Dark matter halo response to the disk growth

We consider the sensitivity of the circular-orbit adiabatic contraction approximation (Barnes & White 1984; Blumenthal et al. 1986) to the timing of baryon condensation and the orbital structure of dark matter halos in the ΛCDM paradigm. Using one-dimensional hydrodynamic simulations including the dark matter halo mass accretion history and gas cooling, we demonstrate that the adiabatic approximation is approximately valid even though halos and disks may assemble simultaneously. We further demonstrate the validity of the simple approximation for ΛCDM halos (e.g. Navarro, Frenk & White 1997, hereafter NFW) with isotropic velocity distributions using three-dimensional N-body simulations. This result is easily understood: an isotropic velocity distribution in a cuspy halo requires more circular orbits than radial orbits. Conversely, the approximation considerably differs in the extreme case of a radial orbit halo. The approximation overestimates the response a core dark matter halo, where radial orbit fraction is larger. Because no astronomically relevant models are dominated by low-angular momentum orbits in the vicinity of the disk and the growth time scale is never shorter than a dynamical time, we conclude that the adiabatic contraction approximation is generally acceptable in the CDM cosmology.