Beyond Kaiser bias: mildly non-linear two-point statistics of densities in distant spheres

TL;DR

This paper introduces analytic bias functions for two-point density correlations in spheres, extending Kaiser bias to mildly non-linear regimes, validated against simulations, and improving dark matter correlation estimates for large-scale structure surveys.

Contribution

It develops simple, parameter-free analytic bias functions for two-point densities in spheres that generalize Kaiser bias to mildly non-linear regimes using large deviation statistics and spherical collapse models.

Findings

Bias functions are accurate down to 10 Mpc/h scales at redshift 0.

The proposed estimator outperforms traditional methods by a factor of five.

Analytic bias functions effectively predict two-point clustering in the non-linear regime.

Abstract

Simple parameter-free analytic bias functions for the two-point correlation of densities in spheres at large separation are presented. These bias functions generalize the so-called Kaiser bias to the mildly non-linear regime for arbitrary density contrasts. The derivation is carried out in the context of large deviation statistics while relying on the spherical collapse model. A logarithmic transformation provides a saddle approximation which is valid for the whole range of densities and shown to be accurate against the 30 Gpc cube state-of-the-art Horizon Run 4 simulation. Special configurations of two concentric spheres that allow to identify peaks are employed to obtain the conditional bias and a proxy to BBKS extrema correlation functions. These analytic bias functions should be used jointly with extended perturbation theory to predict two-point clustering statistics as they capture the non-linear regime of structure formation at the percent level down to scales of about 10 Mpc/h at redshift 0. Conversely, the joint statistics also provide us with optimal dark matter two-point correlation estimates which can be applied either universally to all spheres or to a restricted set of biased (over- or underdense) pairs. Based on a simple fiducial survey, this estimator is shown to perform five times better than usual two-point function estimators. Extracting more information from correlations of different types of objects should prove essential in the context of upcoming surveys like Euclid, DESI, PFS or LSST.