Peculiarities in Velocity Dispersion and Surface Density Profiles of
  Star Clusters
  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)
