Dark Matter that Interacts with Baryons: Density Distribution within the Earth and New Constraints on the Interaction Cross-section

Abstract: For dark matter (DM) particles with masses in the 0.6 - 6 m_p range, we set stringent constraints on the interaction cross-sections for scattering with ordinary baryonic matter. These constraints follow from the recognition that such particles can be captured by - and thermalized within - the Earth, leading to a substantial accumulation and concentration of DM that interact with baryons. Here, we discuss the probability that DM intercepted by the Earth will be captured, the number of DM particles thereby accumulated over Earth's lifetime, the fraction of such particles retained in the face of evaporation, and the density distribution of such particles within the Earth. In the latter context, we note that a previous treatment of the density distribution of DM, presented by Gould and Raffelt and applied subsequently to DM in the Sun, is inconsistent with considerations of hydrostatic equilibrium. Our analysis provides an estimate of the DM particle density at Earth's surface, which may exceed 1.E+14 cm-3 for the mass range under consideration. Based upon our determination of the DM density at Earth's surface, we derive constraints on the scattering cross-sections. These constraints are placed by four considerations: (1) the lifetime of the relativistic proton beam at the Large Hadron collider (LHC); (2) the orbital decay of spacecraft in low Earth orbit (LEO); (3) the vaporization rate of cryogenic liquids in well-insulated storage dewars; and (4) the thermal conductivity of Earth's crust. As an example application of our results, we show that for the scattering cross-sections that were invoked recently in Barkana's original explanation for the anomalously deep 21 cm absorption reported by EDGES, DM particle masses in the 0.6 - 4 m_p range are ruled out.