A tale of dark matter capture, sub-dominant WIMPs, and neutrino observatories

Weakly Interacting Massive Particles (WIMPs), which are among the best motivated dark matter (DM) candidates, could make up all or only a fraction of the total DM budget. We consider a scenario in which WIMPs are a sub-dominant DM component; such a scenario would affect both current direct and indirect bounds on the WIMP-nucleon scattering cross section. In this paper we focus on indirect searches for the neutrino flux produced by annihilation of sub-dominant WIMPs captured by the Sun or the Earth via either spin-dependent or spin-independent scattering. We derive the annihilation rate and the expected neutrino flux at neutrino observatories. In our computation, we include an updated chemical composition of the Earth with respect to the previous literature, leading to an increase of the Earth's capture rate for spin-dependent scattering by a factor three. Results are compared with current bounds from Super-Kamiokande and IceCube. We discuss the scaling of bounds from both direct and indirect detection methods with the WIMP abundance.