An Ising model for galaxy bias

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.