`Eppur Si Muove': On The Motion of the Acoustic Peak in the Correlation Function

TL;DR

The paper investigates how nonlinear evolution, bias, and redshift-space distortions shift the BAO peak in the galaxy two-point correlation function. It combines a large-volume simulation suite (~105 (h^{-1} Gpc)^3) with a physical model based on the pair conservation equation and the method of characteristics to separate apparent (smoothing-induced) shifts from physical (mode-coupling–induced) shifts. The results show percent-level apparent shifts at z=0 (up to ~3% for biased tracers) that are amplified in redshift space and mitigated at higher redshift, along with smaller but real physical shifts (~0.4–3%) not accounted for by simple smoothing; the analytic model reproduces these trends, including halo-mass dependence. These findings have direct implications for BAO-based cosmology and motivate reconstruction approaches that incorporate nonlinear velocity and bias effects to unbias the acoustic peak.

Abstract

The baryonic acoustic signature in the large-scale clustering pattern of galaxies has been detected in the two-point correlation function. Its precise spatial scale has been forwarded as a rigid-rod ruler test for the space-time geometry, and hence as a probe for tracking the evolution of Dark Energy. Percent-level shifts in the measured position can bias such a test and erode its power to constrain cosmology. This paper addresses some of the systematic effects that might induce shifts: namely non-linear corrections from matter evolution, redshift space distortions and biasing. We tackle these questions through analytic methods and through a large battery of numerical simulations, with total volume of the order ~100[Gpc\h]^3. A toy-model calculation shows that if the non-linear corrections simply smooth the acoustic peak, then this gives rise to an `apparent' shifting to smaller scales. However if tilts in the broad band power spectrum are induced then this gives rise to more pernicious `physical' shifts. Our numerical simulations show evidence of both: in real space and at z=0, for the dark matter we find percent level shifts; for haloes the shifts depend on halo mass, with larger shifts being found for the most biased samples, up to 3%. From our analysis we find that physical shifts are greater than ~0.4% at z=0. In redshift space these effects are exacerbated, but at higher redshifts are alleviated. We develop an analytical model to understand this, based on solutions to the pair conservation equation using characteristic curves. When combined with modeling of pairwise velocities the model reproduces the main trends found in the data. The model may also help to unbias the acoustic peak.

Figures (9)

• Figure 1: Halo correlation functions at $z=0$ in real (top) and redshift (bottom) space. Different symbols in each panel show results for massive (top) to less massive halos (bottom). Table \ref{['halocat']} gives the precise bins in halo mass. Error bars come from the dispersion between the measured $\xi$ in our 50 simulations; a total volume of $105\,(\!\, h^{-1} \, {\rm Gpc})^3$. Solid line in top panel shows the linear theory correlation function multiplied by an arbitrary constant so that it approximately matches the signal from the intermediate mass bin. Vertical dashed line shows the position of the acoustic peak in this linear correlation function: it lies at $106\, h^{-1} \, {\rm Mpc}$.
• Figure 2: Same as Fig. \ref{['xiz0']} but at $z=0.5$.
• Figure 3: Same as Fig. \ref{['xiz0']} but at $z=1$.
• Figure 4: Mean (solid points), scatter (shaded region) and error on the mean (error bars) for the halo-halo correlation functions measured in the ensemble of 50 simulations. The long dashed curves show the linearly biased, linear theory; the central solid curve shows linear theory, smoothed with a Gaussian filter radius $R$ and linearly biased $b$ (best fit values for these parameters are expressed in the figure annotations). The inner and outer solid curves enclosing the best fit model show the expected scatter in the continuum limit and the discrete Poisson sample limit, respectively -- see text for full explanation. The vertical lines represent the local maximum of the linear theory $\xi$ (right most dash line) and the best fit smoothed linear theory model (solid line) and the best-fit Tchebychev polynomial fit (triple dot dashed lines). The bottom panels show the ratio of the measurements to the central solid line and again the error bars are the errors on the mean.
• Figure 5: Same as previous figure, but in redshift space.