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 as well as spin-dependent elastic scattering cross sections of low mass (similar to 2-20 GeV) weakly interacting massive particles (WIMPs) with protons, imposed by the upper limit on the neutrino flux from WIMP annihilation in the Sun given by the Super-Kamiokande (S-K) experiment, and their compatibility with the "DAMA-compatible" regions of the WIMP parameter space-the regions of the WIMP mass versus cross-section 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 framework of a self-consistent model of the finite-size dark matter halo of the Galaxy. The halo model includes the gravitational influence of the observed visible matter of the Galaxy on the phase-space distribution function of the WIMPs constituting the Galaxy's dark matter halo in a self-consistent manner. Unlike in the "standard halo model'' used in earlier analyses, the velocity distribution of the WIMPs in our model is non-Maxwellian, with a high-velocity cutoff determined self-consistently by the model itself. The parameters of the model are determined from a fit to the rotation curve data of the Galaxy. We find that, for our best-fit halo model, for spin-independent interaction, while the S-K upper limits do not place additional restrictions on the DAMA-compatible region of the WIMP parameter space if the WIMPs annihilate dominantly to (b) over barb and/or (c) over barc, portions of the DAMA-compatible region can be excluded if WIMP annihilations to T+T- and v (v) over bar occur at larger than 35% and 0.4% levels, respectively. For spin-dependent interaction, on the other hand, the restrictions on the possible annihilation channels are much more stringent: they rule out the entire DAMA region if WIMPs annihilate to (b) over barb and (c) over barc final states at greater than similar to 0.05% and 0.0005% levels, respectively, and/or to (b) over barb and (c) over barc at greater than similar to 0.5% levels. The very latest results from the S-K Collaboration [T. Tanaka et al., Astrophys. J. 742, 78 (2011)] make the above constraints on the branching fractions of various WIMP annihilation channels even more stringent by roughly a factor of 3-4.