Neutrino pair bremsstrahlung due to electromagnetic collisions in neutron star cores revisited

TL;DR

This paper reevaluates neutrino pair bremsstrahlung from electromagnetic collisions in neutron star cores, revealing a suppressed emissivity in non-superconducting matter and a standard temperature dependence in superconducting matter, with analytical formulas provided.

Contribution

It presents a revised calculation of neutrino bremsstrahlung emissivity considering plasma screening effects and superconductivity, correcting previous overestimations and clarifying the process's significance.

Findings

In non-superconducting matter, emissivity scales as T^{23/3} and is smaller than previously thought.

Superconducting matter restores the T^{8} temperature dependence for neutrino emission.

The process is less important in practice due to lower emissivity values.

Abstract

We reconsider the problem of neutrino pair bremsstrahlung emission originating from the electromagnetic collisions of charged particles in nucleonic ($npe\mu$) 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.