Neutrino emissivity from $e^{-}$ synchrotron and $e^{-}{e}^{+}$ annihilation processes in a strong magnetic field: General formalism and nonrelativistic limit

A general formalism is developed for calculating the neutrino emissivities of synchrotron and $e^{-}{e}^{+}$ annihilation radiations in a plasma in the presence of a large magnetic field $B\sim {10}^{12}-{10}^{14}$ G. As a first step, the formalism is used to calculate the synchrotron and annihilation radiations from a nonrelativistic electron plasma (density $\rho \lesssim {10}^6$ g ${\mathrm{cm}}^{-3\mathrm{}}$, temperature $T\lesssim 6\times {10}^9$ K) including the cases of nondegenerate and degenerate electrons, and of quantizing and nonquantizing magnetic fields. We conclude that these processes can be important for neutrino production in a hot plasma of neutron star envelopes.