Testing the accuracy of clustering redshift with simulations

Abstract: We explore the accuracy of the clustering-based redshift inference within the MICE2 simulation. This method uses the spatial clustering of galaxies between a spectroscopic reference sample and an unknown sample. The goal of this study is to give a preview of the redshift accuracy one can reach with this method. To do so, we first highlight the requirements of this technique in term of number of objects in both the reference and unknown samples. We also confirm that this method does not require a representative spectroscopic sample for calibration. We estimate that a density of spectroscopic objects of $10^{-5}$ arcmin$^{-2}$ per redshift bin of width $\delta z = 0.01$ over $9000 \ \text{deg}^{2}$ allows to reach 0.1 \% accuracy in the mean redshift for a galaxy density compatible with next generation of cosmological surveys. This number is compatible with the density of the Quasi Stellar Objects in BOSS. Second we demonstrate our ability to measure individual redshifts for galaxies independently from the photometric redshifts procedure. The resulting individual clustering redshifts have a bias=$-0.001$, an outlier fraction of $\eta=3.57\%$ and a scatter of $\sigma=0.027$ to $i<25$. The advantage of this procedure is threefold: i) it allows the use of clustering redshifts for any field in astronomy, ii) it allows the possibility to combine photometric and clustering based redshifts to get an improved redshift estimation, iii) it allows the use of cluster-$z$ to define tomographic bins for weak lensing. Finally we explore this last option and build 5 clustering redshift selected tomographic bins from redshift 0.2 to 1. We found a bias on the mean redshift estimate of $0.002$ per bin.