Making sense of the local Galactic escape speed estimates in direct dark matter searches

Direct detection (DD) of dark matter (DM) candidates in the $\lesssim$10 GeV mass range is very sensitive to the tail of their velocity distribution. The important quantity is the maximum WIMP speed in the observer's rest frame, i.e. in average the sum of the local Galactic escape speed $v_{\rm esc}$ and of the circular velocity of the Sun $v_c$. While the latter has been receiving continuous attention, the former is more difficult to constrain. The RAVE Collaboration has just released a new estimate of $v_{\rm esc}$ (Piffl {\em et al.}, 2014 --- P14) that supersedes the previous one (Smith {\em et al.}, 2007), which is of interest in the perspective of reducing the astrophysical uncertainties in DD. Nevertheless, these new estimates cannot be used blindly as they rely on assumptions in the dark halo modeling which induce tight correlations between the escape speed and other local astrophysical parameters. We make a self-consistent study of the implications of the RAVE results on DD assuming isotropic DM velocity distributions, both Maxwellian and ergodic. Taking as references the experimental sensitivities currently achieved by LUX, CRESST-II, and SuperCDMS, we show that: (i) the exclusion curves associated with the best-fit points of P14 may be more constraining by up to $\sim 40$% with respect to standard limits, because the underlying astrophysical correlations induce a larger local DM density; (ii) the corresponding relative uncertainties inferred in the low WIMP mass region may be moderate, down to 10-15% below 10 GeV. We finally discuss the level of consistency of these results with other independent astrophysical constraints. This analysis is complementary to others based on rotation curves.