Scale-dependent bias and the halo model

We use a simplified version of the halo model with a power law power spectrum to study scale dependence in galaxy bias at the very large scales relevant to baryon oscillations. In addition to providing a useful pedagogical explanation of the scale dependence of galaxy bias, the model provides an analytic tool for studying how changes in the Halo Occupation Distribution (HOD) impact the scale dependence of galaxy bias on scales 10 < k−1 < 1000 h−1 Mpc, which is useful for interpreting the results of complex N-body simulations. We find that changing the mean number of galaxies per halo of a given mass will change the scale dependence of the bias, but that changing the way the galaxies are distributed within the halo has a smaller effect on the scale dependence of bias at large scales. We use the model to explain the decay in amplitude of the baryon oscillations as k increases, and generalize the model to make predictions about scale dependent galaxy bias when redshift space distortions are introduced.