Density Fluctuations in the Galactic Halo and Experimental Searches for Dark Matter

The interpretation of the results of experiments designed to search for elementary particle dark matter in the Milky Way halo relies on specific suppositions concerning the local mass density and velocity distribution of the unseen particles. Predicted detection rates have all been computed under the assumptions that the halo density profile is smooth, and the velocity distribution is at least approximately Maxwellian, with a one-dimensional velocity dispersion σ = Vc/ √ 2 ≈ 160 km s, where Vc ≈ 220 km s is the Galactic rotation speed. However, an experiment that operates for a time T ∼ 1 yr only probes a region that extends to a distance D ∼ σT ∼ 5× 10 cm ≈ 35A.U., which is about the distance to the planet Pluto; for comparison, the distance to the center of the Galaxy is D0 ≈ 8.5 kpc ≈ 2 × 10 A.U.. While few would doubt that the halo density may be regarded as smooth on some intermediate length scale, say <∼ 0.01 − 1 kpc, there is reason to question whether the halo really ought to be perfectly smooth on length scales of order the size of the inner Solar System, ∼ 10 − 10 kpc. If the halo is clumpy on small scales, then it is possible that presently the Earth is not immersed in a bath of dark matter particles, so that the non-detection of such particles need not imply their absence. As a simple but extreme example, suppose that the dark matter particles are organized into lumps of internal density ρcl ≫ ρ, where ρ ≈ 0.01M⊙ pc is the mean halo density locally; then the probability that the Earth sits in a dark matter clump is the volume filling factor, f = ρ/ρcl ≪ 1. If instead the halo contains a continuous mass spectrum of dark matter lumps, so that ρψ(M)dM is the contribution to the local halo density from clumps of mass M and internal density ρcl(M), then the volume filling factor of the halo is