An Ising model for galaxy bias

TL;DR

This paper introduces a physically-motivated galaxy bias model based on the Ising model, which outperforms traditional models on small scales and handles voids more realistically in galaxy surveys.

Contribution

The authors develop a new galaxy bias model inspired by the Ising model, with only two parameters, improving accuracy in low-density regions compared to conventional models.

Findings

Ising model outperforms linear and quadratic bias models on scales <10h^{-1}Mpc.

Conventional models perform better on scales >30h^{-1}Mpc.

Model effectively handles voids with no galaxies in survey pixels.

Abstract

A reliable model of galaxy bias is necessary for interpreting data from future dense galaxy surveys. Conventional bias models are inaccurate, in that they can yield unphysical results ($\delta_g < -1$) for voids that might contain half of the available cosmological information. For this reason, we present a physically-motivated bias model based on an analogy with the Ising model. With only two free parameters, the model produces sensible results for both high- and low-density regions. We also test the model using a catalog of Millennium Simulation galaxies in cubical survey pixels with side lengths from $2h^{-1}$--$31h^{-1}$Mpc, at redshifts from 0 to 2. We find the Ising model markedly superior to linear and quadratic bias models on scales smaller than $10h^{-1}$Mpc, while those conventional models fare better on scales larger than $30h^{-1}$Mpc. While the largest scale where the Ising model is applicable might vary for a specific galaxy catalog, it should be superior on any scale with a non-negligible fraction of cells devoid of galaxies.