Neutrino Transport in Strongly Magnetized Proto-Neutron Stars and the Origin of fast Spinning Pulsar Kicks

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Addis Ababa University


The Fermi LAT collaboration has recently reported the discovery of the pul- sations of the -ray pulsar J1823-3021A with a luminosity which is the highest observed to date for any millisecond pulsar (MSP). This large luminosity implies a large spin down rate _P and therefore a large magnetic eld which seems to be incompatible with the observed short rotation period P . In proto-neutron stars with strong magnetic elds, the cross section for e ( e) absorption on neutrons (protons) depends on the local magnetic eld strength resulting from the quantiza- tion of energy levels for the e􀀀 (e+) produced in the nal state. If the neutron star possesses an asymmetric magnetic eld topology in the sense that the magnitude of magnetic eld in the north pole is di erent from that in the south pole, then asymmetric neutrino emission may be generated. We calculate the absorption cross sections of e and e in strong magnetic elds as a function of the neutrino energy. These cross sections exhibit oscillatory behaviors that occur because new Landau levels for the e􀀀 (e+) become accessible as the neutrino energy increases. By evaluating the appropriately averaged neutrino opacities, we demonstrate that the change in the local neutrino ux caused by the modi ed opacities is rather small. To generate appreciable kick velocity ( 300 km s􀀀1) to the newly formed neutron star, the di erence between the eld strengths at the two opposite poles of the star must be at least 1016 G. We also consider the magnetic eld e ect on the spectral neutrino energy uxes. The oscillatory features in the absorption opacities give rise to modulations in the emergent spectra of e and e