Locating the Baryon Acoustic Peak

TL;DR

This paper analyzes how photometric redshift surveys can detect the baryon acoustic peak through angular galaxy clustering, addressing projection effects, and proposes an improved prediction method for the signal.

Contribution

It introduces a single-integral approach to better predict the acoustic peak in angular correlation functions, surpassing the Limber approximation in accuracy.

Findings

The position of the acoustic peak depends on the angular diameter distance.

Thicker redshift bins shift features to smaller angular scales.

Precise redshift error measurement is crucial for dark energy studies.

Abstract

Forthcoming photometric redshift surveys should provide an accurate probe of the acoustic peak in the two-point galaxy correlation function, in the form of angular clustering of galaxies within a given shell in redshift space. We investigate the form of the anticipated signal, quantifying the distortions that arise due to projection effects, and in particular explore the validity of applying the Limber approximation. A single-integral prescription is presented, which provides an alternative to Limber's equation, and produces a significantly improved prediction in the regime of interest. The position of the acoustic peak within the angular correlation function relates to the angular diameter distance to the far side of the redshift bin. Thicker redshift bins therefore shift comoving features towards smaller angular scales. As a result, the value of the photometric redshift error acquires a greater significance, particularly at lower redshifts. In order to recover the dark energy equation of state to a level of 1%, we find the total redshift dispersion must be determined to within \Delta \sigma_z ~ 10^-3, which may prove challenging to achieve in practice.