Neutrino synchrotron emission from dense magnetized electron gas of neutron stars

We study the synchrotron emission of neutrino pairs by relativistic, degenerate electrons in strong magnetic fields. Particular attention is paid to the case in which the dominant contribution comes from one or several lowest cyclotron harmonics. Calculations are performed using the exact quantum formalism and the quasiclassical approach. Simple analytic fits to the neutrino synchrotron emissivity are obtained in the domain of magnetized, degenerate and relativistic electron gas provided the electrons populate either many Landau levels or the ground level alone. The significance of the neutrino synchrotron energy losses in the interiors of cooling neutron stars is discussed.