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Ultrahigh Energy Cosmic Ray Nuclei from Extragalactic Pulsars and the effect of their Galactic counterparts

The acceleration of ultrahigh energy nuclei in fast spinning newborn pulsars can explain the observed spectrum of ultrahigh energy cosmic rays and the trend towards heavier nuclei for energies above $10^{19}\,$eV as reported by the Auger Observatory. Pulsar acceleration implies a hard injection spectrum ($\sim E^{-1}$) due to pulsar spin down and a maximum energy $E_{\rm max} \sim Z \, 10^{19}$ eV due to the limit on the spin rate of neutron stars. We have previously shown that the escape through the young supernova remnant softens the spectrum, decreases slightly the maximum energy, and generates secondary nuclei. Here we show that the distribution of pulsar birth periods and the effect of propagation in the interstellar and intergalactic media modifies the combined spectrum of all pulsars. By assuming a normal distribution of pulsar birth periods centered at 300 ms, we show that the contribution of extragalactic pulsar births to the ultrahigh energy cosmic ray spectrum naturally gives rise to a contribution to very high energy cosmic rays (VHECRs, between $10^{16}$ and $10^{18}$ eV) by Galactic pulsar births. The required injected composition to fit the observed spectrum depends on the absolute energy scale, which is uncertain, differing between Auger Observatory and Telescope Array. The contribution of Galactic pulsar births can also bridge the gap between predictions for cosmic ray acceleration in supernova remnants and the observed spectrum just below the ankle, depending on the composition of the cosmic rays that escape the supernova remnant and the diffusion behavior of VHECRs in the Galaxy.