Excursion set peaks: the role of shear

TL;DR

This paper introduces an analytical model combining excursion set and peaks theory that incorporates shear effects, improving predictions of dark halo abundance, bias, and protohalo properties in cosmological simulations.

Contribution

The model explicitly includes tidal shear effects in the collapse threshold, providing a simple, analytically tractable approach that aligns well with simulation data.

Findings

Accurately predicts halo mass function and bias across various masses and redshifts.

First direct estimate of Lagrangian nonlocal bias in N-body simulations.

Model's simplicity allows for efficient fitting functions for cosmological applications.

Abstract

Recent analytical work on the modelling of dark halo abundances and clustering has demonstrated the advantages of combining the excursion set approach with peaks theory. We extend these ideas and introduce a model of excursion set peaks that incorporates the role of initial tidal effects or shear in determining the gravitational collapse of dark haloes. The model -- in which the critical density threshold for collapse depends on the tidal influences acting on protohaloes -- is well motivated from ellipsoidal collapse arguments and is also simple enough to be analytically tractable. We show that the predictions of this model are in very good agreement with measurements of the halo mass function and traditional scale dependent halo bias in N-body simulations across a wide range of masses and redshift. The presence of shear in the collapse threshold means that halo bias is naturally predicted to be nonlocal, and that protohalo densities at fixed mass are naturally predicted to have Lognormal-like distributions. We present the first direct estimate of Lagrangian nonlocal bias in N-body simulations, finding broad agreement with the model prediction. Finally, the simplicity of the model (which has essentially a single free parameter) opens the door to building efficient and accurate non-universal fitting functions of halo abundances and bias for use in precision cosmology.