# Excursion set peaks in energy as a model for haloes

## TL;DR

This paper introduces a new model for dark matter halo formation based on energy peaks and gravitational flow convergence, offering a more physically motivated and divergence-free approach that aligns with simulation results.

## Contribution

It replaces the traditional density maxima assumption with energy minima and gravitational flow convergence, providing a more physically grounded and divergence-free model for halo formation.

## Key findings

- Predicts scatter in protohalo overdensities consistent with simulations
- Removes divergences present in standard models for cosmological power spectra
- Shows that energy-based peaks can serve as a robust alternative to density maxima

## Abstract

The simplest models of dark matter halo formation are based on the heuristic assumption, motivated by spherical collapse, that virialized haloes originate from initial regions that are maxima of the smoothed density field. Here, we replace this notion with the dynamical requirement that protohalo patches be regions where the local gravitational flow converges to a point. For this purpose, we look for spheres whose gravitational acceleration at the boundary -- relative to their center of mass -- points towards their geometric center: that is, spheres with null dipole moment. We show that these configurations are minima of the total energy, i.e. the most energetically bound spheres. For this reason, we study peaks of the energy overdensity field, and argue that the approach shows considerable promise. This change simply requires that one modify the standard top-hat filter, with the added important benefit that, for power spectra of cosmological interest, the resulting model is no longer plagued by divergences. Although the formalism is no more complicated than the overdensity based approach, the model is richer in the sense that it naturally predicts scatter in the overdensities of protohalo patches that are destined to form haloes of the same mass, in qualitative agreement with simulations of halo formation.