Stacked speed distributions of the Old Untraceable (yellow) and Young Untraceable (magenta) DM components in the solar annulus for three representative MW analogs (each containing one GSE-like Traceable merger) with varying Young Untraceable fractions. The SHM (black curve) is shown for each halo as a Maxwell–Boltzmann distribution with scale velocity v₀ 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 km s⁻¹ between the SHM and the Untraceable DM. For the middle and right panels, the EMD values increase to 14 km s⁻¹ and 28 km s⁻¹, respectively, reflecting the growing deviations from a Maxwell–Boltzmann shape as the Young Untraceable fraction becomes larger.