A halo-independent lower bound on the dark matter capture rate in the
  Sun from a direct detection signal
  We show that a positive signal in a dark matter (DM) direct detection
experiment can be used to place a lower bound on the DM capture rate in the
Sun, independent of the DM halo. For a given particle physics model and DM mass
we obtain a lower bound on the capture rate independent of the local DM
density, velocity distribution, galactic escape velocity, as well as the
scattering cross section. We illustrate this lower bound on the capture rate by
assuming that upcoming direct detection experiments will soon obtain a
significant signal. When comparing the lower bound on the capture rate with
limits on the high-energy neutrino flux from the Sun from neutrino telescopes,
we can place upper limits on the branching fraction of DM annihilation channels
leading to neutrinos. With current data from IceCube and Super-Kamiokande
non-trivial limits can be obtained for spin-dependent interactions and direct
annihilations into neutrinos. In some cases also annihilations into $\tau\tau$
or $b\bar b$ start getting constrained. For spin-independent interactions
current constraints are weak, but they may become interesting for data from
future neutrino telescopes.
