We introduce redMaGiC, an automated algorithm for selecting Luminous Red Galaxies (LRGs). The algorithm was specifically developed to minimize photometric redshift uncertainties in photometric large-scale structure studies. redMaGiC achieves this by
self-training the color-cuts necessary to produce a luminosity-thresholded LRG sample of constant comoving density. We demonstrate that redMaGiC photozs are very nearly as accurate as the best machine-learning based methods, yet they require minimal spectroscopic training, do not suffer from extrapolation biases, and are very nearly Gaussian. We apply our algorithm to Dark Energy Survey (DES) Science Verification (SV) data to produce a redMaGiC catalog sampling the redshift range $zin[0.2,0.8]$. Our fiducial sample has a comoving space density of $10^{-3} (h^{-1} Mpc)^{-3}$, and a median photoz bias ($z_{spec}-z_{photo}$) and scatter $(sigma_z/(1+z))$ of 0.005 and 0.017 respectively. The corresponding $5sigma$ outlier fraction is 1.4%. We also test our algorithm with Sloan Digital Sky Survey (SDSS) Data Release 8 (DR8) and Stripe 82 data, and discuss how spectroscopic training can be used to control photoz biases at the 0.1% level.
In order to study the galaxy population of galaxy clusters with photometric data one must be able to accurately discriminate between cluster members and non-members. The redMaPPer cluster finding algorithm treats this problem probabilistically. Here,
we utilize SDSS and GAMA spectroscopic membership rates to validate the redMaPPer membership probability estimates for clusters with $zin[0.1,0.3]$. We find small - but correctable - biases, sourced by three different systematics. The first two were expected a priori, namely blue cluster galaxies and correlated structure along the line of sight. The third systematic is new: the redMaPPer template fitting exhibits a non-trivial dependence on photometric noise, which biases the original redMaPPer probabilities when utilizing noisy data. After correcting for these effects, we find exquisite agreement ($approx 1%$) between the photometric probability estimates and the spectroscopic membership rates, demonstrating that we can robustly recover cluster membership estimates from photometric data alone. As a byproduct of our analysis we find that on average unavoidable projection effects from correlated structure contribute $approx 6%$ of the richness of a redMaPPer galaxy cluster. This work also marks the second public release of the SDSS redMaPPer cluster catalog.
Maximizing the utility of upcoming photometric cluster surveys requires a thorough understanding of the richness-mass relation of galaxy clusters. We use Monte Carlo simulations to study the impact of various sources of observational scatter on this
relation. Cluster ellipticity, photometric errors, photometric redshift errors, and cluster-to-cluster variations in the properties of red-sequence galaxies contribute negligible noise. Miscentering, however, can be important, and likely contributes to the scatter in the richness-mass relation of galaxy maxBCG clusters at the low mass end, where centering is more difficult. We also investigate the impact of projection effects under several empirically motivated assumptions about cluster environments. Using SDSS data and the maxBCG cluster catalog, we demonstrate that variations in cluster environments can rarely (approx 1% - 5% of the time) result in significant richness boosts. Due to the steepness of the mass/richness function, the corresponding fraction of optically selected clusters that suffer from these projection effects is approx 5% - 15%. We expect these numbers to be generic in magnitude, but a precise determination requires detailed, survey-specific modeling.
