  We propose and successfully test against new cosmological simulations a novel
analytical description of the physical processes associated with the origin of
cored dark matter density profiles. In the simulations, the potential in the
central kiloparsec changes on sub-dynamical timescales over the redshift
interval 4 > z > 2 as repeated, energetic feedback generates large underdense
bubbles of expanding gas from centrally-concentrated bursts of star formation.
The model demonstrates how fluctuations in the central potential irreversibly
transfer energy into collisionless particles, thus generating a dark matter
core. A supply of gas undergoing collapse and rapid expansion is therefore the
essential ingredient. The framework, based on a novel impulsive approximation,
breaks with the reliance on adiabatic approximations which are inappropriate in
the rapidly-changing limit. It shows that both outflows and galactic fountains
can give rise to cusp-flattening, even when only a few per cent of the baryons
form stars. Dwarf galaxies maintain their core to the present time. The model
suggests that constant density dark matter cores will be generated in systems
of a wide mass range if central starbursts or AGN phases are sufficiently
frequent and energetic.
