On the bin sensitivity of the transverse BAO

TL;DR

This paper analyzes how redshift-bin choices bias the detection of the transverse BAO signal, comparing Gaussian, top-hat, and semi-Gaussian bin shapes for SKA and DESI using Fisher forecasts. It shows that the projection effect, which mixes BAO signals from different epochs, depends on bin width $\sigma_z$ and central redshift $z_c$, and that a semi-Gaussian bin optimally balances shot-noise and projection to recover $\theta_{\rm BAO}$ and constrain CPL parameters $w_0$, $w_a$. A semi-statistical correction using adjacent redshift halves is proposed to mitigate projection effects, improving the accuracy of BAO position measurements. The results advocate for adopting semi-Gaussian binning, especially at low $z$, while recognizing higher-$z$ surveys can tolerate or benefit from alternative bin configurations depending on $\sigma_z$.

Abstract

The BAO characteristic scale is a useful tool for understanding the evolution of the universe, especially the influence of dark energy on this evolution. In this work, we study the projection effect in transverse BAO, namely the mixing of BAO signals from different epochs caused by $z_c$ uncertainty within a chosen bin. We focus our forecast on two surveys of interest: the Square Kilometre Array (SKA) HI galaxy redshift survey and the Dark Energy Spectroscopic Instrument (DESI)'s final Luminous Red Galaxy (LRG) sample. We test the sensitivity in finding the transverse BAO depending of three bin configurations: a Gaussian, a top-hat and an intermediate of them semi-Gaussian. We also analyse the precision the bin widths $σ_z$ from smaller to wider bins $0.01<σ_z<0.1$. In order to correct these deviations, we propose a correction based on adjacent redshift to $z_c$, this would provide a semi-statistical correction instead of only relying on fiducial cosmology. Finally, we conclude that despite the higher shot-noise than the top-hat bin separation, the semi-Gaussian bin is the most accurate case to find the BAO signal and to constrain parameters through the angular power spectrum. A Gaussian binning gives the least precise parameter constraints compared to the other two cases.

Figures (19)

• Figure 1: Representation of the projection effect in the transverse BAO feature. The z axis points to increasing redshift, when the BAO feature has a reduced angular size. The circles represent the expected BAO projected in the sky, with a radius of $\theta_{\rm BAO}$, the dots can be thought as detected galaxies distributed preferably at this scale. A background projection shows the bin redshift distribution $N(z)$, in this example, the central redshift $z_c$ is the desired redshift for the BAO feature we are looking for, but the projection effect due to the galaxies in the denser and less dense regions can dilute the signal.
• Figure 2: DESI LRG redshift distribution separated in different redshift bins, Gaussian (upper panel), Semi-Gaussian (middle panel), and Top-hat (bottom panel). The colours from blue to black represent and increase in redshift.
• Figure 3: SKA redshift distribution separated in different redshift bins, Gaussian (upper panel), Semi-Gaussian (middle panel), and Top-hat (bottom panel). The colours from blue to black represent and increase in redshift.
• Figure 4: Angular correlation function for different bin configuration for a DESI-like survey. The Top-hat (black dashed line) and semi-Gaussian (gray line) is in the left y-axis while the Gaussian (blue line) is the right one in all panels. The upper panel has $z_c=0.62$, the middle one $z_c=0.66$, and the bottom panel has $z_c=0.7$.
• Figure 5: Angular correlation function for different bin configuration for a SKA-like survey. The Top-hat (black dashed line) and semi-Gaussian (gray line) is in the left y-axis while the Gaussian (blue line) is the right one in all panels. The upper panel has $z_c=0.11$, the middle one $z_c=0.16$, and the bottom panel has $z_c=0.2$.