Bye-bye, Local-in-matter-density Bias: The Statistics of the Halo Field Are Poorly Determined by the Local Mass Density

TL;DR

This study shows that assuming halo bias depends solely on local matter density is invalid, as it leads to inaccurate predictions of halo distribution across scales, highlighting the need for more complex bias models.

Contribution

The paper demonstrates through simulations that local-in-matter-density bias models fail to accurately predict halo distributions, emphasizing the necessity for models incorporating additional factors or correlations.

Findings

Permuted halo fields show scale-dependent bias with >25% more power.

Local-in-matter-density bias models cannot reproduce halo distribution across scales.

Bias models that ignore voxel correlations distort power spectra.

Abstract

Bias models relating the dark matter field to the spatial distribution of halos are widely used in current cosmological analyses. Many models predict halos purely from the local Eulerian matter density, yet bias models in perturbation theory require other local properties. We assess the validity of assuming that only the local dark matter density can be used to predict the number density of halos in a model-independent way and in the non-perturbative regime. Utilising $N$-body simulations, we study the properties of the halo counts field after spatial voxels with near-equal dark matter density have been permuted. If local-in-matter-density biasing were valid, the statistical properties of the permuted and un-permuted fields would be indistinguishable since both represent equally fair draws of the stochastic biasing model. If the Lagrangian radius is greater than approximately half the voxel size and for halos less massive than $\sim10^{15}\,h^{-1}{\rm\,M_\odot}$, we find the permuted halo field has a scale-dependent bias with greater than 25% more power on scales relevant for current surveys. These bias models remove small-scale power by not modelling correlations between neighbouring voxels, which substantially boosts large-scale power to conserve the field's total variance. This conclusion is robust to the choice of initial conditions and cosmology. Assuming local-in-matter-density halo biasing cannot, therefore, reproduce the distribution of halos across a large range of scales and halo masses, no matter how complex the model. One must either allow the biasing to be a function of other quantities and/or remove the assumption that neighbouring voxels are statistically independent.