Bye bye, local bias: the statistics of the halo field are poorly determined by the local mass density
arxiv(2024)
摘要
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 the inclusion of 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. For voxels of side length ∼4-30 h^-1 Mpc and for
halos less massive than ∼10^15 h^-1 M_⊙, we find that the
permuted halo field has a scale-dependent bias with greater than 25
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.
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