(Main panel) The baryonic mass  interior to, from top line to bottom, 1kpc, 500pc and 200pc (HT  simulation). Bursty central star formation coupled to strong supernova  feedback causes coherent, rapid oscillations in the potential interior  to 1kpc. The orbital time of typical dark matter particles interior to  1kpc is & 25Myr. By contrast the simulated supernova bubbles can  encompass the inner kiloparsec in around 3Myr, far too rapidly for the  adiabatic approximation to be valid. The lower panel shows the  disk-plane density during the starburst event at t = 2:56Gyr, z = 2:67. A  large underdense bubble has formed at the centre of the disk through  thermal expansion of gas heated by multiple supernova explosions. The  cross marks the halo
centre.

The mechanism for injecting energy into the dark matter orbits,  illustrated by the exact solution for a time-varying harmonic oscillator  potential. The lower panel shows (solid line) a solution to the  equations of motion where !2 = 1 (blue) at early and late times, while  at intermediate times !2 = 0:1 (red) mimicking baryonic blowout and  recondensation. The changes in potential occur instantaneously; in this  case the final amplitude of the oscillation is approximately twice that  of the initial orbit. The dashed line shows the solution when the  potential changes smoothly over several orbital periods; this gives  adiabatic behaviour, so that the final orbit regains the initial  amplitude, demonstrating the necessity for relatively sudden potential
jumps.  The inset figures (top) illustrate how the post-blowout orbit expansion  implies that the late-time energy gain dominates over the initial  energy loss.

We propose and  successfully test a novel physical model explaining the origin of cored  dark matter density profiles, motivated by recent numerical simulations  of dwarf galaxies. In the simulations, the potential in the central  kiloparsec repeatedly fluctuates on sub-dynamical timescales over the  redshift interval 4 > z > 2 because energetic feedback generates  large underdense bubbles from recurrent, centrally-concentrated bursts  of star formation. These fluctuations are shown to be responsible for  generating a core. Analytic models are presented which describe how  particles orbiting in such rapidly fluctuating gravitational potentials  gain energy. We proceed from first principles, breaking with a  historical reliance on adiabatic approximations which are inappropriate  in the rapidly-changing limit. In the new picture, outflows and galactic  fountains can both give rise to cusp-flattening. Concentrations of  baryons undergoing cycles of rapid expansion and recollapse are the  essential ingredient. Constant density dark matter cores should  therefore be generated in systems of a wide mass range if central  starbursts or AGN phases are sufficiently frequent and energetic.

See the webside for more details.http://arxiv.org/abs/1106.0499 (SY)