Peaks theory and the excursion set approach

TL;DR

This paper introduces a combined model of dark matter halo formation that integrates peaks theory and the excursion set approach, accounting for correlations and nonlocal effects to improve predictions of halo abundance and clustering.

Contribution

It develops a unified formalism for peaks and excursion sets, providing new expressions for mass function and bias, including a k-dependent bias factor due to nonlocality.

Findings

Linear halo bias factor is k-dependent due to nonlocal effects.

Model predicts little need for rescaling delta_c at high masses.

Provides a unified framework applicable to large-scale structure analyses.

Abstract

We describe a model of dark matter halo abundances and clustering which combines the two most widely used approaches to this problem: that based on peaks and the other based on excursion sets. Our approach can be thought of as addressing the cloud-in-cloud problem for peaks and/or modifying the excursion set approach so that it averages over a special subset, rather than all possible walks. In this respect, it seeks to account for correlations between steps in the walk as well as correlations between walks. We first show how the excursion set and peaks models can be written in the same formalism, and then use this correspondence to write our combined excursion set peaks model. We then give simple expressions for the mass function and bias, showing that even the linear halo bias factor is predicted to be k-dependent as a consequence of the nonlocality associated with the peak constraint. At large masses, our model has little or no need to rescale the variable delta_c from the value associated with spherical collapse, and suggests a simple explanation for why the linear halo bias factor appears to lie above that based on the peak-background split at high masses when such a rescaling is assumed. Although we have concentrated on peaks, our analysis is more generally applicable to other traditionally single-scale analyses of large-scale structure.