Ultra-High Energy Cosmic Rays: The Annihilation of Super-Heavy Relics

We investigate the possibility that ultra-high energy cosmic rays (UHECRs) originate from the annihilation of relic superheavy (SH) dark matter in the Galactic halo. In order to fit the data on UHECRs, a cross section of $<{\sigma }_{A}v>\sim {10}^{-26}{\text{cm}}^2(M_X\mathrm{/}{10}^{12}\text{GeV}{)}^{3\mathrm{/}2}$ is required if the SH dark matter follows a Navarro–Frenk–White (NFW) density profile. This would require extremely large-$l$ contributions to the annihilation cross section. An interesting finding of our calculation is that the annihilation in sub-galactic clumps of dark matter dominates over the annihilations in the smooth dark matter halo, thus implying much smaller values of the cross section needed to explain the observed fluxes of UHECRs.