Production of high-energy μ neutrinos from young neutron stars

Young, rapidly rotating neutron stars could accelerate protons to energies of $\sim 1$ PeV close to the stellar surface, which scatter with x-rays from the stellar surface through the $\Delta$ resonance and produce pions. The pions subsequently decay to produce muon neutrinos. We find that the energy spectrum of muon neutrinos consists of a sharp rise at $\sim 50$ TeV, corresponding to the onset of the resonance, above which the flux drops as $\epsilon_\nu^{-2}$ up to an upper-energy cut-off that is determined by either kinematics or by the maximum energy to which protons are accelerated. We predict event rates as high as 10-50 km$^{-2}$ yr$^{-1}$ from relatively young, close neutron stars. Such fluxes would be detectable by IceCube.