Excursion set peaks in energy as a model for haloes

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.

9 pages, 5 figures

References in corpus (7)

• The Excursion Set Theory of Halo Mass Functions, Halo Clustering, and Halo Growth
• The three dimensional skeleton: tracing the filamentary structure of the universe
• Non-linear statistics of primordial black holes from gaussian curvature perturbations
• Non-local Lagrangian bias
• Ellipsoidal halo finders and implications for models of triaxial halo formation
• Application of peaks theory to the abundance of primordial black holes
• Halo Assembly Bias in the Quasi-linear Regime

Cited by in corpus (4)

• A Stochastic Theory of the Hierarchical Clustering II. Halo progenitor mass function and large-scale bias
• Voids and Halos in Voids statistics as a probe of the Expansion History of the Universe
• Mass assembly history of dark matter halos in the light of $H_0$ tension
• A Stochastic Theory of the Hierarchical Clustering III. The Non-universality and Non-stationarity of the Halo Mass Function