Halo Occupation Distribution

Old constant bias models assumed galaxy clustering scale linearly with matter clustering at all scales. HOD is more sophisticated: it explicitly models central and satellite galaxies with different clustering properties. This produces scale-dependent bias—stronger clustering at small scales where satellites dominate than at large scales. HOD's flexibility enables fitting complex clustering patterns.

Generally no. Multiple HOD parameterizations can produce similar galaxy clustering on some scales. This degeneracy is particularly severe for centrals vs. satellites and for halo occupation numbers at the high-mass end. Combined with weak lensing mass measurements or spectroscopic clustering data, degeneracies can be broken, but clustering alone is often insufficient.

Simple HOD assumes halo occupation depends only on halo mass. In reality, galaxy properties depend also on environment (proximity to other structures, infall history). Satellite galaxies in dense regions experience stronger tidal disruption than isolated satellites. These environmental dependencies require more complex HOD parameterizations or separate HOD models for different environments.