Twist and turn: weak lensing image distortions to second order

We account for all the image distortions relevant to weak gravitational lensing to second order. Besides the familiar shear, convergence, rotation and flexions, we find a new image distortion with two distinct descriptions, the twist and the turn. Like rotation, this distortion is not activated gravitationally to first order, but will be activated by systematic effects. We examine the rotational properties of twist and turn, and their effect on images in real and shapelet spaces. We construct estimators for the new distortion, taking into account the centroid shift which it generates. We then use these estimators to make first constraints on twist using the Space Telescope A901/902 Galaxy Evolution Survey Hubble Space Telescope survey; we find that the mean twist estimator is consistent with zero. We measure correlation functions for our twist estimator on the survey, again finding no evidence of systematic effects