Dark matter in the Solar System. II. WIMP annihilation rates in the Sun

We calculate the annihilation rate of weakly interacting massive particles (WIMPs) in the Sun as a function of their mass and elastic scattering cross section. One byproduct of the annihilation, muon neutrinos, may be observed by the next generation of neutrino telescopes. Previous estimates of the annihilation rate assumed that any WIMPs from the Galactic dark halo that are captured in the Sun by elastic scattering off solar nuclei quickly reach thermal equilibrium in the Sun. Using simulations of WIMP orbits in the Solar System in the case that spin-independent scattering dominates in the Sun (and extrapolating to the case when spin-dependent scattering dominates), we show that the optical depth of the Sun to WIMPs and the gravitational forces from planets both serve to decrease the annihilation rate below these estimates. While we find that the sensitivity of upcoming ${\mathrm{km}}^3$-scale neutrino telescopes to $\sim 100\mathrm{GeV}$ WIMPs is virtually unchanged from previous estimates, the sensitivity of these experiments to $\sim 10\mathrm{TeV}$ WIMPs may be an order of magnitude less than the standard calculations would suggest. The new estimates of the annihilation rates should guide future experiment design and improve the mapping from neutrino event rates to WIMP parameter space.

Figure 1

The time required to bring a WIMP with initial semimajor axis $a$ down to $a_f=2R_{\odot }$ as a function of the WIMP-nucleus mass ratio.

Figure 2

Suppression regimes, as defined in the text, as a function of WIMP mass and (left) spin-independent and (right) spin-dependent elastic scattering cross section.

Figure 3

The ratio of the capture rate of WIMPs onto orbits above a certain energy threshold to the total capture rate due to (left) spin-independent and (right) spin-dependent interactions in the Sun as a function of WIMP mass.

Figure 4

The ratio of the estimated annihilation rate in the Sun to the annihilation rate calculated in the instantaneous thermalization model. In all cases, $⟨\sigma v{⟩}_a=3\times {10}^{-26}{\mathrm{cm}}^2$.