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

Direct detection (DD) of dark matter (DM) candidates in the $\lesssim 10\mathrm{GeV}$ mass range is very sensitive to the tail of their velocity distribution. The important quantity is the maximum weakly interacting massive particle speed in the observer’s rest frame, i.e. in average the sum of the local Galactic escape speed $v_{\text{esc}}$ 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 $v_{\text{esc}}$ [T. Piffl et al., Astron. Astrophys. 562, A91 (2014)] that supersedes the previous one [M. C. Smith, et al. Mon. Not. R. Astron. Soc. 379, 755 (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, and (ii) the corresponding relative uncertainties inferred in the low weakly interacting massive particle 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.

Figure 1

P14 likelihood results converted in the plane $v_{\text{esc}}\text{−}{v}_c$. See the text for details.

Figure 2

Comparison between a truncated MB DF and an ergodic DF. Left panel: Assuming the parameters of the P14 best-fit point with $v_c=220\mathrm{km}/\mathrm{s}$, we show the MB curve and several curves for ergodic case to make the impact of the baryonic components explicit. Right panel: Comparison of the MB-like DFs with the ergodic DFs assuming the parameters of the P14 best-fit points with both $v_c=220$ and $240\mathrm{km}/\mathrm{s}$. Here, we also show the DFs associated with the upper and lower corners of the 90% C.L. interval.

Figure 3

P14 90% C.L. results on $v_{\text{esc}}$ converted into DD exclusion curves, from the LUX, CRESST-2, and SuperCDMS data. The dashed lines show the SHM exclusion curves (reproducing the original experimental results). Other exclusion curves and bands are obtained using self-consistent ergodic DFs properly correlated to the local DM density inferred from RAVE P14 results (priors) on $v_{\text{esc}}$ (on $v_c$): plain (dotted) lines correspond to the best-fit values for $v_{\text{esc}}$ obtained with the prior $v_c=240\mathrm{km}/\mathrm{s}$ ($v_c=220\mathrm{km}/\mathrm{s}$)—surrounded by the corresponding 90% C.L. bands. The dotted-dashed lines represent the P14 $v_c$-free case, where the uncertainty bands indicate 1% of the maximum value of the (normalized) likelihood. See the text for more details.

Figure 4

Top panels: experimental limits calculated using the P14 best-fit point with the prior $v_c=240\mathrm{km}/\mathrm{s}$ (${\rho }_{\odot }=0.43\mathrm{GeV}/{\mathrm{cm}}^3$; $v_{\text{esc}}=511\mathrm{km}/\mathrm{s}$) and associated 90% C.L. contour. Bottom panels: relative uncertainties with respect to the central value. Left panels: LUX data. Middle panels: SuperCDMS data. Right panels: CRESST-II data. See the text for details.

Figure 5

Top panels: experimental limits calculated with a combination of the P14 $v_c$-free analysis with additional constraints on $v_c$ from Ref. [55]. Bottom panels: relative uncertainties with respect to the $v_c=240\mathrm{km}/\mathrm{s}$ best-fit point of P14. Left panels: LUX data. Middle panels: SuperCDMS data. Right panels: CRESST-II data. See the text for details.

Figure 6

Same as Fig. 5, but for the $v_c\text{−}{v}_{\text{esc}}$ range supposed to properly take the anticorrelation into account (cite dotted lines in Fig. 1).

Figure 7

Effect of not considering the correlation of the astrophysical parameters (local DM density and relevant speeds) in drawing the relative uncertainty in the LUX DD exclusion curve. The dashed region is the same as the colored region in the bottom left panel of Fig. 6.