  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.
