  Gravitational potential fluctuations driven by bursty star formation can
kinematically 'heat up' dark matter at the centres of dwarf galaxies. A key
prediction of such models is that, at a fixed dark matter halo mass, dwarfs
with a higher stellar mass will have a lower central dark matter density. We
use stellar kinematics and HI gas rotation curves to infer the inner dark
matter densities of eight dwarf spheroidal and eight dwarf irregular galaxies
with a wide range of star formation histories. For all galaxies, we estimate
the dark matter density at a common radius of 150pc, $\rho_{\rm
DM}(150\,\mathrm{pc})$. We find that our sample of dwarfs falls into two
distinct classes. Those that stopped forming stars over 6Gyrs ago favour
central densities $\rho_{\rm DM}(150\,\mathrm{pc})>10^8\,{\rm M}_\odot\,{\rm
kpc}^{-3}$, consistent with cold dark matter cusps, while those with more
extended star formation favour $\rho_{\rm DM}(150\,\mathrm{pc})<10^8\,{\rm
M}_{\odot}\,{\rm kpc}^{-3}$, consistent with shallower dark matter cores. Using
abundance matching to infer pre-infall halo masses, $M_{200}$, we show that
this dichotomy is in excellent agreement with models in which dark matter is
heated up by bursty star formation. In particular, we find that $\rho_{\rm
DM}(150\,\mathrm{pc})$ steadily decreases with increasing stellar mass-to-halo
mass ratio, $M_*/M_{200}$. Our results suggest that, to leading order, dark
matter is a cold, collisionless, fluid that can be kinematically 'heated up'
and moved around.
