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