Baryon acoustic signature in the clustering of density maxima

TL;DR

This paper revisits the two-point correlation of density maxima in Gaussian initial conditions, including spatial derivatives, revealing significant modifications to the baryon acoustic oscillation signature depending on various parameters.

Contribution

It derives the exact leading-order correlation of density peaks including derivatives, showing their impact on the BAO feature, which was previously neglected.

Findings

BAO contrast can be 10-30% larger than in linear matter correlation.

The BAO is amplified for higher threshold heights and damped for lower.

Density maxima exhibit different BAO behavior than linearly biased tracers.

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 \nu=1.673/\sigma(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.