Perturbation theory for nonlinear halo power spectrum: the renormalized bias and halo bias

TL;DR

This paper develops an analytical model combining perturbation theory, local bias, and halo bias to accurately describe nonlinear halo power spectra, including effects of shot noise, in the weakly nonlinear regime.

Contribution

It introduces a renormalized bias model that accounts for nonlinear clustering and shot noise, improving predictions of halo power spectra.

Findings

Model agrees well with N-body simulations up to k≈0.2 h/Mpc at z=0.35.

Incorporates residual shot noise as a free parameter.

Demonstrates scale-dependent bias in the weakly nonlinear regime.

Abstract

We revisit an analytical model to describe the halo-matter cross-power spectrum and the halo auto-power spectrum in the weakly nonlinear regime, by combining the perturbation theory (PT) for matter clustering, the local bias model, and the halo bias. Nonlinearities in the power spectra arise from the nonlinear clustering of matter as well as the nonlinear relation between the matter and halo density fields. By using the "renormalization" approach, we express the nonlinear power spectra by a sum of the two contributions: the nonlinear matter power spectrum with the effective linear bias parameter, and the higher-order PT spectra having the halo bias parameters as the coefficients. The halo auto-power spectrum includes the residual shot noise contamination that needs to be treated as additional free parameter. The term(s) of the higher-order PT spectra and the residual shot noise cause a scale-dependent bias function relative to the nonlinear matter power spectrum in the weakly nonlinear regime. We show that the model predictions are in good agreement with the spectra measured from a suit of high-resolution $N$-body simulations up to $k\simeq 0.2 h$/Mpc at $z=0.35$, for different halo mass bins.