Constraints on the muon fraction and density profile in neutron stars

Muons in neutron stars (NSs) play especially important roles in addressing several interesting new physics questions associated with detecting as well as understanding interactions and astrophysical effects of muonphilic dark matter particles. The key model inputs for studying the latter are the total muon mass $M_{\mu}$, the muon mass fraction $M_{\mu}/M_{\rm NS}$ over the NS mass $M_{\rm NS}$ and the muon radial density profile $\rho_{\mu}(r)$ in NSs of varying masses. We investigate these quantities within a minimum model for the core of NSs consisting of neutrons, protons, electrons, and muons using an explicitly isospin-dependent parametric Equation of State (EOS) constrained by available nuclear laboratory experiments and the latest astrophysical observations of NS masses, radii and tidal deformabilities. We found that the absolutely maximum muon mass $M_{\mu}$ and its mass fraction $M_{\mu}/M_{\rm NS}$ in the most massive NSs allowed by causality are about 0.025 $M_\odot$ and 1.1\%, respectively. For the most massive NS of mass 2.14 $M_\odot$ observed so far, they reduce to about 0.020 $M_\odot$ and 0.9\%, respectively. We also study respective effects of individual parameters describing the EOS of high-density neutron-rich nucleonic matter on the muon contents in NSs with varying masses. We found that the most important but uncertain nuclear physics ingredient for determining the muon contents in NSs is the high-density nuclear symmetry energy.