ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O
tokens: to the lepton number transport; indeed, the neutrino contribution is just a few percent. This is simply because the number density of electron/positron is much larger than that for the neutrinos. The neutrino diffusion in the fluid rest frame is even subtler, although it does exist (see the blue line in Figure 7 ). It should be noted, however, that the momentum feedback from neutrinos is still comparable to the momentum imparted by the matter-pressure gradient, as discussed above. This occurs because the lateral matter-pressure gradient is partially compensated by the temperature asymmetry: the temperature in the northern hemisphere is ∼1% higher than in the southern hemisphere. Although the temperature asymmetry is much smaller than that of Y e , it still reduces the total asymmetry in the matter pressure substantially, because the baryon and photon pressure are dominant in the total pressure. Figure 7. Radial distributions of angle-average lateral number flux of measured in the laboratory frame (red) and fluid rest frame (blue). The counter part of electron/positron gas corresponds to the black line in the panel. It is also important to note that Y e decreases via deleptonization as the matter moves toward the north pole. The Y e -depleted matter then submerges in the PNS envelope near the north pole. When it hits the PNS core, it is deflected and flows southward along the surface of the PNS core, increasing Y e this time by ν e absorptions. The matter emerges again to the PNS surface by the local PNS convection near the south pole. Although the strong downflow induced by the dislocation of PNS tends to suppress the convection around the north pole, the convection activity continues to occur in the vicinity of the south pole and supplies the Y e -rich material to the PNS envelope there. This closes the cycle and creates the coherent lateral circular motion, with the Y e asymmetry sustained. Then the circulation will continue until the PNS convection shuts off or the neutrinos in PNS have dried up, both of which may take more than a few seconds. If this is in fact the case, the PNS may be accelerated to more than a hundred km s −1 , which is the typical proper motion velocity of pulsars. Finally, we give some comments on other works on the asymmetric Y e distributions. Glas et al. ( 2018 ) found a circular motion in the envelope of PNS in their 3D simulations, which produced the LESA phenomenon. They speculated that the thermal instability of spherical shells discussed by Chandrasekhar ( 1961 ) may be responsible for the sustained asymmetric Y e distribution. It seems, however, that the circular motion found in their study was not as coherent as what we observed in our study; indeed, they look more like a superposition of some smaller eddies instead (see Figure 6 in Glas et al. 2018 ). Powell Müller ( 2018 ) also observed LESA in their simulations and suggested that LESA is in effect a manifestation of PNS convections under a different