Including beyond-linear halo bias in halo models

TL;DR

This paper introduces a simple correction to the halo model that incorporates beyond-linear halo bias, significantly improving the accuracy of power spectrum predictions especially at intermediate scales.

Contribution

The authors derive and validate a new prescription for including non-linear halo bias in the halo model, enhancing its predictive power for the matter and galaxy power spectra.

Findings

Boosts two-halo power by a factor of ~2 at k~0.7 h/Mpc

Reduces under-prediction in the transition region between one- and two-halo terms

Improves agreement with N-body simulations for galaxy, halo, and matter spectra

Abstract

We derive a simple prescription for including beyond-linear halo bias within the standard, analytical halo-model power spectrum calculation. This results in a corrective term that is added to the usual two-halo term. We measure this correction using data from $N$-body simulations and demonstrate that it can boost power in the two-halo term by a factor of $\sim2$ at scales $k\sim0.7\,h Mpc^{-1}$, with the exact magnitude of the boost determined by the specific pair of fields in the two-point function. How this translates to the full power spectrum depends on the relative strength of the one-halo term, which can mask the importance of this correction to a greater or lesser degree, again depending on the fields. Generally we find that our correction is more important for signals that arise from lower-mass haloes. When comparing our calculation to simulated data we find that the under-prediction of power in the transition region between the two- and one-halo terms, which typically plagues halo-model calculations, is almost completely eliminated when including the full non-linear halo bias. We show improved results for the auto and cross spectra of galaxies, haloes and matter. In the specific case of matter-matter or matter-halo power we note that a large fraction of the improvement comes from the non-linear biasing between low- and high-mass haloes. We envisage our model being useful in the analytical modelling of cross correlation signals. Our non-linear bias halo-model code is available at https://github.com/alexander-mead/BNL