Including beyond-linear halo bias in halo models

Abstract

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 ∼2 at scales $k\sim 0.7\, h\mathrm{Mpc}^{-1}$, 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 underprediction 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 autospectra 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.