Measuring the local dark matter density in the laboratory

Despite strong evidence for the existence of large amounts of dark matter (DM) in our Universe, there is no direct indication of its presence in our own solar system. All estimates of the local DM density rely on extrapolating results on much larger scales. We demonstrate for the first time the possibility of simultaneously measuring the local DM density and interaction cross section with a direct detection experiment. It relies on the assumption that incoming DM particles frequently scatter on terrestrial nuclei prior to detection, inducing an additional time-dependence of the signal. We show that for sub-GeV DM, with a large spin-independent DM-proton cross section, future direct detection experiments should be able to reconstruct the local DM density with smaller than 50% uncertainty.

Figure 1

Left: Visualization of the local isodetection angle defined in Eq. (5) at LNGS and a specific moment in time. Right: Final velocity of DM particles as a function of isodetection angle and DM-proton cross section ${\sigma }_p^{\mathrm{SI}}$. For illustration only, we assume straight-line trajectories of DM particles [101] with initial speed $v_{\oplus }+v_{\mathrm{esc}}\approx 775\mathrm{km}/\mathrm{s}$, traveling in the mean direction of the DM flux $-{\mathbf{v}}_{\oplus }$ (i.e., left to right in the left panel).

Figure 2

Projected 95% CL contours using both energy and timing of events. In all cases, we assume a benchmark DM density of ${\rho }_{\chi }^{\prime }=0.4\mathrm{GeV}/{\mathrm{cm}}^3$. We consider five different benchmark cross sections, denoted by different colors. Left: Germanium detector and benchmark DM mass $m_{\chi }^{\prime }=400\mathrm{MeV}$. Right: Sapphire detector and benchmark DM mass $m_{\chi }^{\prime }=100\mathrm{MeV}$ Top: detector in the Northern Hemisphere at LNGS. Bottom: detector in the Southern Hemisphere at SUPL. For a germanium detector in the Southern Hemisphere (bottom left), we find no closed contours in the $({\sigma }_p^{\mathrm{SI}},{\rho }_{\chi })$ plane.

Figure 3

Left: Projected 95% C.L. contour for a single benchmark (${\sigma }_p^{\mathrm{SI}\prime }\approx 3\times {10}^{-32}{\mathrm{cm}}^2,m_{\chi }^{\prime }=100\mathrm{MeV},{\rho }_{\chi }^{\prime }=0.4{\mathrm{GeV}\mathrm{cm}}^{-3}$, black cross), assuming a sapphire detector in the Southern Hemisphere. The colored shading shows the best fit DM mass at each point. Right: Log-likelihood contours in $(m_{\chi },{\rho }_{\chi })$ for three fixed cross-section slices through the parameter space, labeled A–C in the left panel. The white dashed lines show the benchmark values. The log-likelihood is shown relative to the best fit point in each slice (red triangle).