On the Robustness of the Acoustic Scale in the Low-Redshift Clustering of Matter

We discuss the effects of non-linear structure formation on the signature of acoustic oscillations in the late-time galaxy distribution. We argue that the dominant non-linear effect is the differential motion of pairs of tracers separated by 150 Mpc. These motions are driven by bulk flows and cluster formation and are much smaller than the acoustic scale itself. We present a model for the non-linear evolution based on the distribution of pairwise Lagrangian displacements that provides a quantitative model for the degradation of the acoustic signature, even for biased tracers in redshift space. The Lagrangian displacement distribution can be calibrated with a significantly smaller set of simulations than would be needed to construct a precise power spectrum. By connecting the acoustic signature in the Fourier basis with that in the configuration basis, we show that the acoustic signature is more robust than the usual Fourier-space intuition would suggest because the beat frequency between the peaks and troughs of the acoustic oscillations is a very small wavenumber that is well inside the linear regime. We argue that any possible shift of the acoustic scale is related to infall on 150 Mpc scale, which is O(0.5%) fractionally at first-order even at z=0. For the matter, there is a first-order cancellation such that the mean shift is O(10^{-4}). However, galaxy bias can circumvent this cancellation and produce a sub-percent systematic bias.