2001ApJ...559..531K

The halo mass function, dn/dM, predicted by hierarchical clustering models can be measured indirectly using dynamical probes like the distribution of gravitational lens image separations, dn/dΔθ, or halo circular velocities, dn/dv_c. These dynamical variables depend on the halo structure as well as the halo mass. Since baryonic physics, particularly cooling, significantly modifies the central density structure of dark matter halos, both observational distributions show a feature corresponding to the mass scale below which the baryons in the halo can cool (i.e., galaxies versus clusters). We use simplified but self-consistent models to show that the structural changes to the halos produced by the cooling baryons explain both distributions. Given a fixed halo mass function, matching the observed image separation distribution or local velocity function depends largely on Ω_b through its effects on the cooling timescales. These baryonic effects on the halo structure also affect the evolution of the velocity function of galaxies with redshift.