Neutrino pair bremsstrahlung due to electromagnetic collisions in neutron star cores revisited
We reconsider the problem of neutrino pair bremsstrahlung emission originating from the electromagnetic collisions of charged particles in nucleonic ($npeμ$) neutron star cores. Two limiting cases are considered: (i) protons are in the normal state and (ii) protons are in the superconducting state. In both cases, the dominant contribution to the bremsstrahlung emissivity $Q^{\mathrm{em}}_{\mathrm{Br}}$ comes from the transverse part of in-medium electromagnetic interactions. For non-superconducting matter, we obtain an unusual $Q^{\mathrm{em}}_{\mathrm{Br}}\propto T^{23/3}$ temperature dependence due to the dynamical character of plasma screening in the transverse channel, but considerably smaller values of $Q^{\mathrm{em}}_{\mathrm{Br}}$ than in previous studies, rendering the considered process unimportant in practice. In contrast, for superconducting and superfluid matter, the neutrino emission processes involving nucleons are suppressed and $Q^{\mathrm{em}}_{\mathrm{Br}}$ due to lepton collisions provides the residual contribution to the neutrino emissivity of neutron star core matter. In the superconducting case, the plasma screening becomes static and the standard $Q^{\mathrm{em}}_{\mathrm{Br}}\propto T^{8}$ temperature scaling is restored. Simple analytical expressions for $Q^{\mathrm{em}}_{\mathrm{Br}}$ in both limiting cases are provided.