  Cosmic rays interacting in the solar atmosphere produce showers that result
in a flux of high-energy neutrinos from the Sun. These form an irreducible
background to indirect solar WIMP co-annihilation searches, which look for
heavy dark matter particles annihilating into final states containing neutrinos
in the Solar core. This background will eventually create a sensitivity floor
for indirect WIMP co-annihilation searches analogous to that imposed by
low-energy solar neutrino interactions for direct dark matter detection
experiments. We present a new calculation of the flux of solar atmospheric
neutrinos with a detailed treatment of systematic uncertainties inherent in
solar atmospheric shower evolution, and we use this to derive the sensitivity
floor for indirect solar WIMP annihilation analyses. We find that the floor
lies less than one order of magnitude beyond the present experimental limits on
spin-dependent WIMP-proton cross sections for some mass points, and that the
high-energy solar atmospheric neutrino flux may be observable with running and
future neutrino telescopes.
