Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

TL;DR

This paper calibrates how halo bias depends on the local cosmic web environment using the Separate Universe technique, providing high-precision functions for different halo masses and redshifts, and extending the framework to secondary properties like halo concentration.

Contribution

It presents the first calibration of non-linear halo bias dependence on the local web environment and extends the analytical framework to secondary properties with Gaussian distributions.

Findings

First demonstration of non-linear bias dependence on web environment

Provides fitting functions for bias dependence on tidal anisotropy

Extends framework to secondary properties like halo concentration

Abstract

We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias $b_1$ and $b_2$ on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy $\alpha$ to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work which exploits the near-Lognormal shape of the distribution of $\alpha$ and results in very high precision calibrations. We present convenient fitting functions for the dependence of $b_1$ and $b_2$ on $\alpha$ over a wide range of halo mass for redshifts $0\leq z\leq1$. Our calibration of $b_2(\alpha)$ is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results which showed that $\alpha$ is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of $b_1$ and $b_2$ on any such secondary property which has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using $\alpha$ as a segregating variable in multi-tracer analyses.