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

TL;DR

This paper models the distribution of gravitationally captured WIMPs in the solar system, finding their density at Earth is low and unlikely to significantly impact direct detection or neutrino telescope observations.

Contribution

It provides the first detailed simulation of WIMP orbits considering gravitational capture by planets, highlighting the minimal impact on detection efforts.

Findings

Captured WIMP density at Earth is small and insensitive to solar scattering details.

External Galactic fields may influence WIMP density, but generally negligible.

Captured WIMPs contribute little to direct detection and are undetectable by neutrino telescopes.

Abstract

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.