Muons and emissivities of neutrinos in neutron star cores

Abstract

In this work we consider the role of muons in various URCA processes relevant for neutrino emissions in the core region of neutron stars. The calculations are done for $β$--stable nuclear matter with and without muons. We find muons to appear at densities $ρ= 0.15$ fm$^{-3}$, slightly around the saturation density for nuclear matter $ρ_0 =0.16$ fm$^{-3}$. The direct URCA processes for nucleons are forbidden for densities below $ρ= 0.5$ fm$^{-3}$, however the modified URCA processes with muons $(n+N\rightarrow p+N +μ+\overlineν_μ, p+N+μ\rightarrow n+N+ν_μ$), where $N$ is a nucleon, result in neutrino emissivities comparable to those from $(n+N\rightarrow p+N +e +\overlineν_e, p+N+e \rightarrow n+N+ν_e$). This opens up for further possibilities to explain the rapid cooling of neutrons stars. Superconducting protons reduce however these emissivities at densities below $0.4$ fm$^{-3}$.