Baryon acoustic signature in the clustering of density maxima

Abstract

We reexamine the two-point correlation of density maxima in Gaussian initial conditions. Spatial derivatives of the linear density correlation, which were ignored in the calculation of Bardeen, Bond, Kaiser & Szalay (1986), are included in our analysis. These functions exhibit large oscillations around the sound horizon scale for generic CDM power spectra. We derive the exact leading-order expression for the correlation of density peaks and demonstrate the contribution of those spatial derivatives. In particular, we show that these functions can modify significantly the baryon acoustic signature of density maxima relative to that of the linear density field. The effect depends upon the exact value of the peak height, the filter shape and size, and the small-scale behaviour of the transfer function. In the LambdaCDM cosmology, for maxima identified in the density field smoothed at mass scale M\approx 10^{12}-10^{14}M_sun/h and with linear threshold height ν=1.673/σ(M), the contrast of the BAO can be a few tens of percent larger than in the linear matter correlation. Overall, the BAO is amplified (damped) for threshold heights larger (less) than unity. Density maxima thus behave quite differently than linearly biased tracers of the density field, whose acoustic signature is a simple scaled version of the linear baryon acoustic oscillation. We also calculate the mean streaming of peak pairs in the quasi-linear regime. We show that the leading-order 2-point correlation and pairwise velocity of density peaks are consistent with a nonlinear, local biasing relation involving gradients of the density field. Biasing will be an important issue in ascertaining how much of the enhancement of the BAO in the primeval correlation of density maxima propagates into the late-time clustering of galaxies.