Galaxy-galaxy lensing estimators and their covariance properties

TL;DR

This paper analyzes the covariance properties of galaxy-galaxy lensing estimators using SDSS data and mocks, highlighting the importance of subtracting lensing around random points to reduce errors and validating covariance models.

Contribution

It provides a detailed comparison of empirical and analytical covariance estimates for galaxy-galaxy lensing, emphasizing the effects of subtraction and the neglect of certain covariance terms.

Findings

Subtracting lensing around random points reduces errors.

Empirical covariances agree with theoretical estimates.

Connected 4-point and super-sample covariance are negligible for current noise levels.

Abstract

We study the covariance properties of real space correlation function estimators -- primarily galaxy-shear correlations, or galaxy-galaxy lensing -- using SDSS data for both shear catalogs and lenses (specifically the BOSS LOWZ sample). Using mock catalogs of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens over-density field. While the measurement using the lens density field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the over-density, we find that the errors are dominated by the shape noise and lens clustering, that empirically estimated covariances (jackknife and standard deviation across mocks) are consistent with theoretical estimates, and that both the connected parts of the 4-point function and the super-sample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically-determined covariances.