Culminating the peak CUSP to descry the dark side of halos

TL;DR

This paper completes the CUSP formalism, demonstrating its ability to predict detailed dark matter halo properties from first principles, independent of assembly history, and clarifies the role of Gaussian smoothing in halo formation.

Contribution

It finalizes the CUSP framework, showing its predictions are robust and independent of halo assembly history, and emphasizes the unique role of Gaussian smoothing in the formalism.

Findings

Halo properties are independent of assembly history.

Gaussian smoothing uniquely captures collapsing patches.

CUSP accurately reproduces simulation results.

Abstract

The ConflUent System of Peak trajectories (CUSP) is a rigorous formalism in the framework of the peak theory that allows one to derive from first principles andno free parameters the typical halo properties from the statistics of peaks in the filtered Gaussian random field of density perturbations. The predicted halo mass function, spherically averaged density, velocity dispersion, velocity anisotropy, ellipticity, prolateness and potential profiles, as well as the abundance and number density profiles of accreted and stripped subhalos and diffuse dark matter accurately recover the results of cosmological $N$-body simulations. CUSP is thus a powerful tool for the calculation, in any desired hierarchical cosmology with Gaussian perturbations, of halo properties beyond the mass, redshift and radial ranges covered by simulations. More importantly, CUSP unravels the origin of the characteristic features of those properties. In the present Paper we culminate its construction. We show that all halo properties but those related with subhalo stripping are independent of the assembly history of those objects, and that the Gaussian is the only smoothing window able to find the finite collapsing patches while properly accounting for the entropy increase produced in major mergers.