Reconstructing the galaxy density field with photometric redshifts: I. Methodology and validation on stellar mass functions

TL;DR

This study assesses how photometric redshift uncertainties impact the measurement of galaxy environments and the galaxy stellar mass function, providing guidelines for future large-scale surveys like Euclid.

Contribution

It introduces a methodology to evaluate environment reconstruction accuracy using mock catalogues and quantifies the effects of photometric redshift errors on galaxy environment and GSMF measurements.

Findings

High-precision photometric redshifts (σ ≤ 0.01) enable accurate environment reconstruction.

Volume height matching the photometric redshift error improves environment measurement.

Photometric redshift errors dampen GSMF differences by about 0.3 dex, but differences remain detectable.

Abstract

Measuring environment for large numbers of distant galaxies is still an open problem, for which we need galaxy positions and redshifts. Photometric redshifts are more easily available for large numbers of galaxies, but at the price of larger uncertainties than spectroscopic ones. In this work we study how photometric redshifts affect the measurement of galaxy environment and how this may limit an analysis of the galaxy stellar mass function (GSMF) in different environments. Using mock galaxy catalogues, we measured the environment with a fixed aperture method, using each galaxy's true and photometric redshifts. We varied the fixed aperture volume parameters and the photometric redshift uncertainties. We then computed GSMF as a function of redshift and environment. We found that only when using high-precision photometric redshifts with $\sigma_{\Delta z/(1+z)} \le 0.01$, the most extreme environments can be reconstructed in a fairly accurate way, with a fraction $\ge 60\div 80\%$ of galaxies placed in the correct density quartile and a contamination of $\le 10\%$ by opposite quartile interlopers. A volume height comparable to the $\pm 1.5\sigma$ error of photometric redshifts grants a better reconstruction than other volume configurations. When using such an environmental measure, we found that any differences between the starting GSMF (divided accordingly to the true galaxy environment) will be damped on average of $\sim 0.3$ dex when using photometric redshifts, but will be still resolvable. These results may be used to interpret real data as we obtained them in a way that is fairly independent from how well the mock catalogues reproduce the real galaxy distribution. This work represents a preparatory study for future wide area photometric redshift surveys such as the Euclid Survey and we plan to apply these results to an analysis of the GSMF in the UltraVISTA Survey in future work.