Observationally inferred dark matter phase-space distribution and direct detection experiments

Abstract

We present a detailed analysis of the effect of an observationally determined dark matter (DM) velocity distribution function (VDF) of the Milky Way (MW) on DM direct detection rates. We go beyond local kinematic tracers and use rotation curve data up to 200 kpc to construct a MW mass model and self-consistently determine the local phase-space distribution of DM. This approach mitigates any incomplete understanding of local dark matter-visible matter degeneracies that can affect the determination of the VDF. Comparing with the oft used Standard Halo Model (SHM), which assumes an isothermal VDF, we look at how the tail of the empirically determined VDF alters our interpretation of the present direct detection WIMP DM cross section exclusion limits. While previous studies have suggested a very large difference (of more than an order of magnitude) in the bounds at low DM masses, we show that accounting for the detector response at low threshold energies, the difference is still significant although less extreme. The change in the number of signal events, when using the empirically determined DM VDF in contrast to the SHM VDF, is most prominent for low DM masses for which the shape of the recoil energy spectrum depends sensitively on the detector threshold energy as well as detector response near the threshold. We demonstrate that these trends carry over to the respective DM exclusion limits, modulo detailed understanding of the experimental backgrounds. With the unprecedented precision of astrometric data in the GAIA era, use of observationally determined DM phase-space will become a critical and necessary ingredient for DM searches. We provide an accurate fit to the current best observationally determined DM VDF (and self-consistent local DM density) for use in analyzing current DM direct detection data by the experimental community.

Non-parametric uncertainties in the dark matter velocity distribution

“…The number of terms in the sum is equal to the number of unique ways of partitioning q into any number of smaller terms, i.e., the partition function of q. The first ten partitions are 1,2,3,5,7,11,15,22,30 and 42, and, asymptotically, the number of partitions grows exponentially with q. The formula allows us to express complicated moments of a multinomial in terms of simpler ones; in this regard, it is similar to Wick's theorem for Gaussian moments.…”

Inferred Evidence for Dark Matter Kinematic Substructure with SDSS–Gaia

“…One possibility is to use the motion of stars to constrain the local gravitational potential (or density) and to subsequently infer the velocity distribution using the Jeans theorem. A variety of proposals of this nature have been made (Hansen & Moore 2006;Chaudhury et al 2010;Lisanti et al 2011;Catena & Ullio 2012;Bhattacharjee et al 2013;Bozorgnia et al 2013;Fornasa & Green 2014;Mandal et al 2018), but they typically rely on the assumption that the DM is isotropic and/or in equilibrium, either of which may be violated depending on the Milky Way's accretion history.…”

Bracketing the impact of astrophysical uncertainties on local dark matter searches

“…[34]). Deviations from this simple model of the DM halo are expected in the Milky Way [35][36][37][38] and while the parameters associated with the SHM (such as the Sun's velocity [39], the local circular velocity [40] and the Galactic escape velocity [41]) can be estimated observationally, they carry with them an associated uncertainty [10,42,43]. In addition, numerical simulations have suggested the possibility of non-Maxwellian structure in the DM velocity distribution [44][45][46][47][48][49][50][51].…”