Neutrino-pair bremsstrahlung by electrons in neutron star crusts

Neutrino-pair bremsstrahlung by relativistic degenerate electrons in a neutron-star crust at densities 109 g cm −3 <∼ ρ <∼ 1.5 × 1014 g cm−3 is analyzed. The processes taken into account are neutrino emission due to Coulomb scattering of electrons by atomic nuclei in a Coulomb liquid, and electronphonon scattering (the phonon contribution) and Bragg diffraction (the static-lattice contribution) in a Coulomb crystal. The static-lattice contribution is calculated including the electron band-structure effects for cubic Coulomb crystals of different types and also for the liquid crystal phases composed of rodand plate-like nuclei near the bottom of the neutron-star crust (1014 g cm−3 <∼ ρ <∼ 1.5 × 1014 g cm−3). The phonon contribution is evaluated with proper treatment of the multi-phonon processes which removes a jump in the neutrino bremsstrahlung emissivity at the melting point obtained in previous works. Generally, bremsstrahlung in the solid phase does not differ significantly from that in the liquid. At ρ <∼ 1013 g cm−3, the results are rather insensitive to the nuclear form factor, but results for the solid state near the melting point are affected significantly by the Debye–Waller factor and multi-phonon processes. At higher densities the Debye–Waller factor and multi-phonon processes become less important but the nuclear form factor becomes more significant. With growing ρ, the phonon contribution becomes smaller. Near the bottom of the neutron star crust bremsstrahlung becomes less efficient due to the reduction of the effective electron–nucleus matrix element by the electron band-structure effects and the nuclear form factor. A comparison of the various neutrino generation mechanisms in neutron star crusts shows that electron bremsstrahlung is among the most important ones.