Sliding into DM: Determining the local dark matter density and speed distribution using only the local circular speed of the Galaxy

Abstract: We use FIRE-2 zoom simulations of Milky Way size disk galaxies to derive easy-to-use relationships between the observed circular speed of the Galaxy at the Solar location, $v_\mathrm{c}$, and dark matter properties of relevance for direct detection experiments: the dark matter density, the dark matter velocity dispersion, and the speed distribution of dark matter particles near the Solar location. We find that both the local dark matter density and 3D velocity dispersion follow tight power laws with $v_\mathrm{c}$. Using this relation together with the observed circular speed of the Milky Way at the Solar radius, we infer the local dark matter density and velocity dispersion near the Sun to be $\rho = 0.42\pm 0.06\ \mathrm{GeV}\,\mathrm{cm^{-3}}$ and $\sigma_{\rm 3D} = 280^{+19}_{-18}\,\mathrm{km\,s^{-1}}$. We also find that the distribution of dark matter particle speeds is well-described by a modified Maxwellian with two shape parameters, both of which correlate with the observed $v_{\rm c}$. We use that modified Maxwellian to predict the speed distribution of dark matter near the Sun and find that it peaks at a most probable speed of $257\,\mathrm{km\,s^{-1}}$ and begins to truncate sharply above $470\,\mathrm{km\,s^{-1}}$. This peak speed is somewhat higher than expected from the standard halo model, and the truncation occurs well below the formal escape speed to infinity, with fewer very-high-speed particles than assumed in the standard halo model.