The probability distribution of ellipticity: implications for weak lensing measurement

The weak lensing effect generates spin-2 distortions, referred to as shear, on the observable shape of distant galaxies, induced by intervening gravitational tidal fields. Traditionally, the spin-2 distortion in the light distribution of distant galaxies is measured in terms of a galaxy ellipticity. This is a very good unbiased estimator of the shear field in the limit that a galaxy is measured at infinite signal-to-noise. However, the ellipticity is always defined as a ratio between two quantities (for example, between the polarisation and measurement of the galaxy size, or between the semi-major and semi-minor axis of the galaxy) and therefore requires some non-linear combination of the image pixels. This means, in any realistic case, this would lead to biases in the measurement of the shear (and hence in the cosmological parameters) whenever noise is present in the image. This type of bias can be understood from the particular shape of the 2D probability distribution of the ellipticity of an object measured from data. Moreover this probability distribution can be used to explore strategies for calibration of noise biases in present and future weak lensing surveys (e.g. KiDS, DES, HSC,Euclid, LSST...)