In this Letter we present the result of an axisymmetric core-collapse supernovae simulation conducted with appropriate treatments of neutrino transport and proper motions of proto-neutron stars (PNSs), in which a remarkable PNS acceleration is observed in association with asymmetric neutrino emissions 300 ms after bounce. We find that these asymmetric neutrino emissions play important roles in the acceleration of PNSs in this phase. The correlation between the PNS proper motion and the asymmetric ejecta is similar to that in a neutron star (NS) kick of hydrodynamic origin. Both electron-type neutrinos (ν e) and their anti-particles () have a ∼10% level of asymmetry between the northern and southern hemispheres, while other heavy-leptonic neutrinos (ν x) have much a smaller asymmetry of ∼1%. The emissions of and ν x are higher in the hemisphere of stronger shock expansion, whereas the ν e emission is enhanced in the opposite hemisphere: in total, the neutrinos carry some linear momentum to the hemisphere of the stronger shock expansion. This asymmetry is attributed to the non-spherical distribution of electron-fraction (Y e) in the envelope of PNS. Although it is similar to lepton-emission self-sustained asymmetry, the Y e asymmetry seems to be associated with the PNS motion: the latter triggers lateral circular motions in the envelope of PNS by breaking the symmetry of the matter distribution there, which is then sustained by a combination of convection, lateral neutrino diffusion, and matter-pressure gradient. Our findings may have an influence on the current theories on the NS kick mechanism, although long-term simulations are required to assess their impact on later evolution.
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