tokens: is evaluated. The θ = 0 plane corresponds to the equatorial plane of the system. Bottom : angular ejection distribution after the most energetic interaction. Other elements in the plots are the same as in the top three plots. In contrast, we find that Pops. II and III are more isotropically distributed. These are the stars that come from outer regions on centrophilic orbits, and therefore the effect of random motion of the black holes does not play a role, like it does in the case of Pop. I. We notice that the third and especially second population show a prevalence of ejections along the SMBH binary orbital plane. This is in agreement with previous studies which find that HVSs are primarily ejected near the SMBH binary orbital plane when their SMBH orbital plane is aligned with the rotational place of the system (e.g., Sesana et al. 2006 ; Wang et al. 2014 ; Zhong et al. 2014 ; Lezhnin Vasiliev 2019 ; Rasskazov et al. 2019 ). Our findings show that not all of our three populations are uniformly distributed in the azimuthal direction. While there is some disagreement in the literature over the existence of a preferential ejection direction in eccentric binaries ( Rasskazov et al. 2019 ), in the case of a circular SMBH binary like ours, previous studies report a uniform distribution of ejected stars in the orbital plane ( Rasskazov et al. 2019 ; Lezhnin Vasiliev 2019 ; Sesana et al. 2006 ). We argue that the motion of black holes around the center can result in anisotropic ejections for the central population of stars (Pop. I), while stars originating from outside of the SMBH binary influence sphere are uniformly distributed (Pop. II and III). From the apocenter distribution in Fig. 11 , we conclude that Populations II and III correspond to stars on centrophilic orbits that are responsible for repopulating the loss cone. Depending on the shape and degree of nonsphericity of the nuclei (e.g., axisymmetric or triaxial), different orbital families may fulfil this role ( Merritt 2013b ). We can distinguish between the different orbital families if we look at their angular momentum at a time significantly before the interaction. Namely, because of the symmetries of different geometries, we can distinguish between spherical, axisymmetric, and triaxial orbits. Spherical orbits have conserved angular momentum, and in order to satisfy Eq. ( 12 ) are necessarily contained at all times within the bottom dashed square region of the top panel of Fig. 12 . Axisymmetric orbits, such as the saucer and tube orbits, in turn have conservation of the z -component of angular momentum and are therefore necessarily contained in the | L z / L crit | 1 region of phase space, denoted by vertical dashed lines in the same figures. Finally, triaxial orbits (pyramids, boxes or chaotic orbits) can have arbitrarily small or large values in the ( L , L z ) plane as a result of a lack of an integral of motion in that plane. This simple classification scheme is inspired
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