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Abstract: In weak gravitational lensing, the image distortion caused by shear measuresthe projected tidal gravitational field of the deflecting mass distribution. Tolowest order, the shear is proportional to the mean image ellipticity. If theimage sizes are not small compared to the scale over which the shear varies,higher-order distortions occur, called flexion. For ordinary weak lensing, theobservable quantity is not the shear, but the reduced shear, owing to themass-sheet degeneracy. Likewise, the flexion itself is unobservable. Rather,higher-order image distortions measure the reduced flexion, i.e., derivativesof the reduced shear. We derive the corresponding lens equation in terms of thereduced flexion and calculate the resulting relation between brightness momentsof source and image. Assuming an isotropic distribution of source orientations,estimates for the reduced shear and flexion are obtained; these are then testedwith simulations. In particular, the presence of flexion affects thedetermination of the reduced shear. The results of these simulations yield theamount of bias of the estimators, as a function of the shear and flexion. Wepoint out and quantify a fundamental limitation of the flexion formalism, interms of the product of reduced flexion and source size. If this productincreases above the derived threshold, multiple images of the source are formedlocally, and the formalism breaks down. Finally, we show how a generalreduced flexion field can be decomposed into its four components: two of themare due to a shear field, carrying an E- and B-mode in general. The other twocomponents do not correspond to a shear field; they can also be split up intocorresponding E- and B-modes.

Autor: Peter Schneider AIfA Bonn, Xinzhong Er AIfA and MPIfR

Fuente: https://arxiv.org/

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