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