Optimizing galaxy samples for clustering measurements in photometric surveys

When analysing galaxy clustering in multiband 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 includes 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 Ω_m and σ₈ in the context of Λ cold dark matter (ΛCDM) 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 δz to the photo-z precision σ_z. When cross-correlations are included and the redshift bin width is allowed to vary, the highest FoM is achieved when δz ∼ σ_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 σ_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.