We present a simulation analysis of weak gravitational lensing flexion and shear measurement using shapelet decomposition, and identify differences between flexion and shear measurement noise in deep survey data. Taking models of galaxies from the Hubble Space Telescope Ultra Deep Field (HUDF) and applying a correction for the HUDF point spread function we generate lensed simulations of deep, optical imaging data from Hubbles Advanced Camera for Surveys (ACS), with realistic galaxy morphologies. We find that flexion and shear estimates differ in our measurement pipeline: whereas intrinsic galaxy shape is typically the dominant contribution to noise in shear estimates, pixel noise due to finite photon counts and detector read noise is a major contributor to uncertainty in flexion estimates, across a broad range of galaxy signal-to-noise. This pixel noise also increases more rapidly as galaxy signal-to-noise decreases than is found for shear estimates. We provide simple power law fitting functions for this behaviour, for both flexion and shear, allowing the effect to be properly accounted for in future forecasts for flexion measurement. Using the simulations we also quantify the systematic biases of our shapelet flexion and shear measurement pipeline for deep Hubble data sets such as Galaxy Evolution from Morphology and SEDs, Space Telescope A901/902 Galaxy Evolution Survey or the Cosmic Evolution Survey. Flexion measurement biases are found to be significant but consistent with previous studies.
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