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

Understand

We calculate the non-linear virialization density, $\Delta_c$, of halos under spherical collapse from peaks with an arbitrary initial and final density profile.

• This is in contrast to the standard calculation of $\Delta_c$ 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 $\Delta_c$ for halos in an Einstein de-Sitter and $\Lambda$CDM universe.