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Dark Matter (DM) properties at small scales remain uncertain. Recenttheoretical and observational advances have provided the tools to narrow themdown. Here, we show for the first time that the correlation between internalvelocities and sizes of dwarf galaxies is a sharp probe of small-scale DMproperties. We study modified DM power spectra, motivated by DM productionduring inflation. Using semi-analytic models and scaling relations, we showthat such models can change the kinematics and structure of dwarf galaxieswithout strongly affecting their total abundance. We analyze data from MilkyWay classical satellite galaxies and those discovered with the Sloan DigitalSky Survey (SDSS), finding that the DM power spectrum at comoving scales ${4\,\mathrm{Mpc}^{-1} < k < 37\,\mathrm{Mpc}^{-1}}$ cannot deviate by more than afactor of 2 from scale invariance. Our results are robust against baryonicuncertainties such as the stellar mass-halo mass relation, halo occupationfraction, and subhalo tidal disruption; allowing us to independently constrainthem. This work thus opens a window to probe both dwarf galaxy formation modelsand small-scale DM properties.

Milky Way satellite velocities reveal the Dark Matter power spectrum at small scales