The structural and dynamical properties of star clusters are generally
derived by means of the comparison between steady-state analytic models and the
available observables. With the aim of studying the biases of this approach, we
fitted different analytic models to simulated observations obtained from a
suite of direct N-body simulations of star clusters in different stages of
their evolution and under different levels of tidal stress to derive mass, mass
function and degree of anisotropy. We find that masses can be
under/over-estimated up to 50% depending on the degree of relaxation reached by
the cluster, the available range of observed masses and distances of radial
velocity measures from the cluster center and the strength of the tidal field.
The mass function slope appears to be better constrainable and less sensitive
to model inadequacies unless strongly dynamically evolved clusters and a
non-optimal location of the measured luminosity function are considered. The
degree and the characteristics of the anisotropy developed in the N-body
simulations are not adequately reproduced by popular analytic models and can be
detected only if accurate proper motions are available. We show how to reduce
the uncertainties in the mass, mass-function and anisotropy estimation and
provide predictions for the improvements expected when Gaia proper motions will
be available in the near future.Comment: 14 pages, 8 figures, accepted for publication by MNRA
