Diagnosing and Improving the Peak-to-Halo Model: A Predictive Theory of Dark Matter Halo Formation

Abstract

Regions with higher matter density than their surroundings collapse into gravitationally bound structures called halos. Prof. Erickcek and other members of her research group developed the Peak-to-Halo (P2H) model, which predicts the density profiles of simulated halos using the properties of the density peaks that they collapsed from (Delos, Bruff, & Erickcek 2019). The properties of local maxima in a Gaussian field can be derived from the field’s power spectrum (Bardeen et al. 1986), so the P2H model can predict the halo population directly from the dark matter power spectrum. The P2H model performs well for halos that form from initial conditions with a sharp small-scale cut-off in their power spectrum, but it gives nonphysical results for power spectra with shallow cut-offs, such as those resulting from dark matter with both warm and cold components. This project seeks to diagnose the origin of this breakdown and correct it by combining theoretical peak analysis with N-body simulations. By tracing the evolution of density peaks through cosmic time using GADGET-4 N-body simulations, we will identify which assumptions in the P2H model fail and provide corrections. Because the abundance and structure of the smallest halos are sensitive to the nature of dark matter, improving the model has broad implications for cosmology and astrophysics, particularly for understanding the conditions that set the formation of the first stars and galaxies.