Excursion Set Halo Mass Function and Bias in a Stochastic Barrier Model of Ellipsoidal Collapse

TL;DR

This paper employs the Excursion Set formalism with a stochastic barrier model to accurately predict dark matter halo mass functions and bias, aligning well with N-body simulations across various redshifts.

Contribution

It extends the stochastic barrier model to higher redshifts and provides an analytical expression for halo bias, improving the theoretical understanding of halo formation.

Findings

Mass function matches N-body simulations within 5%.

Monte Carlo simulations confirm the path-integral approach.

Halo bias deviations are within 20%.

Abstract

We use the Excursion Set formalism to compute the properties of the halo mass distribution for a stochastic barrier model which encapsulates the main features of the ellipsoidal collapse of dark matter halos. Non-markovian corrections due to the sharp filtering of the linear density field in real space are computed with the path-integral technique introduced by Maggiore & Riotto (2010). Here, we provide a detailed derivation of the results presented in Corasaniti & Achitouv (2011) and extend the mass function analysis to higher redshift. We also derive an analytical expression for the linear halo bias. We find the analytically derived mass function to be in remarkable agreement with N-body simulation data from Tinker et al. (2008) with differences smaller than ~5% over the range of mass probed by the simulations. The excursion set solution from Monte Carlo generated random walks shows the same level of agreement, thus confirming the validity of the path-integral approach for the barrier model considered here. Similarly the analysis of the linear halo bias shows deviations no greater than 20%. Overall these results indicate that the Excursion Set formalism in combination with a realistic modeling of the conditions of halo collapse can provide an accurate description of the halo mass distribution.