Galactic Substructure and Direct Detection of Dark Matter

TL;DR

The paper develops a local-density PDF $P(\rho)$ to quantify how Galactic halo substructure affects direct detection and WIMP annihilation signals. It employs two complementary strategies: a scale-invariant analytic model for early, dense subhalos and a simulation-inspired model for later substructures, finding a skewed $P(\rho)$ with a mean near $\rho_\odot\approx 0.4$ GeV cm$^{-3}$ but possible lower values around $\sim$0.04–0.2 GeV cm$^{-3}$. The work shows that large annihilation boosts require strong survival of early subhalos and near-constant survival fractions across the hierarchy, while direct-detection rates depend on the reduced local density in many realizations. It also provides concrete results for discrete subhalo populations and outlines how the PDF and boost factor vary with radius, concentration, and subhalo mass function, arguing for using $P(\rho; r)$ or $B(r)$ in interpreting experiments. Overall, the study highlights the importance of incorporating halo substructure into null-search analyses and the interpretation of potential annihilation signals.

Abstract

We study the effects of substructure in the Galactic halo on direct detection of dark matter, on searches for energetic neutrinos from WIMP annihilation in the Sun and Earth, and on the enhancement in the WIMP annihilation rate in the halo. Our central result is a probability distribution function (PDF) P(ρ) for the local dark-matter density. This distribution must be taken into account when using null dark-matter searches to constrain the properties of dark-matter candidates. We take two approaches to calculating the PDF. The first is an analytic model that capitalizes on the scale-invariant nature of the structure--formation hierarchy in order to address early stages in the hierarchy (very small scales; high densities). Our second approach uses simulation-inspired results to describe the PDF that arises from lower-density larger-scale substructures which formed in more recent stages in the merger hierarchy. The distributions are skew positive, and they peak at densities lower than the mean density. The local dark-matter density may be as small as 1/10th the canonical value of ~ 0.4 GeV/cm^3, but it is probably no less than 0.2 GeV/cm^3.

Figures (3)

• Figure 1: The local dark-matter-density probability distribution function $P(\rho)$ for the analytic model, as a function of the density $\rho$ scaled by the mean density $\rho_\odot$, for $\{f(\rho_\odot),\alpha\}=\{0.05,0\}$ (black solid curve), $\{0.2,0\}$, (dotted red curve), $\{0.05,1\}$, (short-dash blue curve) $\{0.2,1\}$ (long-dash green curve). We smooth the Dirac delta function for the smooth component to a Gaussian of rms one-tenth the smooth-component density. The power-law tails are due to subhalos.
• Figure 2: The local dark-matter-density probability distribution function $P(\rho)$, for the discrete-subhalo model, as a function of the density $\rho$ scaled by the mean density $\rho_\odot$, for $c_{\rm v}=10$ (black solid curve) and $c_{\rm v}=2$ (dotted red curve).
• Figure 3: The probability distribution function in the solar neighborhood for the simulation-inspired calculation. The solid, long-dash and dot-dash curves correspond to $\xi=0.1$, 0.5, and 0.8 respectively. As in Fig. \ref{['fig:logPDF']}, we smooth the Dirac delta function for the density value of the smooth component with a Gaussian of rms a tenth of the smooth-component density. The upper and lower curves for each value of $\xi$ show the range of contribution of the subhalo population that arises from uncertainties in the subhalo mass function, as well as the subhalo population (see text).