tokens: the tail in the velocity distribution is produced independently of η, with velocities up to ∼1000 km s −1 . However, different eccentricities do not change the shape of the distribution function with respect to the case of the circular orbit. Therefore, these results suggest that the energy exchange between the generic star of the GC and the BHB is almost independent on the eccentricity, depending only on the initial total energy of the binary. Figure 3. Comparison among the velocity distributions of escaping stars for an SMBHB with mass ratio ν = 1/4 and different eccentricities (η = 0, 0.25, 0.75). The distributions are cut on the left side at 212 km s −1 , which corresponds to the escape velocity from the system evaluated at 20 pc. For what regards the branching ratios, Table 2 shows the branching ratios as function of η. From this table, it is clear that the branching ratio remains nearly constant for different eccentricities. Therefore, not only the shape of the velocity distribution is preserved, but also the probability of star ejection. Table 2. The values of the Branching Ratios (BR) for ν = 1/4 and different BHB orbital eccentricities, η. To conclude, the BHB orbital eccentricity does not affect neither the shape of the velocity distribution nor the branching ratio of ejected stars. Therefore, the main features of the ejected stars depend on the binary mass ratio ν, but not on the binary eccentricity. 3.3 The role of the GC orbital inclination In our scattering experiments, the GC orbits are coplanar with the BHB orbital plane. This means that the angular momentum of the GC and that of the BHs are aligned. In order to explore the role of the GC orbital inclination, we performed a set of simulations in the extreme case of GC orbits perpendicular with respect to the BHB orbital plane, in the case of mass ratios ν = (1/20, 1/10, 1/5, 1/3). The results of our scattering experiments reveal that the GC orbital inclination plays an important role both for the branching ratio and the resulting velocity distribution. Fig. 2 shows the branching ratios for both the coplanar and perpendicular cases. In the perpendicular case, the branching ratios of the ejected stars are reduced. Actually, the angle between the two angular momentum vectors results to have an important role in the output of the scattering experiments, as the relative inclination of the angular momenta of the GC and of the test star has. Therefore, the actual value of the branching ratio comes from a combination of two effects due to the two-mentioned relative inclinations. Calling β and γ the angles between the pairs of (GC, BHB) and (test star, GC), respectively, the higher probabilities are obtained when β ∼ 0 and γ ∼ 0. Finally, when ν ≲ 1/20, the branching ratio tends to the value of the single BH case, for which β is not defined and consequently only γ has a role in the output. The effect of the GC orbital inclination is significant also in the velocity distribution of the
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