Optimizing galaxy samples for clustering measurements in photometric surveys

TL;DR

This paper investigates the optimal balance between galaxy sample size and photometric redshift accuracy for clustering measurements in photometric surveys, providing guidance for future survey data analysis.

Contribution

It systematically analyzes the trade-off between sample size and photo-z precision using Fisher forecasts, highlighting the importance of cross-correlations and bin width in optimizing cosmological constraints.

Findings

Optimal FoM occurs when redshift bin width is similar to photo-z precision.

Including cross-correlations enhances the benefits of larger, less precise samples.

Overlap in redshift bins enables self-calibration and tighter constraints.

Abstract

When analyzing galaxy clustering in multi-band imaging surveys, there is a trade-off between selecting the largest galaxy samples (to minimize the shot noise) and selecting samples with the best photometric redshift (photo-z) precision, which generally include only a small subset of galaxies. In this paper, we systematically explore this trade-off. Our analysis is targeted towards the third year data of the Dark Energy Survey (DES), but our methods hold generally for other data sets. Using a simple Gaussian model for the redshift uncertainties, we carry out a Fisher matrix forecast for cosmological constraints from angular clustering in the redshift range $z = 0.2-0.95$. We quantify the cosmological constraints using a Figure of Merit (FoM) that measures the combined constraints on $\Omega_m$ and $\sigma_8$ in the context of $\Lambda$CDM cosmology. We find that the trade-off between sample size and photo-z precision is sensitive to 1) whether cross-correlations between redshift bins are included or not, and 2) the ratio of the redshift bin width $\delta z$ and the photo-z precision $\sigma_z$. When cross-correlations are included and the redshift bin width is allowed to vary, the highest FoM is achieved when $\delta z \sim \sigma_z$. We find that for the typical case of $5-10$ redshift bins, optimal results are reached when we use larger, less precise photo-z samples, provided that we include cross-correlations. For samples with higher $\sigma_{z}$, the overlap between redshift bins is larger, leading to higher cross-correlation amplitudes. This leads to the self-calibration of the photo-z parameters and therefore tighter cosmological constraints. These results can be used to help guide galaxy sample selection for clustering analysis in ongoing and future photometric surveys.