Angular Correlation Function Estimators Accounting for Contamination from Probabilistic Distance Measurements

With the advent of surveys containing millions to billions of galaxies, it is imperative to develop analysis techniques that utilize the available statistical power. In galaxy clustering, even small sample contamination arising from distance uncertainties can lead to large artifacts, which the standard estimator for two-point correlation functions does not account for. We first introduce a formalism, termed decontamination, that corrects for sample contamination by utilizing the observed cross-correlations in the contaminated samples; this corrects any correlation function estimator for contamination. Using this formalism, we present a new estimator that uses the standard estimator to measure correlation functions in the contaminated samples but then corrects for contamination. We also introduce a weighted estimator that assigns each galaxy a weight in each redshift bin based on its probability of being in that bin. We demonstrate that these estimators effectively recover the true correlation functions and their covariance matrices. Our estimators can correct for sample contamination caused by misclassification between object types as well as photometric redshifts; they should be particularly helpful for studies of galaxy evolution and baryonic acoustic oscillations, where forward modeling the clustering signal using the contaminated redshift distribution is undesirable.