Precision measurement of the local bias of dark matter halos

TL;DR

This paper accurately measures the local bias of dark matter halos using advanced simulations, compares results with theoretical models, and provides fitting formulas for nonlinear bias parameters.

Contribution

It introduces a precise measurement method for halo bias using separate universe simulations and evaluates theoretical models against these measurements.

Findings

Good agreement between simulation and bispectrum measurements

Standard peak-background split matches linear bias within 10%

Excursion set-peaks approach predicts bias more accurately

Abstract

We present accurate measurements of the linear, quadratic, and cubic local bias of dark matter halos, using curved "separate universe" N-body simulations which effectively incorporate an infinite-wavelength overdensity. This can be seen as an exact implementation of the peak-background split argument. We compare the results with the linear and quadratic bias measured from the halo-matter power spectrum and bispectrum, and find good agreement. On the other hand, the standard peak-background split applied to the Sheth & Tormen (1999) and Tinker et al. (2008) halo mass functions matches the measured linear bias parameter only at the level of 10%. The prediction from the excursion set-peaks approach performs much better, which can be attributed to the stochastic moving barrier employed in the excursion set-peaks prediction. We also provide convenient fitting formulas for the nonlinear bias parameters $b_2(b_1)$ and $b_3(b_1)$, which work well over a range of redshifts.