Gaussian Lagrangian galaxy bias

¹ Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
² Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
³ IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain

^⋆ Corresponding author; jens.stuecker@univie.ac.at; mpelleje@ed.ac.uk

Received: 19 June 2024
Accepted: 3 December 2024

Abstract

Understanding 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 – the probability of forming galaxies 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-parametric way. Our measurements show that the Lagrangian bias function is very close to a Gaussian for halo selections of any mass. Therefore, we introduce a new Gaussian bias model that has several intriguing properties: (1) it predicts only strictly positive probabilities, f > 0 (unlike expansion models), (2) it has a simple analytic re-normalised form, and (3) it behaves gracefully in many scenarios in which the classical expansion converges poorly. We show that the Gaussian bias model generally describes the galaxy environment distribution, p(δ|g), the scale-dependent bias function, f, and the re-normalised bias function, F, of haloes and galaxies as well as a second-order expansion with the same number of parameters, or significantly better than it. We suggest that a Gaussian bias approach may enhance the range of validity of bias schemes in which the canonical expansion converges poorly, and further that it may make new applications possible, since it guarantees the positivity of predicted galaxy densities.