Calibrating the baryon oscillation ruler for matter and halos

We characterize the nonlinear evolution of the baryon acoustic feature as traced by the dark matter and halos, using a combination of perturbation theory and N-body simulations. We confirm that the acoustic peak traced by the dark matter is both broadened and shifted as structure forms, and that this shift is well described by second-order perturbation theory. These shifts persist for dark matter halos, and are a simple function of halo bias, with the shift (mostly) increasing with increasing bias. Extending our perturbation theory results to halos with simple two parameter bias models (both in Lagrangian and Eulerian space) quantitatively explains the observed shifts. In particular, we demonstrate that there are additional terms that contribute to the shift that are absent for the matter. At z = 0 for currently favored cosmologies, the matter shows shifts of similar to 0.5%, b = 1 halos shift the acoustic scale by similar to 0.2%, while b = 2 halos shift it by similar to 0.5%; these shifts decrease by the square of the growth factor D(z) at higher redshifts. These results are easily generalized to galaxies within the halo model, where we show that simple galaxy models show marginally larger shifts than the correspondingly biased halos, due to the contribution of satellites in high mass halos. While our focus here is on real space, our results make specific predictions for redshift space. For currently favored cosmological models, we find that the shifts for halos at z = 0 increase by similar to 0.3%; at high z, they increase by similar to 0.5% D-2. Our results demonstrate that these theoretical systematics are smaller than the statistical precision of upcoming surveys, even if one ignored the corrections discussed here. Simple modeling, along the lines discussed here, has the potential to reduce these systematics to below the levels of cosmic variance limited surveys.