Web-Halo Model Peak-Background Split (WHM-PBS): halo bias as a distribution, not a number

Abstract

We present the Web-Halo Model Peak-Background Split (WHM-PBS), an analytic theory in which the large-scale bias of a dark-matter halo is inherited from its cosmic-web environment. Building on the Web-Halo Model, we use the Shen et al. moving barriers for ellipsoidal collapse generating the web hierarchy in which every halo sits inside a host filament, itself inside a sheet. Combined with the peak-background split, this picture replaces the deterministic bias-mass relation $b(M_h)$ with the bias of the host environment, averaged over the conditional mass function. As a result, halo bias $b(M_h)$ is no longer a number but a strongly skewed distribution. In this work we make use of this distribution in three different ways: as (i) a physically motivated prior on bias relations, (ii) a prediction on halo stochasticity, and (iii) a framework for assembly bias models. Regarding (i) we find that the density bias relations $b_2(b_1)$ and $b_3(b_1)$ stay tight, while the tidal bias $b_{s^2}(b_1)$ shows significant scatter, as found in $N$-body simulations. Regarding (ii), once including halo exclusion, our model reproduces the super- to sub-Poisson shot-noise trend of Baldauf et al. which we convert into a prior band on the EFT stochasticity amplitude parameters. Finally, regarding (iii) in the density sector it explains the bias-concentration-correlation inversion of Paranjape et al. at the characteristic mass ($M_\mathrm{h}\simeq 1.7\times 10^{13}\,h^{-1} M_\odot$), with no parameter tuned to assembly bias. We apply the resulting priors on synthetic data, demonstrating that the WHM-PBS priors mitigate projection effects arising when all nuisance parameters are varied freely, while fixed priors may fail severely. The code to reproduce our results is publicly available at https://github.com/SamuelBrieden/whmpbs.git.