Gaussian Lagrangian Galaxy Bias

TL;DR

This paper introduces a Gaussian bias model for galaxy formation that can be directly measured from simulations, offering advantages over traditional parametric expansions by ensuring positivity and better convergence.

Contribution

The paper demonstrates that the Lagrangian bias function is nearly Gaussian and introduces a new Gaussian bias model with advantageous properties for galaxy bias modeling.

Findings

Gaussian bias function closely matches simulation measurements

The model predicts positive probabilities and has a simple analytic form

It outperforms second order expansions in describing galaxy bias

Abstract

Understanding $\textit{galaxy bias}$ -- that is the statistical relation between matter and galaxies -- is of key importance for extracting cosmological information from galaxy surveys. While the bias function $f$ -- that is the probability of forming galaxy in a region with a given density field -- is usually approximated through a parametric expansion, we show here, that it can also be measured directly from simulations in a non-parameteric way. Our measurements show that the Lagrangian bias function is very close to a Gaussian for halo selections of any mass. Therefore, we newly introduce a Gaussian bias model with several intriguing properties: (1) It predicts only strictly positive probabilities $f > 0$ (unlike expansion models), (2) It has a simple analytic renormalized form and (3) It behaves gracefully in many scenarios where the classical expansion converges poorly. We show that the Gaussian bias model describes the galaxy environment distribution $p(\delta | \mathrm{g})$, the scale dependent bias function $f$ and the renormalized bias function $F$ of haloes and galaxies generally equally well or significantly better than a second order expansion with the same number of parameters. We suggest that a Gaussian bias approach may enhance the range of validity of bias schemes where the canonical expansion converges poorly and further, that it may make new applications possible, since it guarantees the positivity of predicted galaxy densities.