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

Context. Measuring environment for large numbers of galaxies in the distant Universe is an open problem in astrophysics, as environment is important in determining many properties of galaxies during their formation and evolution. In order to measure galaxy environments, 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 redshifts. Aims. We study how photometric redshifts a ect the measurement of galaxy environment and how the reconstruction of the density field may limit an analysis of the galaxy stellar mass function (GSMF) in di erent environments. Methods. Through the use of mock galaxy catalogues, we measured galaxy environment with a fixed aperture method, using each galaxy's true and photometric redshifts. We varied the parameters defining the fixed aperture volume and explored di erent configurations. We also used photometric redshifts with di erent uncertainties to simulate the case of various surveys. We then computed GSMF of the mock galaxy catalogues as a function of redshift and environment to see how the environmental estimate based on photometric redshifts a ects their analysis. Results. We found that the most extreme environments can be reconstructed in a fairly accurate way only when using high-precision photometric redshifts with σΔz=(1+z) ≤ 0:01, with a fraction ≥60 ÷ 80% of galaxies placed in the correct density quartile and a contamination of ≤10% by opposite quartile interlopers. A length of the volume in the radial direction comparable to the ±1.5σ error of photometric redshifts and a fixed aperture radius of a size similar to the physical scale of the studied environment grant a better reconstruction than other volume configurations. When using this kind of an estimate of the density field, we found that any di erence between the starting GSMF (divided accordingly to the true galaxy environment) is damped on average by ~0.3 dex with photometric redshifts, but is still resolvable. Although derived with mock galaxy catalogues, these results may be used to interpret real data, as we obtained them by comparing results between the true redshift and photometric redshift case, therefore, in a way that does not completely depend on how well the mock catalogues reproduce the real galaxy distribution. Conclusions. This work allows us several useful considerations on how to interpret results of an analysis of the GSMF in di erent environments when the density field is measured with photometric redshifts and represents a preparatory study for future wide area photometric redshift surveys, such as the Euclid Survey. We plan to apply the result of this work to an environmental analysis of the GSMF in the UltraVISTA Survey in future work.