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 ( < -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 -31 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 Mpc, while those conventional models fare better on scales larger than 30 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.