Non-Gaussian bias: insights from discrete density peaks

TL;DR

This paper investigates the impact of primordial non-Gaussianity on halo bias, showing that a peak-based approach aligns with peak-background split predictions, unlike standard local bias models.

Contribution

It introduces a simplified peak clustering formalism that accurately models non-Gaussian bias, highlighting the need for variables beyond local mass overdensity.

Findings

Peak-based bias models agree with peak-background split predictions.

Standard local bias models fail to capture non-Gaussian bias effects.

A formalism for thresholded regions and constraints on the density field is developed.

Abstract

Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastly simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out that statistics of thresholded regions can be computed using the same formalism. Our results suggest that halo clustering statistics can be modelled consistently (in the sense that the Gaussian and non-Gaussian bias factors agree with peak-background split expectations) from a Lagrangian bias relation only if the latter is specified as a set of constraints imposed on the linear density field. This is clearly not the case of standard Lagrangian local bias. Therefore, one is led to consider additional variables beyond the local mass overdensity.