tokens: the outermost regions of clusters. For example, Fig. 8 shows a snapshot of the plane ( J z , R ) for model KF05, with the potential escapers highlighted in green. It is evident that almost all of the outer cluster stars beyond approximately 0.5 r J are potential escapers. This result is in general agreement with the findings of Küpper et al. ( 2010 ), who first showed that the behaviour of the surface brightness and velocity dispersion radial profiles are significantly affected by the presence of an outer population of potential escapers. Figure 8. The same as the last panel of Fig. 5 , but with the unbound particles highlighted in green. The fraction of unbound particles as a function of the fraction of the mass remaining in the cluster for all our locked models is illustrated in Fig. 9 . As discussed in Fukushige Heggie ( 2000 ) and Baumgardt ( 2001 ), initial conditions set by sampling, for example, a King model may include a fraction of stars which are unbound when an external tidal field is added. This is the case for our KF1 model. For this model, we show the evolution of the fraction of potential escapers both with and without this population of primordial potential escapers. All the other models do not have any primordial potential escapers. Figure 9. The fraction of unbound particles as a function of fraction of mass remaining in the cluster for all locked models. For KF1, there are two separate lines for including primordially unbound particles and excluding them. Fig. 9 also shows that the fraction of potential escapers increases significantly over time reaching a fraction of the remaining mass equal to about 15 per cent by the end of our simulations. Such a behaviour is qualitatively consistent with the findings reported by Baumgardt ( 2001 ), in which tidally perturbed models (initialised as critically filling King model W 0 = 3, i.e. characterized by a much higher fraction of primordial potential escapers, about 15 per cent) possess approximately 20 per cent of potential escapers during the final stages of evolution. We have examined the evolution of the fraction of prograde and retrograde particles within the populations of bound and unbound particles in models KF1 and KF025, as representative of the two filling regimes (see Figs 10 and 11 , respectively). The larger fraction of retrograde particles in the population of unbound particles is the result of the two effects discussed in Section 3.2 : the preferential escape of prograde particles and the fact that, in the transition from bound to unbound, some particles move on more eccentric/radial orbits becoming retrograde as they move outwards. Figure 10. The time evolution of model KF1 of the fraction of retrograde stars within the entire system, and within energetically bound and unbound particles. The bottom panel is a zoomed in version. The red line shows the fraction of unbound particles that do not include the primordially unbound stars. Note that the black solid lines
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