  The cooling of gas in the centers of dark matter halos is expected to lead to
a more concentrated dark matter distribution. The response of dark matter to
the condensation of baryons is usually calculated using the model of adiabatic
contraction, which assumes spherical symmetry and circular orbits. In contrast,
halos in the hierarchical structure formation scenarios grow via multiple
violent mergers and accretion along filaments, and particle orbits in the halos
are highly eccentric. We study the effects of the cooling of gas in the inner
regions of halos using high-resolution cosmological simulations which include
gas dynamics, radiative cooling, and star formation. We find that the
dissipation of gas indeed increases the density of dark matter and steepens its
radial profile in the inner regions of halos compared to the case without
cooling. For the first time, we test the adiabatic contraction model in
cosmological simulations and find that the standard model systematically
overpredicts the increase of dark matter density in the inner 5% of the virial
radius. We show that the model can be improved by a simple modification of the
assumed invariant from M(r)r to M(r_av)r, where r and r_av are the current and
orbit-averaged particle positions. This modification approximately accounts for
orbital eccentricities of particles and reproduces simulation profiles to
within 10-20%. We present analytical fitting functions that accurately describe
the transformation of the dark matter profile in the modified model and can be
used for interpretation of observations.
