  If the Milky Way is populated by WIMPs as predicted by cosmological models of
the large-scale structure of the universe and as motivated by SUSY, the capture
of high-mass WIMPs by the Sun would affect the temperature, density and
chemical composition of the solar core. We use the sound speed and the density
profiles inferred from the helioseismic instruments on the Solar and
Heliospheric Observatory (SOHO) to discuss the effect of WIMP accretion and
annihilation on the evolution of the Sun. The WIMP transport of energy inside
the Sun is not negligible for WIMPs with a mass smaller than 60 GeV and
annihilating WIMPs with <sigma_a v>~ 10^{-27}cm^3/sec. WIMP-accreting models
with WIMP masses smaller than 30 GeV are in conflict with the most recent
seismic data. We combine our new constraints with the analysis of predicted
neutrino fluxes from annihilating WIMPs in the solar core. Working in the
framework of the Minimal Supersymmetric Standard Model and considering the
neutralino as the best dark matter particle candidate, we find that
supersymmetric models, consistent with solar seismic data and with recent
measurements of dark matter relic density, lead to a measured muon flux on
Earth in the range of 1 to 10^4 km^{-2} yr^{-1}, for neutralino masses between
30 and 400 GeV.
