Fourier Band-Power E B-mode Estimators For Cosmic Shear

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We introduce new Fourier band-power estimators for cosmic shear information evaluation and E/B-mode separation. We consider both the case the place one performs E/B-mode separation and the case the place one does not. The resulting estimators have a number of nice properties which make them perfect for cosmic shear knowledge analysis. First, they can be written as linear combos of the binned cosmic shear correlation features. Second, they account for the survey window perform in real-area. Third, they're unbiased by shape noise since they don't use correlation function knowledge at zero separation. Fourth, the band-energy window capabilities in Fourier space are compact and largely non-oscillatory. Fifth, they can be used to construct band-energy estimators with very efficient knowledge compression properties. 10-400 arcminutes for single tomographic bin will be compressed into solely three band-energy estimates. Finally, we will achieve these rates of data compression whereas excluding small-scale information where the modeling of the shear correlation capabilities and power spectra is very difficult.



Given these fascinating properties, these estimators might be very helpful for professional landscaping shears cosmic shear data evaluation. Cosmic shear, or the weak gravitational lensing of background galaxies by large-scale structure, is one of the crucial promising cosmological probes as a result of it will possibly in principle present direct constraints on the amplitude and shape of the projected matter power spectrum. It is anticipated that these cosmic shear experiments will probably be troublesome, being subject to many potential systematic effects in both the measurements and the modeling (see, e.g., Weinberg et al., 2013, for a review). Cosmic shear measurements are made by correlating the lensed shapes of galaxies with each other. As galaxies are approximately, but not exactly (see, e.g., Troxel & Ishak, 2014, for a review), randomly oriented in the absence of lensing, we are able to attribute large-scale correlations among the many galaxy shapes to gravitational lensing. However, we observe galaxies by means of the environment and telescope which change their shapes via the point spread perform (PSF).



These instrumental effects can probably be a lot bigger than the alerts we are in search of and may mimic true cosmic shear alerts. Thus they must be eliminated fastidiously. Luckily, cosmic shear has several built-in null exams than can be utilized to seek for and verify the absence of contamination in the indicators. Checking for B-mode contamination in the cosmic shear alerts is one among crucial of those null checks (Kaiser, 1992). Weak gravitational lensing on the linear stage solely produces parity-free E-mode shear patterns. Small quantities of shear patterns with web handedness, often called B-mode patterns, can be produced by higher-order corrections, but their amplitude is usually a lot too small be observed by present surveys (e.g., professional landscaping shears Krause & Hirata, 2010). Thus we are able to use the absence or presence of B-mode patterns within the noticed shear discipline to look for systematic errors. PSF patterns generally have similar ranges of E- and B-modes in contrast to true cosmic shear indicators.



Note that ensuring the extent of B-modes in a survey is per zero is a necessary however not sufficient situation for the shear measurements to be error free. The significance of checking cosmic shear alerts for B-mode contamination has motivated a big amount of work on devising statistical measures of the B-mode contamination (e.g., Schneider et al., 1998; Seljak, 1998; Hu & White, 2001; Schneider et al., 2002a; Schneider & Kilbinger, 2007; Schneider et al., 2010; Hikage et al., 2011; Becker, 2013). The principle obstacle confronting each B-mode estimator is the mixing of E/B-modes within the estimator and the effect of ambiguous modes. This mixing occurs on large-scales when one considers instead of an infinitely massive survey, a survey of finite size. For a finite sized survey, modes with wavelengths of order the patch dimension can sometimes not be uniquely categorized as either E- or B-modes (e.g., Bunn, 2003). These ambiguous modes can contaminate the E- and B-mode estimators. If all of the power within the survey is sourced by E-modes, then the ambiguous modes are actually E-modes which then results in mixing of E-modes into B-modes.