Neutrinos from WIMP annihilation in the Sun : Implications of a self-consistent model of the Milky Way's dark matter halo

Upper limits on the spin-independent (SI) as well as spin-dependent (SD) elastic scattering cross sections of WIMPs with protons, imposed by the Super-Kamiokande (S-K) upper limit on the neutrino flux from WIMP annihilation in the Sun, and their compatibility with the "DAMA-compatible" regions of the WIMP parameter space within which the annual modulation signal observed by the DAMA/LIBRA experiment is compatible with the null results of other direct detection experiments, are studied within the frame work of a self-consistent model of the finite-size dark matter (DM) halo of the Galaxy, the parameters of which are determined by a fit to the rotation curve data of the Galaxy. We find that the S-K implied upper limits on the WIMP-proton elastic cross section as a function of WIMP mass impose stringent restrictions on the branching fractions of the various WIMP annihilation channels. For SI interaction, while the S-K upper limits are consistent with the DAMA-compatible region of the WIMP parameter space if the WIMPs annihilate dominantly to $\bbarb$\ and/or $\cbarc$, portions of the DAMA-compatible region can be excluded if WIMP annihilations to $\tautau$ and $\nu\anu$ occur at larger than ~ 10% and 0.1% levels, respectively. For SD interaction, the restrictions on the possible annihilation channels are much more stringent, essentially ruling out the DAMA-compatible region of the WIMP parameter space if the relatively low-mass ($\sim$ 2 -- 20 GeV) WIMPs under consideration annihilate predominantly to any mixture of $\bbarb$, \ $\cbarc$, \ $\tautau$, \ and $\nu\anu$ final states.