A Method for Weak-Lensing Flexion Analysis by the HOLICs Moment Approach^*

We have developed a method for measuring higher order weak-lensing distortions of faint background galaxies, namely, the weak gravitational flexion, by fully extending the Kaiser, Squires, and Broadhurst method to include higher order lensing image characteristics (HOLICs) introduced by Okura, Umetsu, and Futamase. We take into account explicitly the weight function in calculations of noisy shape moments and the effect of higher order point-spread function (PSF) anisotropy, as well as isotropic PSF smearing. Our HOLICs formalism allows accurate measurements of flexion from practical observational data in the presence of a noncircular, anisotropic PSF. We test our method using mock observations of simulated galaxy images and actual, ground-based Subaru observations of the massive galaxy cluster A1689 (z = 0.183). From the high-precision measurements of the spin-1 first flexion, we obtain a high-resolution mass map in the central region of A1689. The reconstructed mass map shows a bimodal feature in the central 4' × 4' region of the cluster. The major, pronounced peak is associated with the brightest cluster galaxy and central cluster members, while the secondary mass peak is associated with a local concentration of bright galaxies. The refined, high-resolution mass map of A1689 demonstrates the power of the generalized weak-lensing analysis techniques for quantitative and accurate measurements of the weak gravitational lensing signal.