Testing warm dark matter with kinematics of the smallest galaxies

Every dark matter halo forms with a $\rho\propto r^{-1.5}$ density cusp at its center. For warm dark matter (WDM), these prompt cusps can be massive enough to influence the kinematics of dwarf galaxies. By implementing prompt cusps in the Galacticus galaxy formation model, we show that the measured velocity dispersions of Tucana V and Triangulum II are serious outliers for dwarf galaxies arising in WDM models. For thermal-relic dark matter, the three faintest Milky Way satellites together constrain the particle mass to be $m_\chi>5.8$ keV at 95 percent confidence or $m_\chi>9.4$ keV at 90 percent confidence. Improved velocity dispersion measurements for these systems could greatly refine this constraint, as could identification and kinematic characterization of more such galaxies.