Including beyond-linear halo bias in halo models

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 ∼ 0.7 hMpc −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.

Probing galaxy bias and intergalactic gas pressure with KiDS Galaxies-tSZ-CMB lensing cross-correlations

“…To make sure that our non-linear models are not sensitive to the precise shape of the non-linear power spectrum, we only fit C 's in each tomographic bin within an angular scale corresponding to k < 0.7 Mpc −1 via the Limber approximation. In addition, Mead & Verde (2020) points out that the halo model is not accurate in the transition between the one-and two-halo regions. To attempt to correct for this, we follow Koukoufilippas et al (2020) and multiply the power spectra given by 1) and 3) with a scale-dependent quantity:…”

“…where P HF (k) is from HALOFIT and P hm MM (k) is the matter-matter power evaluated via the halo model (with NFW profiles). Although Mead & Verde (2020) showed that the correction required to the halo model in the transition region is not universal, and instead depends on the tracers being modelled, it was shown that attempting some correction is better than no correction at all.…”

An Analytic Hybrid Halo + Perturbation Theory Model for Small-scale Correlators: Baryons, Halos, and Galaxies

“…[91], while the LSE may be more related to nonlinear bias (e.g. [43,93]). It would be interesting to consider an expanded hybrid modeling approach in which the LSE is modeled with a more complex nonlinear biasing model than linearly-biased ZA as the two-halo term.…”

“…halos/galaxies) and is not necessarily coincident with the nonlinear scale. Recently, some pragmatic semi-analytic models have partially circumvented this issue by considering bias with respect to a fitting function for the non-linear matter power [41], using bias templates measured from simulations [42], or by extending the halo model via functions fit to simulations [43]. In the halo occupation model approach, luminous tracers are assigned to a catalog of dark matter halos via a prescription for stochastically populating the halos -this is the Halo Occupation Distribution (HOD) framework [14,44,45].…”

Cosmology at high redshift -- a probe of fundamental physics

“…[20,[63][64][65] for related work on forecasts and ref. [66] for inclusion of scale-dependent biases in the halo model). We consider a general quadratic bias model and non-linear evolution up to one-loop order in perturbation theory.…”