Kinematics of HVSs with different ejection speeds. Panel a: magnitude of the galactocentric latitudinal velocity, |v_ϑ|, as a function of the galactocentric radial velocity, v_r, for HVSs ejected with different speeds, v_ej, and traveling in a spherical DM halo. Initially, the star velocity is purely radial, and |v_ϑ| = 0; as time goes on, |v_ϑ| becomes non-null due to the nonspherical potential of the Galactic disk (see Eq. (4)). For stars with lower ejection speeds (v_ej ≲ 800 km s⁻¹), radial and angular dynamics are coupled: this coupling results in a fast growth of |v_ϑ| after the first turnaround of the star. However, such couplings are not manifested for stars with higher ejection speeds. Panel b: galactocentric radial velocity, v_r, as a function of the galactocentric distance, r, for HVSs ejected radially outward with different ejection velocities, v_ej. The vertical dashed line of panel a and the horizontal dashed line of panel b correspond to v_r = 0, while the vertical dashed line of panel b corresponds to r = 10 kpc. In both panels, HVSs are ejected in the direction with a travel time of 160 Myr, which is the largest possible travel time for a 4 M_⊙ star.