LERMA UMR8112

While cold dark matter numerical simulations predict steep, `cuspy' density profiles for dark matter halos, observations favour shallower `cores'. The introduction of baryonic physics alleviates this discrepancy, notably as feedback-driven outflow episodes contribute to expand the dark matter distribution for stellar masses between 10^7 and 10^10 Msun. I will first present a parametrization of dark matter halo density profiles with variable inner slope and concentration that enables to describe the variety of halo responses to baryons and has analytic expressions for the gravitational potential, the velocity dispersion, and lensing properties. This parametrization provides a useful tool to study the evolution of dark matter haloes, to model rotation curves of galaxies and gravitational lenses, and to be implemented in semi-analytical models of galaxy evolution. I will then present two theoretical models describing core formation in dark matter haloes. In the first one, sudden bulk outflows induced by stellar feedback reorganise the halo mass distribution while it relaxes to a new equilibrium. In the second one, small stochastic density fluctuations induce kicks to collisionless particles that progressively deviate them from their orbits. Both models are tested against numerical simulations and provide a simple understanding of the transition from cusps to cores by feedback-driven outflows.