Galaxy‐Galaxy Flexion: Weak Lensing to Second Order

In this paper, we develop a new gravitational lensing inversion technique. While traditional approaches assume that the lensing field varies little across a galaxy image, we note that this variation in the field can give rise to a "flexion," or bending of a galaxy image, which may then be used to detect a lensing signal with increased signal-to-noise ratio. Since the significance of the flexion signal increases on small scales, this is ideally suited to galaxy-galaxy lensing. We develop an inversion technique based on the "shapelets" formalism of Refregier. We then demonstrate the proof of this concept by measuring a flexion signal in the Deep Lens Survey. Assuming an intrinsically isothermal distribution, we find from the flexion signal alone a velocity width of v c = 221 ± 12 km s -1 for lens galaxies of r < 21.5, subject to uncertainties in the intrinsic flexion distribution.