  The core-cusp problem remains as one of the unsolved discrepancies between
observations and theories predicted by the standard paradigm of cold dark
matter (CDM) cosmology. To solve this problem, we perform N-body simulations to
study the nonlinear response of CDM halos to the variance of the gravitational
potential induced by gas removal from galaxy centers. In this study, we focus
on the timescale of the gas ejection, which is strongly correlated with stellar
activities, and demonstrate that it is one of the key factors in determining
the dynamical response of CDM halos. The results of simulations show that the
power-low index of the mass-density profile of the dark matter halo correlated
with the timescale of the mass loss, and it is flatter when the mass loss
occurs over a short time than when it occurs over a long time. However, it is
still larger than typical observational values; in other words, the central
cusp remains for any mass loss model in the simulations. Moreover, for the slow
mass-loss case, the final density profile of the dark matter halo recovers the
universal density profiles predicted by the CDM cosmology. Therefore, mass loss
driven by stellar feedback may not be an effective mechanism to flatten the
central cusp.
