Fourier Band-Power E/B-mode Estimators for Cosmic Shear

TL;DR

This paper introduces new Fourier band-power estimators for cosmic shear that improve data analysis by providing unbiased, compact, and efficient ways to extract cosmological information while excluding problematic small-scale data.

Contribution

The paper presents novel Fourier band-power estimators that are linear, unbiased, and highly efficient for cosmic shear analysis, enabling significant data compression and improved E/B-mode separation.

Findings

Estimators are linear combinations of binned correlation functions.

They effectively account for survey window functions.

They enable compression of all relevant information into only three band-power estimates.

Abstract

We introduce new Fourier band-power estimators for cosmic shear data analysis and E/B-mode separation. We consider both the case where one performs E/B-mode separation and the case where one does not. The resulting estimators have several nice properties which make them ideal for cosmic shear data analysis. First, they can be written as linear combinations of the binned cosmic shear correlation functions. Second, they account for the survey window function in real-space. Third, they are unbiased by shape noise since they do not use correlation function data at zero separation. Fourth, the band-power window functions in Fourier space are compact and largely non-oscillatory. Fifth, they can be used to construct band-power estimators with very efficient data compression properties. In particular, we find that all of the information on the parameters $\Omega_{m}$, $\sigma_{8}$ and $n_{s}$ in the shear correlation functions in the range of $\sim10-400$ arcminutes for single tomographic bin can be compressed into only three band-power estimates. Finally, we can achieve these rates of data compression while excluding small-scale information where the modeling of the shear correlation functions and power spectra is very difficult. Given these desirable properties, these estimators will be very useful for cosmic shear data analysis.