Robust covariance estimation of galaxy-galaxy weak lensing: validation and limitation of jackknife covariance

TL;DR

This paper develops a simulation-based method to evaluate the error covariance in galaxy-galaxy weak lensing, compares it with the traditional jackknife method, and discusses the limitations of jackknife covariance estimation.

Contribution

The study introduces a simulation approach for covariance estimation and assesses the accuracy and limitations of the jackknife method in galaxy-galaxy weak lensing analysis.

Findings

Jackknife covariance varies across mock realizations.

Average jackknife covariance approximates true covariance up to certain scales.

Jackknife underestimates covariance at large scales, especially in denser surveys.

Abstract

We develop a method to simulate galaxy-galaxy weak lensing by utilizing all-sky, light-cone simulations and their inherent halo catalogs. Using the mock catalog to study the error covariance matrix of galaxy-galaxy weak lensing, we compare the full covariance with the "jackknife" (JK) covariance, the method often used in the literature that estimates the covariance from the resamples of the data itself. We show that there exists the variation of JK covariance over realizations of mock lensing measurements, while the average JK covariance over mocks can give a reasonably accurate estimation of the true covariance up to separations comparable with the size of JK subregion. The scatter in JK covariances is found to be $\sim10\%$ after we subtract the lensing measurement around random points. However, the JK method tends to underestimate the covariance at the larger separations, more increasingly for a survey with a higher number density of source galaxies. We apply our method to the the Sloan Digital Sky Survey (SDSS) data, and show that the 48 mock SDSS catalogs nicely reproduce the signals and the JK covariance measured from the real data. We then argue that the use of the accurate covariance, compared to the JK covariance, allows us to use the lensing signals at large scales beyond a size of the JK subregion, which contains cleaner cosmological information in the linear regime.