How to Build an Empirical Speed Distribution for Dark Matter in the Solar Neighborhood

TL;DR

The paper tackles the problem of inferring the local dark matter speed distribution relevant to direct detection by constructing an observationally anchored, two-component model. Using 98 Milky Way analogues from IllustrisTNG50, it separates local DM into Old/Young Untraceable (approximated by a Maxwell–Boltzmann SHM with $v_0 = \sqrt{GM(<R_\odot)/R_\odot}$) and Traceable components tied to recent massive mergers, whose DM is traced by the kinematics of associated stellar debris after applying a dispersion-boost correction with $\Delta\sigma = 34_{-11}^{+10}$ km s$^{-1}$. The total local DM speed distribution is reconstructed as a weighted sum of the SHM background and traced mergers, demonstrated to match exact distributions with typical Earth Mover’s Distances $\mathrm{EMD} = 8^{+3}_{-2}$ km s$^{-1}$ across MW analogues, and $\mathrm{EMD} \approx 6^{+5}_{-3}$ km s$^{-1}$ when applied to the Milky Way with Gaia GSE data. This framework provides a practical, observation-based pathway to more accurately model the local DM speed distribution, with quantified uncertainties from merger weights $w_{\mathrm{tr}}$ and dispersion boosts, with implications for direct detection rate predictions and high-speed tail assessments.

Abstract

The dark matter flux in a direct detection experiment depends on its local speed distribution. This distribution has been inferred from simulations of Milky Way-like galaxies, but such models serve only as proxies given that no simulation directly captures the detailed evolution of our own Galaxy. This motivates alternative approaches which obtain this distribution directly from observations. In this work, we utilize 98 Milky Way analogues from the IllustrisTNG50 simulation to develop and validate a procedure for inferring the dark matter speed distribution using the kinematics of nearby stars. We find that the dark matter that originated from old mergers, plus that from recent non-luminous accretions, is well described by a Maxwell-Boltzmann speed distribution centered at the local standard-of-rest velocity. Meanwhile, recently accreted dark matter from massive mergers has speeds that can be traced from the associated stellar debris of these events. The stellar populations systematically underestimate the velocity dispersion of their dark matter counterparts, but a simple kinematic boost brings the two into good alignment. Using the TNG50 host galaxies, we demonstrate that combining these two contributions provides an accurate reconstruction of the local dark matter speeds. As an application of the procedure to our own Galaxy, we utilize stellar kinematic data from Gaia to quantify how the dark matter remnants from the Milky Way's last major merger impact its speed distribution in the Solar neighborhood.

Figures (14)

