  The condensation of gas and stars in the inner regions of dark matter halos
leads to a more concentrated dark matter distribution. While this effect is
based on simple gravitational physics, the question of its validity in
hierarchical galaxy formation has led to an active debate in the literature. We
use a collection of several state-of-the-art cosmological hydrodynamic
simulations to study the halo contraction effect in systems ranging from dwarf
galaxies to clusters of galaxies, at high and low redshift. The simulations are
run by different groups with different codes and include hierarchical merging,
gas cooling, star formation, and stellar feedback. We show that in all our
cases the inner dark matter density increases relative to the matching
simulation without baryon dissipation, at least by a factor of several. The
strength of the contraction effect varies from system to system and cannot be
reduced to a simple prescription. We present a revised analytical model that
describes the contracted mass profile to an rms accuracy of about 10%. The
model can be used to effectively bracket the response of the dark matter halo
to baryon dissipation. The halo contraction effect is real and must be included
in modeling of the mass distribution of galaxies and galaxy clusters.
