New highly precise weak gravitational lensing flexions measurement method based on ERA method

Abstract

ABSTRACT Weak gravitational lensing flexions are a kind of weak lensing distortion that are defined as the spin 1 and spin 3 combinations of the third order derivatives of gravitational lensing potential. Since the shear has spin 2 combination of the second-order derivative, the flexion signal gives partly independent information from shear signal and is more sensitive to the local mass distribution than shear signal. Thus its measurement is expected to play important roles in observational cosmology. However, since the weakness of the flexion signal, as well as the complicatedness of its intrinsic noise, made its accurate observation very difficult. We propose a new method of measuring the flexion signal using ERA method which is a method to measure weak lensing shear without any approximation. We find two particular combinations of the flexions which provide the quantities with only lensing information and free of intrinsic noise when taken average. It is confirmed by simple numerical simulation that the statistical average of these combinations do not in fact depend on the strength of the intrinsic distortion. Then, we introduce a method which measures flexions with PSF correction. This method is developed by applying the ERA method for flexion distortions and we call this method the FIRE method. It uses the expansion technique with an assumption of weak flexion, and we show by using typical examples of 1st and 2nd flexion images that the estimated errors become less than 1 per cent in most cases with the lowest order of the expansion. Finally, we apply the method for real data to measure flexion components in real galaxy images.