  We present and test an effective model for N -body simulations that aims at
mimicking the impact of supernova (SN) feedback on the dark matter (DM)
distribution of isolated halos hosting dwarf galaxies. Although the model is
physically decoupled from the cosmological history of both the DM halo and the
dwarf galaxy, it allows us to study the impact of different macroscopic
parameters such as galaxy concentration, total feedback energy and energy
injection time in the process of SN-driven core formation in a physically clear
way. Using our effective model in a suite of N -body simulations of an isolated
halo with different SN feedback parameters, we find that whether or not a DM
core forms depends primarily on the total amount of injected SN feedback
energy. At a fixed injected energy, the size of the DM core is larger the
faster the energy injection occurs and the more compact the dwarf galaxy is.
Analyzing the orbital evolution of kinematic tracers, we demonstrate that a
core forms through SN feedback only if the energy injection is impulsive
relative to the dynamical timescale of particles in the inner halo. The
converse statement, however, is not true. Consequently, the presence of
signatures of impulsive changes of the gravitational potential is not a
sufficient condition for dwarf-size halos to have cored density profiles.
