Gravitational diffusion of solar system WIMPs

Abstract

Gravitational diffusion will cause the phase-space density of solar-bound Earth-crossing weakly interacting massive particles (WIMPs) to equal the phase-space density of the low-velocity free-space WIMPs. This diffusion is generated by encounters with the Earth, Jupiter and Venus. Direct capture by the Earth of bound plus unbound WIMPs is therefore equal to what would be captured were the Earth in free space. Moreover, indirect capture (where WIMPs are first weakly captured into solar orbits and from there truly captured by the Earth) is shown to be negligible. Thus, one may use the free-space formulae for capture, even though the Earth is deep within the potential well of the Sun.