Weakly interacting massive particle diffusion in the solar system including solar depletion and its effect on Earth capture rates

Weakly interacting massive particles (WIMPs) can be captured by the Earth, where they eventually sink to the core, annihilate, and produce, e.g., neutrinos that can be searched for with neutrino telescopes. The Earth is believed to capture WIMPs not dominantly from the Milky Way halo directly, but instead from a distribution of WIMPs that have diffused around in the solar system due to gravitational interactions with the planets in the solar system. Recently, doubts have been raised about the lifetime of these WIMP orbits due to solar capture. We investigate this issue here by detailed numerical simulations. Compared to earlier estimates, we find that the WIMP velocity distribution is significantly suppressed below about 70 km/s, which results in a suppression of the capture rates mainly for heavier WIMPs (above $\ensuremath{\sim}100\mathrm{GeV}).$ At 1 TeV and above the reduction is almost a factor of 10. We apply these results to the case where the WIMP is a supersymmetric neutralino and find that, within the minimal supersymmetric standard model, the annihilation rates and thus the neutrino fluxes are reduced even more than the capture rates. At high masses (above $\ensuremath{\sim}1\mathrm{TeV}),$ the suppression is almost two orders of magnitude. This suppression will make the detection of neutrinos from heavy WIMP annihilations in the Earth much harder compared to earlier estimates.