Full reconstruction of the local DM speed distribution. (Left) Speed distributions of the Traceable (blue), Young Untraceable (magenta), and Old Untraceable (yellow) components in the solar annulus for an example MW analog, stacked such that the outer envelope is the total exact DM speed distribution. The reconstructions are comprised of a Maxwell–Boltzmann distribution and an empirical distribution derived from accreted stars according to Equation (7). The reconstruction that uses the true values for the Traceable DM fraction (﹩{w}_{{\rm{tr}}}﹩) and the boost applied to the stellar tracers (Δσ, Equation (5)) is shown in light dashed green and has an EMD of 10 km s⁻¹ from the exact speed distribution. The solid dark green band indicates the 16th–84th percentile range across all reconstructions, sampling over the uncertainty induced by varying these parameters. Even with this uncertainty, the sampled distributions closely match the exact DM distribution, with an EMD between them of ﹩{8}_{-2}^{+3}\,\,\rm{km}\,\,{\,\rm{s}\,}^{-1}﹩. The SHM alone (not shown here) aligns well with the reconstructions for this example. (Right) Distribution of EMDs between the exact speed distributions and the reconstructions across all 70 MW analogs with Traceable mergers, for models using the true values of Δσ and ﹩{w}_{{\rm{tr}}}﹩ (dashed light green) and those that sample the uncertainty in these parameters (solid dark green). The true-value models are ﹩1{0}_{-4}^{+6}\,\,\rm{km}\,\,{\,\rm{s}\,}^{-1}﹩ away from the exact speed distributions, while accounting for uncertainty in the parameters modestly inflates these EMDs to ﹩1{1}_{-4}^{+6}\,\,\rm{km}\,\,{\,\rm{s}\,}^{-1}﹩. These results indicate that the model provides a good fit, even when accounting for uncertainty in the parameters. We also compare the exact distributions to the SHM alone (solid black), which yields an EMD of ﹩1{4}_{-6}^{+15}\,\,\rm{km}\,\,{\,\rm{s}\,}^{-1}﹩. This shows that the SHM provides a reasonable overall approximation, but the inference of the speed distribution improves when including a model of the Traceable component.