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The next generation of dark matter (DM) direct detection experiments andneutrino telescopes will probe large swaths of dark matter parameter space. Inorder to interpret the signals in these experiments, it is necessary to havegood models of both the halo DM streaming through the solar system and thepopulation of DM bound to the solar system. In this paper, the first in aseries of three on DM in the solar system, we present simulations of orbits ofDM bound to the solar system by solar capture in a toy solar system consistingof only the Sun and Jupiter, assuming that DM consists of a single species ofweakly interacting massive particle (WIMP). We describe how the size of thebound WIMP population depends on the WIMP mass, spin-independent cross section,and spin-dependent cross section. Using a standard description of the GalacticDM halo, we find that the maximum enhancement to the direct detection eventrate, consistent with current experimental constraints on the WIMP-nucleoncross section, is < 1% relative to the event rate from halo WIMPs, while theevent rate from neutrinos from WIMP annihilation in the center of the Earth isunlikely to meet the threshold of next-generation, km^3-sized (IceCube, KM3NeT)neutrino telescopes.

Dark matter in the solar system I: The distribution function of WIMPs at the Earth from solar capture