What's kickin' in partial tidal disruption events?

Stars partially destroyed by a supermassive black hole (SMBH) in a partial tidal disruption event (TDE) can be ejected from the SMBH. Previous investigations attributed this positive-energy/velocity kick to asymmetries in the mass lost by the star near pericenter. We propose that asymmetric mass loss is not predominantly responsible for "kicking" the star, and that these kicks instead arise from the combination of a) the reformation of the core following an initial phase of quasi-ballistic motion, and b) the differential shear between the unbound and marginally bound (to the SMBH) material during this phase. We predict that the kick speed $v_{\rm kick}$ is weakly dependent on the stellar properties, and for SMBH masses $M_{\bullet} \gtrsim 10^{3} M_{\odot}$, $v_{\rm kick}$ is independent of SMBH mass, is not limited to the stellar escape speed $v_{\rm esc}$, and is related to the surviving core mass $M_{\rm c}$ approximately as $v_{\rm kick} \simeq 0.45 \left(M_{\rm c}/M_{\star}\right)^{-1/3}$, where $M_{\star}$ is the original stellar mass. For $M_{\bullet} \lesssim 10^{3} M_{\odot}$, we find that the maximum-attainable kick speed depends on SMBH mass, satisfies $v_{\rm kick, max} \simeq 0.4 \, v_{\rm esc}\left(M_{\bullet}/M_{\star}\right)^{1/6}$, and is reached for core masses that satisfy $M_{\rm c}/M_{\star} \lesssim 1.7\left(M_{\bullet}/M_{\star}\right)^{-1/2}$. This model predicts that massive stars with $M_{\star}\gtrsim few\times 10 M_{\odot}$ could be ejected at speeds $\gtrsim (1-2)\times 10^3$ km s$^{-1}$ if stripped of $\gtrsim 50\%$ of their mass.