  The cooling of baryons in the centers of dark matter halos leads to a more
concentrated dark matter distribution. This effect has traditionally been
calculated using the model of adiabatic contraction, which assumes spherical
symmetry, while in hierarchical formation scenarios halos grow via multiple
violent mergers. We test the adiabatic contraction model in high-resolution
cosmological simulations and find that the dissipation of gas indeed increases
the density of dark matter and steepens its radial profile compared to the case
without cooling. Although the standard model systematically overpredicts the
increase of dark matter density, a simple modification of the assumed invariant
from M(r)r to M(<r>)r, where <r> is the orbit-averaged particle position,
reproduces the simulated profiles within 10%.
