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A variety of methods have been proposed to define and to quantify galaxyenvironments. While these techniques work well in general with spectroscopicredshift samples, their application to photometric redshift surveys remainsuncertain. To investigate whether galaxy environments can be robustly measuredwith photo-z samples, we quantify how the density measured with the nearestneighbor approach is affected by photo-z uncertainties by using the Durham mockgalaxy catalogs in which the 3D real-space environments and the properties ofgalaxies are exactly known. Furthermore, we present an optimization scheme inthe choice of parameters used in the 2D projected measurements which yield thetightest correlation with respect to the 3D real-space environments. Byadopting the optimized parameters in the density measurements, we show that thecorrelation between the 2D projected optimized density and real-space densitycan 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 to0.06. 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 acomparable performance of small-scale density measurement to a shallower $i\sim$ 22.5 spectroscopic sample with $\sim$ 10% sampling rate. Finally, wediscuss the application of the local density measurements to the Pan-STARRS1Medium Deep survey, one of the largest deep optical imaging surveys. Using datafrom $\sim5$ square degrees of survey area, our results show that it ispossible to measure local density and to probe the color-density relation with3$\sigma$ confidence level out to $z \sim 0.8$ in the PS-MDS. The color-densityrelation, however, quickly degrades for data covering smaller areas.

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