Neutrino-nucleon interactions in magnetized neutron-star matter: The effects of parity violation - art. no. 043001

We study neutrino-nucleon scattering and absorption in a dense, magnetized nuclear medium. These are the most important sources of neutrino opacity go verning the cooling of a proto-neutron star in the first tens of seconds af ter its formation. Because the weak interaction is parity violating, the ab sorption and scattering cross sections depend asymmetrically on the directi ons of the neutrino momenta with respect to the magnetic field. We develop the moment formalism of neutrino transport in the presence of such asymmetr ic opacities and derive explicit expressions for the neutrino flux and othe r angular moments of the Boltzmann transport equation: For a given neutrino species, there is a drift flux of neutrinos along the magnetic field in ad dition to the usual diffusive flux. This drift flux depends on the deviatio n of the neutrino distribution function from thermal equilibrium. Hence, de spite the fact that the neutrino cross sections are asymmetric throughout t he star, the asymmetric neutrino Aux can be generated only in the outer reg ion of the proto-neutron star where the neutrino distribution deviates sign ificantly from thermal equilibrium. The deviation from equilibrium is simil arly altered by the asymmetric scattering and absorption, although its magn itude will still be quite small in the interior of the star. We clarify two reasons why previous studies have led to misleading results. First, inelas ticity must be included in the phase space integrals in order to satisfy de tail balance. Second, nucleon recoil must be included in order to find the leading order asymmetric cross sections correctly, even though it can be ig nored to leading order to get the zero field opacities. In addition to the asymmetric absorption opacity arising from nucleon polarization, we also de rive the contribution of the electron (or positron) ground state Landau lev el. For neutrinos of energy less than a few times the temperature, this is the dominant source of asymmetric opacity. Last, we discuss the implication of our result to the origin of pulsar kicks: in order to generate kick vel ocity of a few hundred km s(-1) from asymmetric neutrino emission using the parity violation effect, the proto-neutron star must have a dipole magneti c field of at least 10(15)-10(16) G. [S0556-2821(99)02616-8].