  Dark matter cores within galaxy haloes can be formed by energy feedback from
star forming regions: an energy balance suggests that the maximum core
formation efficiency arises in galaxies with
M$_{\star}\sim10^{8.5}$M$_{\odot}$. We show that a model population of
galaxies, in which the density profile has been modified by such baryonic
feedback, is able to explain the observed galaxy velocity function and
Tully-Fisher relations significantly better than a model in which a universal
cuspy density profile is assumed. Alternative models, namely warm or
self-interacting dark matter, also provide a better match to these observed
relations than a universal profile model does, but make different predictions
for how halo density profiles vary with mass compared to the baryonic feedback
case. We propose that different core formation mechanisms may be distinguished
based on the imprint they leave on galaxy populations over a wide range of
mass. Within the current observational data we find evidence of the expected
signatures of the mass dependence of core formation generated by baryonic
feedback.
