Empirical Determination of Dark Matter Velocities Using Metal-Poor Stars

The Milky Way dark matter halo is formed from the accretion of smaller subhalos. These sub-units also harbor stars—typically old and metal-poor—that are deposited in the Galactic inner regions by disruption events. In this Letter, we show that the dark matter and metal-poor stars in the Solar neighborhood share similar kinematics due to their common origin. Using the high-resolution eris simulation, which traces the evolution of both the dark matter and baryons in a realistic Milky Way analog galaxy, we demonstrate that metal-poor stars are indeed effective tracers for the local, virialized dark matter velocity distribution. The local dark matter velocities can therefore be inferred from observations of the stellar halo made by the Sloan Digital Sky Survey within 4 kpc of the Sun. This empirical distribution differs from the standard halo model in important ways and suggests that the bounds on the spin-independent scattering cross section may be weakened for dark matter masses below $\sim 10\mathrm{GeV}$. Data from Gaia will allow us to further refine the expected distribution for the smooth dark matter component, and to test for the presence of local substructure.

Figure 1

The density distribution as a function of Galactocentric radius for the dark matter (black) and all stars (cyan) in eris. The distributions for subsamples of stars with $[\alpha /\mathrm{Fe}]>0.2$ and $[\mathrm{Fe}/\mathrm{H}]<-1,-2,-3$ are also shown (dotted brown, dashed red, and solid orange, respectively). The density of the most metal-poor stellar population exhibits the same dependence on radius as the dark matter near the Sun’s position, $r_{\odot }\sim 8\mathrm{kpc}$.

Figure 2

Distributions of the three separate velocity components of the DM (solid black) and stars in eris. The velocities are in the Galactocentric frame, where the $z$ axis is oriented along the stellar angular momentum vector. The stellar distributions are shown separately for different metallicities, with $[\alpha /\mathrm{Fe}]>0.2$ and iron abundance varying from $[\mathrm{Fe}/\mathrm{H}]<-1$ (dotted brown) to $[\mathrm{Fe}/\mathrm{H}]<-3$ (solid orange). The distribution for all stars—dominated primarily by the disk—is also shown (solid cyan). All distributions are shown for $|r-r_{\odot }|\le 2\mathrm{kpc}$; the DM is additionally required to lie within 2 kpc of the plane. To guide the eye, the orange shading highlights the differences between the DM and $[\mathrm{Fe}/\mathrm{H}]<-3$ distributions. The discrepancy in the $v_{\varphi }$ distributions is due to the preferential disruption of subhalos on prograde orbits in eris; observations of the Milky Way halo do not see such pronounced prograde rotation [60, 61].

Figure 3

Galactocentric speed distributions for SDSS stars within 4 kpc of the Sun and Galactocentric distances of $7<r<10\mathrm{kpc}$, based on results from [64]. The distributions are shown for $[\mathrm{Fe}/\mathrm{H}]\in [-2.2,-2]$ (solid purple) and $[\mathrm{Fe}/\mathrm{H}]<-2.2$ (solid orange). For comparison, we show the standard halo model (dashed gray) with $v_c=220\mathrm{km}/\mathrm{s}$. Not captured by this figure is the fact that the stellar distributions are not isotropic, as is typically assumed for the standard halo model. The inset shows the expected background-free 95% C.L. limit on the DM spin-independent scattering cross section, assuming the exposure and energy threshold of the LUX experiment [65] for the SDSS and SHM velocity distributions.