  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. 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 km^3-scale neutrino telescopes to ~100 GeV WIMPs is virtually
unchanged from previous estimates, the sensitivity of these experiments to ~10
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.
