Non-Gaussian Halo Bias Re-examined: Mass-dependent Amplitude from the Peak-Background Split and Thresholding

TL;DR

This paper re-examines theoretical models of non-Gaussian halo bias, identifying a mass-dependent correction that improves agreement with N-body simulations beyond the simplest non-Gaussian models.

Contribution

It introduces a previously overlooked correction to the peak-background split approach, enhancing the accuracy of non-Gaussian halo bias predictions for complex models.

Findings

Thresholded regions statistics cannot explain the deviations.

A new mass-dependent correction significantly improves bias predictions.

Good agreement with N-body simulations for various non-Gaussianities.

Abstract

Recent results of N-body simulations have shown that current theoretical models are not able to correctly predict the amplitude of the scale-dependent halo bias induced by primordial non-Gaussianity, for models going beyond the simplest, local quadratic case. Motivated by these discrepancies, we carefully examine three theoretical approaches based on (1) the statistics of thresholded regions, (2) a peak-background split method based on separation of scales, and (3) a peak-background split method using the conditional mass function. We first demonstrate that the statistics of thresholded regions, which is shown to be equivalent at leading order to a local bias expansion, cannot explain the mass-dependent deviation between theory and N-body simulations. In the two formulations of the peak-background split on the other hand, we identify an important, but previously overlooked, correction to the non-Gaussian bias that strongly depends on halo mass. This new term is in general significant for any primordial non-Gaussianity going beyond the simplest local fNL model. In a separate paper, we compare these new theoretical predictions with N-body simulations, showing good agreement for all simulated types of non-Gaussianity.