Halo Sampling, Local Bias and Loop Corrections

TL;DR

This paper introduces a new test for local bias in halo density fields that preserves scatter, avoids perturbation theory reliance, and improves agreement with simulations, especially at large scales.

Contribution

It presents a novel sampling method for local bias that accounts for scatter and running bias parameters, reducing loop corrections and aligning better with simulations.

Findings

Bias parameters depend on smoothing scale R for large-scale power spectrum.

No significant positive noise detected in halo power spectrum at low k.

Nonlocal bias effects impact the power spectrum only slightly in the weakly nonlinear regime.

Abstract

We develop a new test of local bias, by constructing a locally biased halo density field from sampling the dark matter-halo distribution. Our test differs from conventional tests in that it preserves the full scatter in the bias relation and it does not rely on perturbation theory. We put forward that bias parameters obtained using a smoothing scale R can only be applied to computing the halo power spectrum at scales k ~ 1/R. Our calculations can automatically include the running of bias parameters and give vanishingly small loop corrections at low-k. Our proposal results in much better agreement of the sampling and perturbation theory results with simulations. In particular, unlike the standard interpretation of local bias in the literature, our treatment of local bias does not generate a constant power in the low-k limit. We search for extra noise in the Poisson corrected halo power spectrum at wavenumbers below its turn-over and find no evidence of significant positive noise (as predicted by the standard interpretation) while we find evidence of negative noise coming from halo exclusion for very massive halos. Using perturbation theory and our non-perturbative sampling technique we also demonstrate that nonlocal bias effects discovered recently in simulations impact the power spectrum only at the few percent level in the weakly nonlinear regime.