The virialization density of peaks with general density profiles under spherical collapse

Abstract

We calculate the non-linear virialization density, Δc, of halos under spherical collapse from peaks with an arbitrary initial and final density profile. This is in contrast to the standard calculation of Δc which assumes top-hat profiles. Given our formalism, the non-linear halo density can be calculated once the shape of the initial peak's density profile and the shape of the virialized halo's profile are provided. We solve for Δc for halos in an Einstein de-Sitter and a ΛCDM universe. As examples, we consider power-law initial profiles as well as spherically averaged peak profiles calculated from the statistics of a Gaussian random field.We find that, depending on the profiles used, Δc is smaller by a factor of a few to as much as a factor of 10 as compared to the density given by the standard calculation ( ≈ 200). Using our results, we show that, for halo finding algorithms that identify halos through an over-density threshold, the halo mass function measured from cosmological simulations can be enhanced at all halo masses by a factor of a few. This difference could be important when using numerical simulations to assess the validity of analytic models of the halo mass function.