Bracketing the impact of astrophysical uncertainties on local dark matter searches

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.