The effect of relative velocity and density perturbations between baryons and dark matter on the clustering of galaxies

Pre-recombination acoustic oscillations induce non-adiabatic perturbations between baryons and dark matter, corresponding to a constant relative-density $\delta_{bc}$ and decaying relative-velocity perturbation $\vec{v}_{bc}$. Due to their significant large-scale correlations and prominent baryon acoustic oscillation (BAO) features, these modes are potentially important for the use of the BAO as standard ruler. We present a complete treatment of the effects of the baryon-CDM perturbations on galaxy clustering in the context of a rigorous perturbative bias expansion. The leading effects are proportional to $\delta_{bc}$ and $\theta_{bc} = \partial_i v_{bc}^i$. We estimate the magnitude of these terms through the excursion set approach. The contribution from $v_{bc}^2$, which has attracted significant attention recently, contributes at subleading (1-loop) order. The relative-density contribution $\delta_{bc}$ is expected to be by far the largest contribution. We also point out contributions to the galaxy velocity bias, the largest of which is simply $v_{bc}$, leading to a term $\propto \mu^2\theta_{bc}$ in the redshift-space galaxy power spectrum $P_g^s(k,\mu)$. Complete expressions of the galaxy power spectrum at 1-loop order are given, which contain several new terms.