Simulations of Wide-Field Weak Lensing Surveys II: Covariance Matrix of Real Space Correlation Functions

TL;DR

This paper investigates the covariance matrix of cosmic shear correlation functions using extensive simulations, revealing the significant impact of non-Gaussian contributions and providing a fitting formula for future survey analyses.

Contribution

It introduces a method to disentangle Gaussian and non-Gaussian covariance contributions and offers a new fitting formula accounting for survey area effects.

Findings

Non-Gaussian covariance dominates at small scales, exceeding Gaussian by factors of 10-20.

Analytical Gaussian covariance overestimates true covariance due to finite survey area effects.

Halo model predictions qualitatively match simulations but show amplitude discrepancies.

Abstract

Using 1000 ray-tracing simulations for a {\Lambda}-dominated cold dark model in Sato et al. (2009), we study the covariance matrix of cosmic shear correlation functions, which is the standard statistics used in the previous measurements. The shear correlation function of a particular separation angle is affected by Fourier modes over a wide range of multipoles, even beyond a survey area, which complicates the analysis of the covariance matrix. To overcome such obstacles we first construct Gaussian shear simulations from the 1000 realizations, and then use the Gaussian simulations to disentangle the Gaussian covariance contribution to the covariance matrix we measured from the original simulations. We found that an analytical formula of Gaussian covariance overestimates the covariance amplitudes due to an effect of finite survey area. Furthermore, the clean separation of the Gaussian covariance allows to examine the non-Gaussian covariance contributions as a function of separation angles and source redshifts. For upcoming surveys with typical source redshifts of z_s=0.6 and 1.0, the non-Gaussian contribution to the diagonal covariance components at 1 arcminute scales is greater than the Gaussian contribution by a factor of 20 and 10, respectively. Predictions based on the halo model qualitatively well reproduce the simulation results, however show a sizable disagreement in the covariance amplitudes. By combining these simulation results we develop a fitting formula to the covariance matrix for a survey with arbitrary area coverage, taking into account effects of the finiteness of survey area on the Gaussian covariance.