On the signature of the baryon-dark matter relative velocity in the two- and three-point galaxy correlation functions

We develop a configuration-space picture of the relative velocity between baryons and dark matter that clearly explains how it can shift the baryon acoustic oscillation (BAO) scale in the galaxy-galaxy correlation function. The shift occurs because the relative velocity is non-zero only within the sound horizon and thus adds to the correlation function asymmetrically about the BAO peak. We further show that in configuration space the relative velocity has a localized, distinctive signature in the three-point galaxy correlation function (3PCF). In particular, we find that a multipole decomposition is a favourable way to isolate the relative velocity in the 3PCF, and that there is a strong signature in the l = 1 multipole for triangles with two sides around the BAO scale. Finally, we investigate a further compression of the 3PCF to a function of only one triangle side that preserves the localized nature of the relative velocity signature while also nicely separating linear from non-linear bias. We expect that this scheme will substantially lessen the computational burden of finding the relative velocity in the 3PCF. The relative velocity's 3PCF signature can be used to correct the shift induced in the galaxy-galaxy correlation function so that no systematic error due to this effect is introduced into the BAO as used for precision cosmology.