• Figure 1: (Left:) Fraction of DM in the solar annulus (6--10 kpc in cylindrical radius and height $|z|\leq2$ kpc) originating from Traceable mergers versus the fraction accreted prior to redshift 3 (Old Untraceable DM), across the 98 MW analogues. Points are colored by the number of Traceable mergers and shaped by the presence (star markers) or absence (circle markers) of a GSE-like event in that galaxy's history. Marginal histograms show the distribution of each quantity across the sample given the number of Traceable mergers. For systems with one Traceable merger, $58^{+12}_{-17}\%$ of the DM in the solar annulus is Old Untraceable, while $18^{+15}_{-5}\%$ is Traceable. The remaining $21^{+11}_{-12}\%$ is contributed after redshift three but lacks a substantial population of luminous tracers (Young Untraceable). (Right:) Speed distributions for the three DM components in the solar annulus: Old Untraceable (yellow), Young Untraceable (magenta), and Traceable (blue). The solid line represents the median probability density, while shaded regions indicate the 16th-to-84th percentile range across the sample. While the Young Untraceable component exhibits greater halo-to-halo variance and is biased toward higher speeds, it typically represents a small fraction of the total Untraceable DM, such that the combined distribution is well described by a Maxwell--Boltzmann profile. The Traceable component can be modeled using the kinematics of the associated stellar debris. The DM components (Old Untraceable, Young Untraceable, and Traceable) are defined in \ref{['subsec:mergers']}.
• Figure 2: Stacked speed distributions of the Old Untraceable (yellow) and Young Untraceable (magenta) DM components in the solar annulus for three representative MW analogues (each containing one GSE-like Traceable merger) with varying Young Untraceable fractions. The Standard Halo Model (SHM, black curve) is shown for each halo as a Maxwell--Boltzmann distribution with scale velocity $v_0$ set by the mass enclosed within the solar radius. When the Young Untraceable fraction is small, as in the left panel, the combined distribution is well described by the SHM, yielding an EMD of 9 $\text{km}~\text{s}^{-1}$ between the SHM and the Untraceable DM. For the middle and right panels, the EMD values increase to 14 $\text{km}~\text{s}^{-1}$ and 28 $\text{km}~\text{s}^{-1}$, respectively, reflecting the growing deviations from a Maxwell--Boltzmann shape as the Young Untraceable fraction becomes larger.
• Figure 3: EMDs between the SHM and the speed distribution of the Old Untraceable DM (solid yellow) or the Untraceable components combined (dashed purple). The Old Untraceable component on its own is well described by a Maxwell--Boltzmann, with an EMD of $13^{+8}_{-6}~\text{km}~\text{s}^{-1}{}$, while the Young Untraceable component alone (not shown in the figure) is not, lying $65^{+52}_{-32}~\text{km}~\text{s}^{-1}{}$ from the SHM. However, since the Young Untraceable component is typically a small fraction of the DM in the solar annulus, combining the Old and Young Untraceable components together is still well modeled by the SHM, with an EMD of $13^{+13}_{-6}~\text{km}~\text{s}^{-1}$.
• Figure 4: Speed distributions of Traceable DM (filled blue) and stars accreted from the same merger (solid orange) for the Traceable merger in each of the three MW analogues from \ref{['fig:2']}. In each case, the stars under-predict the DM speed. To correct for this, we boost the dispersion of the stellar tracers according to \ref{['eq:boost']}, giving the boosted stellar distribution (dashed orange). Before the boost, the EMDs between the DM and stellar speed distributions are 49, 48, and 40 $\text{km}~\text{s}^{-1}$ for the left, middle, and right panels, respectively. The boosted stellar distribution more closely traces the DM distribution, and the resulting EMDs are reduced to 4, 5, and 5 $\text{km}~\text{s}^{-1}$, respectively.
• Figure 5: Correlation between stellar and DM kinematics for the 108 Traceable mergers. The top row shows the mean galactocentric velocities $\bar{v}_i$ for each of the spherical components, $i\in \{r,\phi,\theta\}$, while the bottom row shows the velocity dispersion in each of these components. In each panel, the horizontal axis shows the value for the stars contributed by each merger, while the vertical axis shows the value for the DM contributed by the same merger. Equality is indicated by the dashed gray line, such that probability density along this line indicates good agreement between the DM and the stellar tracers. The probability density across the full sample of mergers is shown in the background (blue, with darker indicating higher probability), with the GSE-like mergers highlighted using star markers. Across the sample, the DM and stars have similar mean velocities, with a difference in $\bar{v}_i$ of $(-1^{+5}_{-3}, -15^{+16}_{-34}, 0^{+4}_{-6})~\text{km}~\text{s}^{-1}{}$ for $(v_r, v_\phi, v_\theta)$. The velocity dispersions, on the other hand, are shifted: the DM exhibits an offset of $\Delta\sigma = 34_{-11}^{+10}~\text{km}~\text{s}^{-1}{}$ with respect to the stars, for $\Delta\sigma$ the directionally-averaged difference in dispersions (\ref{['eq:delta_sigma']}). The dispersions are particularly discrepant ($\Delta \sigma = 43^{+11}_{-10}~\text{km}~\text{s}^{-1}{}$) for the GSE-like mergers, which are chosen based on their radially-biased stars and have lower stellar tangential dispersions relative to the overall population of mergers. The offset in dispersions biases the stellar tracers to predict lower speeds for the DM, as seen in \ref{['fig:4']}, which is corrected for by \ref{['eq:boost']}.