacticon as has often been assumed in other investigations, i.e. a fitted tidal radius is a cluster's time average mean tidal radius and not its perigalactic one. Furthermore, we study the tidal debris in the vicinity of the clusters and find it to be well represented by a power law with a slope of -4 to -5. This steep slope we ascribe to the epicyclic motion of escaped stars in the tidal tails. Star clusters close to apogalacticon show a significantly shallower slope of up to -1, however. We suggest that clusters at apogalacticon can be identified by measuring this slope.