Simulations of Weak Gravitational Lensing - II : Including Finite Support Effects in Cosmic Shear Covariance Matrices

TL;DR

This paper models and quantifies the effects of finite simulation volume on weak lensing statistics, providing correction methods to improve the accuracy of covariance matrices without requiring larger simulations.

Contribution

It introduces a theoretical model for finite support effects in weak lensing simulations and offers semi-analytic correction methods applicable to various estimators and survey conditions.

Findings

Finite support effects significantly suppress shear correlation functions at certain scales.

The impact depends on the ratio of angular separation to simulation box size.

Correction methods effectively mitigate finite volume biases in weak lensing analyses.

Abstract

(Abridged) We investigate and quantify the impact of finite simulation volume on weak lensing two- and four-point statistics. These {\it finite support} (FS) effects are modelled for several estimators, simulation box sizes and source redshifts, and validated against a new large suite of 500 $N$-body simulations. The comparison reveals that our theoretical model is accurate to better than 5 per cent for the shear correlation function $\xi_{+}(\theta)$ and its error. We find that the most important quantities for FS modelling is the ratio between the measured angle $\theta$ and the angular size of the simulation box at the source redshift, $\theta_{box}(z_s)$, or the multipole equivalent $\ell / \ell_{box}(z_s)$. When this ratio reaches 0.1, independently of the source redshift, the shear correlation function $\xi_+$ is suppressed by 5, 10, 20 and 25 percent for $L_{box}= 1000$, $500$, $250$ and $147\mbox{Mpc}/h$ respectively. When it reaches 0.2, the suppression exceeds 25 percent even for the largest box. The same effect is observed in $\xi_{-}(\theta)$, but at much larger angles. This has important consequences for cosmological analyses using $N$-body simulations to calibrate the impact of non-linear gravitational clustering or to estimate errors and systematics effects, and should not be overlooked. We propose simple semi-analytic solutions to correct for these finite box effects with and without the presence of survey masks, and the method can be generalized to any weak lensing estimator. This offers a graceful solution to the important problem of estimating accurate covariance matrices for weak lensing studies: there is no need to run extra large simulation volumes, as long as the box effects are corrected.