Dark matter in the solar system III: The distribution function of WIMPs
  at the Earth from gravitational capture
  In this last paper in a series of three on weakly interacting massive
particle (WIMP) dark matter in the solar system, we focus on WIMPs bound to the
system by gravitationally scattering off of planets. We present simulations of
WIMP orbits in a toy solar system consisting of only the Sun and Jupiter. As
previous work suggested, we find that the density of gravitationally captured
WIMPs at the Earth is small and largely insensitive to the details of elastic
scattering in the Sun. However, we find that the density of gravitationally
captured WIMPs may be affected by external Galactic gravitational fields. If
such fields are unimportant, the density of gravitationally captured WIMPs at
the Earth should be similar to the maximum density of WIMPs captured in the
solar system by elastic scattering in the Sun. Using standard assumptions about
the halo WIMP distribution function, we find that the gravitationally captured
WIMPs contribute negligibly to direct detection event rates. While these WIMPs
do dominate the annihilation rate of WIMPs in the Earth, the resulting event
rate in neutrino telescopes is too low to be observed in next-generation
neutrino telescopes.
