The local dark matter phase-space density and impact on WIMP direct detection

Abstract

Abstract. We present a new determination of the local dark matter phase-space density.This result is obtained implementing, in the limit of isotropic velocity distribution and spherical symmetry, Eddington's inversion formula, which links univocally the dark matter distribution function to the density profile, and applying, within a Bayesian framework, a Markov Chain Monte Carlo algorithm to sample mass models for the Milky Way against a broad and variegated sample of dynamical constraints. We consider three possible choices for the dark matter density profile, namely the Einasto, NFW and Burkert profiles, finding that the velocity dispersion, which characterizes the width in the distribution, tends to be larger for the Burkert case, while the escape velocity depends very weakly on the profile, with the mean value we obtain being in very good agreement with estimates from stellar kinematics. The derived dark matter phase-space densities differ significantly-most dramatically in the high velocity tails-from the model usually taken as a reference in dark matter detection studies, a Maxwell-Boltzmann distribution with velocity dispersion fixed in terms of the local circular velocity and with a sharp truncation at a given value of the escape velocity. We discuss the impact of astrophysical uncertainties on dark matter scattering rates and direct detection exclusion limits, considering a few sample cases and showing that the most sensitive ones are those for light dark matter particles and for particles scattering inelastically. As a general trend, regardless of the assumed profile, when adopting a self-consistent phase-space density, we find that rates are larger, and hence exclusion limits stronger, than with the standard Maxwell-Boltzmann approximation. Tools for applying our result on the local dark matter phase-space density to other dark matter candidates or experimental setups are provided.

Deriving the velocity distribution of Galactic dark matter particles from the rotation curve data

“…ble II are in reasonably good agreement with the values of these quantities quoted in recent literature [8,12,17].…”

Self-consistent phase-space distribution function for the anisotropic dark matter halo of the Milky Way

“…This is consistent with the results of Refs. [13,33]. There seems to be a characteristic speed (around 300 km s −1 ) for which the speed distribution has a minimum uncertainty.…”

“…Therefore we must marginalize over β 0 , β ∞ and L 0 , which can lead to large uncertainties in F(E, L). However, the relevant quantity for direct detection experiments is the local speed distribution f 1 (v), defined as 6 Note that the original Eddington formalism, for a spherical isotropic system, does not require any additional parameters and the speed distribution is completely determined by the gravitational potential [13,[32][33][34]. and f 1 (v) turns out to be much less dependent on the form of F L (L) than F E (E), and therefore it is possible to reconstruct f 1 (v) with reasonable uncertainties even when marginalizing over β 0 , β ∞ and L 0 .…”

Astrophysical uncertainties on the local dark matter distribution and direct detection experiments

“…Catena and Ullio [149] built mass models of the MW, including its luminous components and a range of possibilities for the density profile of the DM halo. They used a large ensemble of astronomical data sets to constrain the parameters of the mass model, and then used the Eddington formalism to self-consistently calculate the speed distribution (see also Ref.…”