Diurnal Effect of Sub-GeV Dark Matter Boosted by Cosmic Rays

We point out a new type of diurnal effect for the cosmic ray boosted dark matter (DM). The DM-nucleon interactions not only allow the direct detection of DM with nuclear recoils but also allow cosmic rays to scatter with and boost the nonrelativistic DM to higher energies. If the DM-nuclei scattering cross sections are sufficiently large, the DM flux is attenuated as it propagates through the Earth, leading to a strong diurnal modulation. This diurnal modulation provides another prominent signature for the direct detection of boosted sub-GeV DM, in addition to signals with higher recoil energy.

Figure 1

Relative sky maps of CRDM fluxes in the Galactic coordinates with amplitude in the GC direction set to unity. The upper and lower panels are for the NFW and Isothermal DM density profiles, respectively.

Figure 2

The CRDM energy spectra at the GC direction for DM masses ${10}^{-4}$, ${10}^{-3}$, ${10}^{-2}$, 0.1, 1.0, and 10 GeV from top to bottom. The scattering cross section ${\sigma }_{\chi p}$ is assumed to be ${10}^{-32}{\mathrm{cm}}^2$. The inset is the distribution of DM velocities, $\beta =v/c$, compared to the Maxwellian distribution of the Standard DM Halo. For a clear comparison, we rescale the Standard DM Halo curve by ${10}^{-4}$ (labeled as $\mathrm{halo}\times {10}^{-4}$ in the inset) so that all curves have a similar height.

Figure 3

The attenuated CRDM spectra for the nadir angles ${\theta }_{\text{nadir}}=30°$ (red), 60° (green), and 90° (blue) with ${\sigma }_{\chi p}={10}^{-32}{\mathrm{cm}}^2$, $m_{\chi }=10\mathrm{MeV}$, and the detector at a depth of 2 km. For comparison, we also show the original standard halo DM flux distribution in the inset.

Figure 4

The survival probability of CRDM arriving at an underground lab at latitude 28°N and a depth of 2 km vs the sidereal hour relative to the number of DM particles arriving at the Earth for two different cross sections ${\sigma }_{\chi p}=1(3)\times {10}^{-32}{\mathrm{cm}}^2$. The red curves correspond to the total CRDM arriving at the detector with $T_{\chi }\ge T_{\chi }^{\min }$, and the blue curves are those above the detector threshold ($T_r>3\mathrm{keV}$ for a liquid xenon detector).

Figure 5

The nuclear recoil spectrum, including the 3 keV detector threshold, for a xenon detector with 1 ton year exposure. To illustrate the attenuation effect, each curve corresponds to the integrated DM flux at a given nadir angle ${\theta }_{\text{nadir}}$.