  This study investigates the dynamical response of dark matter (DM) halos to
recurrent starbursts in forming less-massive galaxies to solve the core-cusp
problem. The gas, which is heated by supernova feedback after a starburst,
expands and the star formation then terminates. This expanding gas loses energy
by radiative cooling and then falls back toward the galactic center.
Subsequently, the starburst is enhanced again. This cycle of expansion and
contraction of the interstellar gas leads to a repetitive change in the
gravitational potential of the gas. The resonance between DM particles and the
density wave excited by the oscillating potential plays a key role in
understanding the physical mechanism of the cusp-core transition of DM halos.
DM halos effectively gain kinetic energy from the baryon potential through the
energy transfer driven by the resonance between the particles and density
waves. We determine that the critical condition for the cusp-core transition is
such that the oscillation period of the gas potential is approximately the same
as the local dynamical time of DM halos. We present the resultant core radius
of a DM halo after the cusp-core transition induced by the resonance by using
the conventional mass density profile predicted by the cold dark matter models.
Moreover, we verify the analytical model by using $N$-body simulations, and the
results validate the resonance model.
