Abstract
Relativistic winds of fast-spinning pulsars have been proposed as a potential site for cosmic-ray acceleration from very high energies (VHE) to ultrahigh energies (UHE). We re-examine conditions for high-energy neutrino production, considering the interaction of accelerated particles with baryons of the expanding supernova ejecta and the radiation fields in the wind nebula. We make use of the current IceCube sensitivity in diffusive high-energy neutrino background, in order to constrain the parameter space of the most extreme neutron stars as sources of VHE and UHE cosmic rays. We demonstrate that the current non-observation of 1018 eV neutrinos put stringent constraints on the pulsar scenario. For a given model, birthrates, ejecta mass and acceleration efficiency of the magnetar sources can be constrained. When we assume a proton cosmic ray composition and spherical supernovae ejecta, we find that the IceCube limits almost exclude their significant contribution to the observed UHE cosmic-ray flux. Furthermore, we consider scenarios where a fraction of cosmic rays can escape from jet-like structures piercing the ejecta, without significant interactions. Such scenarios would enable the production of UHE cosmic rays and help remove the tension between their EeV neutrino production and the observational data.