Spherical models of star clusters with potential escapers
  An increasing number of observations of the outer regions of globular
clusters (GCs) have shown a flattening of the velocity dispersion profile and
an extended surface density profile. Formation scenarios of GCs can lead to
different explanations of these peculiarities, therefore the dynamics of stars
in the outskirts of GCs are an important tool in tracing back the evolutionary
history and formation of star clusters. One possible explanation for these
features is that GCs are embedded in dark matter halos. Alternatively, these
features are the result of a population of energetically unbound stars that can
be spatially trapped within the cluster, known as potential escapers (PEs). We
present a prescription for the contribution of these energetically unbound
members to a family of self-consistent, distribution function-based models,
which, for brevity, we call the Spherical Potential Escapers Stitched (SPES)
models. We show that, when fitting to mock data of bound and unbound stars from
an N-body model of a tidally-limited star cluster, the SPES models correctly
reproduce the density and velocity dispersion profiles up to the Jacobi radius,
and they are able to recover the value of the Jacobi radius itself to within
20%. We also provide a comparison to the number density and velocity dispersion
profiles of the Galactic cluster 47 Tucanae. Such a case offers a proof of
concept that an appropriate modelling of PEs is essential to accurately
interpret Gaia data in the outskirts of GCs, and, in turn, to formulate
meaningful present-day constraints for GC formation scenarios in the early
universe.
