Beyond LIMD bias: a measurement of the complete set of third-order halo bias parameters

TL;DR

This paper measures the complete set of third-order halo bias parameters using the halo-matter-matter-matter trispectrum from N-body simulations, providing new insights into nonlocal bias effects.

Contribution

It introduces a novel method to measure cubic halo bias parameters via the four-point function, expanding the understanding of halo bias beyond previous two- and three-point analyses.

Findings

Broad consistency with the Lagrangian local-in-matter-density prediction for cubic bias parameters involving tidal fields

Detection of a negative Lagrangian tidal bias for quadratic tidal bias

First measurements of halo bias using the four-point function

Abstract

We present direct measurements of cubic bias parameters of dark matter halos from the halo-matter-matter-matter trispectrum. We measure this statistic efficiently by cross-correlating the halo field measured in N-body simulations with specific third-order nonlocal transformations of the initial density field in the same simulation. Together with the recent Abidi & Baldauf (2018), these are the first measurements of halo bias using the four-point function that have been reported to date. We also obtain constraints on the quadratic bias parameters. For all individual cubic parameters involving the tidal field $\mathcal{K}_{ij}$, we find broad consistency with the prediction of the Lagrangian local-in-matter-density ansatz, with some indications of a positive Lagrangian coefficient $b_{\rm td}^L$ multiplying the time derivative of $\mathcal{K}_{ij}$. For the quadratic tidal bias ($b_{K^2}$), we obtain a significant detection of a negative Lagrangian tidal bias.