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

Understand

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.