Flux predictions of high-energy neutrinos from pulsars

Young, rapidly rotating neutron stars could accelerate ions from their surface to energies of $\sim 1$ PeV. If protons reach such energies, they will produce pions (with low probability) through resonant scattering with x-rays from the stellar surface. The pions subsequently decay to produce muon neutrinos. Here we calculate the energy spectrum of muon neutrinos, and estimate the event rates at Earth. The spectrum consists of a sharp rise at $\sim 50$ TeV, corresponding to the onset of the resonance, above which the flux drops with neutrino energy 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 estimate event rates as high as 10-100 km^${-2}$ yr$^{-1}$ from some candidates, a flux that would be easily detected by IceCube. Lack of detection would allow constraints on the energetics of the poorly-understood pulsar magnetosphere.