  The theoretical interpretation of dark matter (DM) experiments is hindered by
uncertainties on the dark matter density and velocity distribution inside the
Solar System. In order to quantify those uncertainties, we present a parameter
that characterizes the deviation of the true velocity distribution from the
standard Maxwell-Boltzmann form, and we then determine for different values of
this parameter the most aggressive and most conservative limits on the dark
matter scattering cross section with nuclei; uncertainties in the local dark
matter density can be accounted for trivially. This allows us to bracket, in a
model independent way, the impact of astrophysical uncertainties on limits from
direct detection experiments and/or neutrino telescopes. We find that current
limits assuming the Standard Halo Model are at most a factor of $\sim 2$ weaker
than the most aggressive possible constraints. In addition, combining neutrino
telescope and direct detection constraints (in a statistically meaningful way),
we show that limits on DM in the mass range $\sim 10 - 1000$ GeV cannot be
weakened by more than around a factor of 10, for all possible velocity
distributions. We finally demonstrate that our approach can also be employed in
the event of a DM discovery, allowing us to avoid bias in the reconstruction of
the DM properties.
