Deciphering the Kinematic Substructure of Local Dark Matter with LAMOST K Giants

Numerical simulations indicate that correlations exist between the velocity distributions of stars and dark matter (DM). We study the local DM velocity distribution based on these correlations. We select K giants from LAMOST DR8 cross-matched with {\gaia} DR3, which have robust measurements of velocity and metallicity, and separate them into the disk, halo substructure and isotropic halo components in the chemodynamical space utilizing the Gaussian Mixture Model. The substructure component is highly radially anisotropic, and possibly related to the \gaia-Enceladus-Sausage (GES) merger event, while the isotropic halo component is accreted from the earliest mergers following the Maxwell-Boltzmann distribution (Standard Halo Model, SHM). We find that the GES-like substructure contributes $\sim85\%$ of the local nondisk stars in the Solar neighbourhood, which is nearly invariant when applying different volume cuts or additional angular momentum constraints. Utilizing the metallicity-stellar mass relation and the stellar mass-halo mass relation, we find that $\sim25_{-15}^{+24}\%$ of local DM is in the kinematic substructure. Combined with the stellar distributions of nondisk components, we modify the heliocentric velocity distribution of local DM. It shifts to a lower speed with a sharper peak compared to the SHM, and updates the detection limits of DM direct detection experiments. We discuss extensively the degeneracies present in the GMM fitting and propose that more kinematic and chemical information such as $\alpha$ abundance could help to break the degeneracy in the future. Our work confirms that the local DM velocity distribution deviates significantly from the SHM, and needs to be properly accounted for in the DM detection experiments.