Scale dependent halo bias in the excursion set approach

TL;DR

This paper analyzes how scale-dependent halo bias arises from correlations in the excursion set approach, proposing methods to isolate and remove these effects using transformations of the mass field.

Contribution

It introduces a novel analysis to distinguish and eliminate various effects causing scale-dependent bias, including an analytic approximation for correlated walk crossings.

Findings

Effective methods to remove scale dependence in halo bias.

Accurate analytic approximation for correlated walk crossings.

Generalization to non-Gaussian fields.

Abstract

If one accounts for correlations between scales, then nonlocal, k-dependent halo bias is part and parcel of the excursion set approach, and hence of halo model predictions for galaxy bias. We present an analysis that distinguishes between a number of different effects, each one of which contributes to scale-dependent bias in real space. We show how to isolate these effects and remove the scale dependence, order by order, by cross-correlating the halo field with suitably transformed versions of the mass field. These transformations may be thought of as simple one-point, two-scale measurements that allow one to estimate quantities which are usually constrained using n-point statistics. As part of our analysis, we present a simple analytic approximation for the first crossing distribution of walks with correlated steps which are constrained to pass through a specified point, and demonstrate its accuracy. Although we concentrate on nonlinear, nonlocal bias with respect to a Gaussian random field, we show how to generalize our analysis to more general fields.