A two-state model for galaxy bias

A reliable model of galaxy bias is necessary for interpreting data from future dense galaxy surveys. Conventional linear and quadratic bias models are unphysical, often predicting negative galaxy densities (δ _g < -1) in voids, which potentially contain half of a survey's available cosmological information. Here we present a physically motivated alternative by assuming two energetically distinct subhalo states. Our approximations - namely, local galaxy formation, rough equivalence of galaxy-hosting subhaloes, and universal energetic favourability for the galaxy-hosting state - result in a bias model with only two free parameters; mathematically, the model (in the correct variables) yields a Fermi-Dirac distribution or (equivalently) an interactionless Ising model with an external field. The model yields sensible (and physical) predictions for both high- and low-density regions. We test the model using a catalogue of Millennium Simulation galaxies in cubical survey pixels with side lengths from 2 h ^-1-31 h ^-1 Mpc, at redshifts from 0 to 2. We find the two-state model markedly superior to linear and quadratic bias models on scales smaller than 10 h ^-1 Mpc, while those conventional models fare better on scales larger than 30 h ^-1 Mpc. Though the largest scale of applicability is likely to depend on the galaxy catalogue employed, the two-state model should be superior on any scale with a non-negligible fraction of cells devoid of galaxies.