The Effect of a Single Supernova Explosion on the Cuspy Density Profile of a Small-Mass Dark Matter Halo

Some observations of galaxies, and in particular dwarf galaxies, indicate a presence of cored density profiles in apparent contradiction with cusp profiles predicted by dark matter N-body simulations. We constructed an analytical model, using particle distribution functions (DFs), to show how a supernova (SN) explosion can transform a cusp density profile in a small-mass dark matter halo into a cored one. Considering the fact that a SN efficiently removes matter from the centre of the first haloes, we study the effect of mass removal through a SN perturbation in the DFs. We found that the transformation from a cusp into a cored profile is present even for changes as small as 0.5% of the total energy of the halo, that can be produced by the expulsion of matter caused by a single SN explosion.