Can We Detect the Color-Density Relation with Photometric Redshifts?

A variety of methods have been proposed to define and to quantify galaxy environments. While these techniques work well in general with spectroscopic redshift samples, their application to photometric redshift surveys remains uncertain. To investigate whether galaxy environments can be robustly measured with photo-z samples, we quantify how the density measured with the nearest neighbor approach is affected by photo-z uncertainties by using the Durham mock galaxy catalogs in which the 3D real-space environments and the properties of galaxies are exactly known. Furthermore, we present an optimization scheme in the choice of parameters used in the 2D projected measurements which yield the tightest correlation with respect to the 3D real-space environments. By adopting the optimized parameters in the density measurements, we show that the correlation between the 2D projected optimized density and real-space density can still be revealed, and the color-density relation is also visible out to $z \sim 0.8$ even for a photo-z uncertainty ($\sigma_{\Delta_{z}/(1+z)}$) up to 0.06. We find that at the redshift $0.3 < z < 0.5$ a deep ($i \sim 25$) photometric redshift survey with $\sigma_{\Delta_{z}/(1+z)} = 0.02$ yields a comparable performance of small-scale density measurement to a shallower $i \sim$ 22.5 spectroscopic sample with $\sim$ 10% sampling rate. Finally, we discuss the application of the local density measurements to the Pan-STARRS1 Medium Deep survey, one of the largest deep optical imaging surveys. Using data from $\sim5$ square degrees of survey area, our results show that it is possible to measure local density and to probe the color-density relation with 3$\sigma$ confidence level out to $z \sim 0.8$ in the PS-MDS. The color-density relation, however, quickly degrades for data covering smaller areas.