An optimal survey geometry of weak lensing survey: minimizing super-sample covariance

TL;DR

This paper identifies optimal survey geometries for weak lensing to minimize super-sample covariance, significantly improving measurement precision and effective area coverage.

Contribution

It proposes specific survey geometries, including elongated and disconnected patch configurations, to reduce super-sample covariance effects in weak lensing surveys.

Findings

Elongated rectangular surveys reduce super-sample covariance by a factor of 2.

Distributing patches with ~15 degrees separation maximizes area coverage and signal-to-noise ratio.

Optimal geometries enable wider multipole coverage and improved measurement precision.

Abstract

Upcoming wide-area weak lensing surveys are expensive both in time and cost and require an optimal survey design in order to attain maximum scientific returns from a fixed amount of available telescope time. The super-sample covariance (SSC), which arises from unobservable modes that are larger than the survey size, significantly degrades the statistical precision of weak lensing power spectrum measurement even for a wide-area survey. Using the 1000 mock realizations of the log-normal model, which approximates the weak lensing field for a $\Lambda$-dominated cold dark matter model, we study an optimal survey geometry to minimize the impact of SSC contamination. For a continuous survey geometry with a fixed survey area, a more elongated geometry such as a rectangular shape of 1:400 side-length ratio reduces the SSC effect and allows for a factor 2 improvement in the cumulative signal-to-noise ratio ($S/N$) of power spectrum measurement up to $\ell_{\rm max}\simeq $ a few $10^3$, compared to compact geometries such as squares or circles. When we allow the survey geometry to be disconnected but with a fixed total area, assuming $1\times 1$ sq. degrees patches as the fundamental building blocks of survey footprints, the best strategy is to locate the patches with $\sim 15$ degrees separation. This separation angle corresponds to the scale at which the two-point correlation function has a negative minimum. The best configuration allows for a factor 100 gain in the effective area coverage as well as a factor 2.5 improvement in the $S/N$ at high multipoles, yielding a much wider coverage of multipoles than in the compact geometry.