  In the indirect detection of dark matter through its annihilation products,
the signals depend on the square of the dark matter density, making precise
knowledge of the distribution of dark matter in the Universe critical for
robust predictions. Many studies have focused on regions where the dark matter
density is greatest, e.g., the Galactic Center, as well as on the cosmic signal
arising from all halos in the Universe. We focus on the signal arising from the
whole Milky Way halo; this is less sensitive to uncertainties in the dark
matter distribution, and especially for flatter profiles, this halo signal is
larger than the cosmic signal. We illustrate this by considering a dark matter
model in which the principal annihilation products are neutrinos. Since
neutrinos are the least detectable Standard Model particles, a limit on their
flux conservatively bounds the dark matter total self-annihilation cross
section from above. By using the Milky Way halo signal, we show that previous
constraints using the cosmic signal can be improved on by 1-2 orders of
magnitude; dedicated experimental analyses should be able to improve both by an
additional 1-2 orders of magnitude.
