There is a population of stars with velocities in excess of 500 km s$^{-1}$ relative to the Galactic center. Many, perhaps most, of these hyper-velocity stars (HVSs) are B stars, similar to the disk and S stars in a nuclear cluster around a super-massive black hole (SMBH) near $rm Sgr~A^{star}$. In the paper I of this series, we showed that the eccentricity of the stars emerged from a hypothetical disk around the SMBH can be rapidly excited by the secular perturbation of its intermediate-mass companion (IMC), and we suggested IRS 13E as a potential candidate for the IMC. Here, we show that this process leads to an influx of stars on parabolic orbits to the proximity of $rm Sgr~A^{star}$ on a secular timescale of a few Myr. This timescale is much shorter than the diffusion timescale into the lost cone through either the classical or the resonant relaxation. Precession of the highly-eccentric stars longitude of periastron, relative to that of the IMC, brings them to its proximity within a few Myr. The IMCs gravitational perturbation scatters a fraction of the stars from nearly parabolic to hyperbolic orbits, with respect to the SMBH. Their follow-up close encounters with the SMBH induce them to escape with hyper-velocity. This scenario is a variant of the hypothesis proposed by Hills based on the anticipated breakup of some progenitor binary stars in the proximity of the SMBH, and its main objective is to account for the limited lifespan of the known HVSs. We generalize our previous numerical simulations of this process with a much wider range of orbital configurations. We demonstrate the robustness and evaluate the efficiency of this channel of HVS formation. From these numerical simulations, we infer observable kinematic properties for the HVSs.
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