Neutrino-pair emission in a strong magnetic field

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We study the neutrino emissivity of strongly magnetized neutron stars due to the charged and neutral current couplings of neutrinos to baryons in strong magnetic fields. The leading order neutral current process is the one-body neutrino-pair bremsstrahlung, which does not have an analogue in the zero field limit. The leading order charged current reaction is the known generalization of the direct Urca processes to strong magnetic fields. While for superstrong magnetic fields in excess of 10¹⁸ G the direct Urca process dominates the one-body bremsstrahlung, we find that for fields on the order 10¹⁶-10¹⁷ G and temperatures a few times 10⁹ K the one-body bremsstrahlung is the dominant process. Numerical computation of the resulting emissivity, based on a simple parametrization of the equation of state of the npe-matter in a strong magnetic field, shows that the emissivity of this reaction is of the same order of magnitude as that of the modified Urca process in the zero field limit.