ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: at t check as a function of the initial virial ratio vir for clusters with different initial fractal degrees. The open circles, crosses and open squares show the average value for clusters with D = 1.6, 2.0 and 3.0, respectively. The red and black symbols show the results for the inner orbit and the outer orbit, respectively. Middle panel: half-mass radius at t check as a function of the initial virial ratio vir for clusters with different initial fractal degrees. Symbols and colours as in the left-hand panel. Right-hand panel: velocity dispersion of the cluster members at t check as a function of the initial virial ratio vir for clusters with different initial fractal degrees. Symbols and colours as in the left-hand panel. We found that the initially virialized clusters experience a smaller mass-loss rate than both supervirial and subvirial clusters of the order of 10percent (see left-hand panel of Fig. 6 ). This result is evident also in the left-hand panel of Fig. 7 , in which we show the mass evolution of three realizations of clusters on the outer orbit as a function of their initial virial state for the first 1Gyr of evolution. Once again, such a trend mirrors the value of the relaxation time at t check . We found that initially sub/supervirial clusters evolve with systematically smaller relaxation times from the very early stages. A collapsing system will then exhibit a shorter crossing time, inducing faster relaxation of the system. On the other hand, in a tidally limited system such as a star cluster in a galaxy it is possible that if the cluster is initially expanding the number of escapers in the early stages can be enhanced, once again reducing the number of cluster members and hence the relaxation time of the system. Figure 7. Evolution of the mass (left-hand panel), half-mass radius (middle panel) and velocity dispersion (right-hand panel) of initially spherical clusters ( D = 3.0) on the outer orbit with different initial virial ratios. The dark blue, red and light blue lines show the results of the simulations of clusters with initial virial ratio D 0.2, 0.5 and 0.8, respectively. The vertical black dashed line indicates the time t check at which the properties have been evaluated in Fig. 6 . This trend is also reflected in the size of the clusters. Initially virialized clusters evolve with slightly bigger half-mass radii. However, we also note that such a variation is of the order of only a few percent and is of the order of the variations associated with the random realizations of the clusters (see the middle panels of Figs 6 and 7 ). Similar to the effect of the initial fractal dimension, the initial virial state of the clusters also does not significantly affect the evolution of the velocity dispersion of the cluster members. Finally, we note that also in this case, the discussed trends are quite well reproduced for both the inner and outer orbits. 3.3 Impact of the initial degree of mass segregation on the long-term