Based on our recent work on tidal tails of star clusters ( 35 ) we investigate star clusters of a few 10 ^ { 4 } \mbox { $ { M } _ { \odot } $ } 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 can not 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 . 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 .