WIMP diffusion in the Solar System including solar WIMP-nucleon scattering

Dark matter in the form of Weakly Interacting Massive Particles (WIMPs) can be captured by the Sun and the Earth, sink to their cores, annihilate and produce neutrinos that can be searched for with neutrino telescopes. The calculation of the capture rates of WIMPs in the Sun and especially the Earth are affected by large uncertainties coming mainly from effects of the planets in the Solar System, reducing the capture rates by up to an order of magnitude (or even more in some cases). We show that the WIMPs captured by weak scatterings in the Sun also constitute an important bound WIMP population in the Solar System. Taking this population and its interplay with the population bound through gravitational diffusion into account cancel the planetary effects on the capture rates, and the capture essentially proceeds as if the Sun and the Earth were free in the galactic halo. The neutrino signals from the Sun and the Earth are thus significantly higher than claimed in the scenarios with reduced capture rates.