Electron and Muon Dynamics in Neutron Stars Beyond Chemical Equilibrium

Abstract

A neutron star harbors of order $10^{56}$ electrons in its core, and almost the same number of muons, with muon decay prohibited by Pauli blocking. However, as macroscopic properties of the star such as its mass, rotational velocity, or magnetic field evolve over time, the equilibrium lepton abundances (dictated by the weak interactions) change as well. Scenarios where this can happen include spin-down, accretion, magnetic field decay, and tidal deformation. We discuss the mechanisms by which a star disrupted in one of these ways re-establishes lepton chemical equilibrium. In most cases, the dominant processes are out-of-equilibrium Urca reactions, the rates of which we compute for the first time. If, however, the equilibrium muon abundance decreases, while the equilibrium electron abundance increases (or decreases less than the equilibrium muon abundance), outward diffusion of muons plays a crucial role as well. This is true in particular for stars older than about 10,000 yrs whose core has cooled to $\lesssim 20$ keV. The muons decay in a region where Pauli blocking is lifted, and we argue that these decays lead to a flux of $\mathcal{O}$(10 MeV) neutrinos. Realistically, however, this flux will remain undetectable for the foreseeable future.