Optimizing galaxy samples for clustering measurements in photometric surveys

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.