Problems using ratios of galaxy shape moments on requirements for weak lensing surveys

The shapes of galaxies can be quantified by ratios of their quadrupole moments. For faint galaxies, observational noise can make the denominator close to zero, so the ratios become ill-defined. Knowledge of these ratios (i.e. their measured standard deviation) is commonly used to assess the efficiency of weak gravitational lensing surveys. Since the requirements cannot be formally tested for faint galaxies, we explore two complementary mitigation strategies. In many weak lensing contexts, the most problematic sources can be removed by a cut in measured size. We investigate how a size cuts affects the required precision of the charge transfer inefficiency model and find slightly wider tolerance margins compared to the full size distribution. However, subtle biases in the data analysis chain may be introduced. Instead, as our second strategy, we propose requirements directly on the quadrupole moments themselves. To optimally exploit a Stage-IV dark energy survey, we find that the mean and standard deviation of a population of galaxies' quadrupole moments must to be known to better than $1.4\times10^{-3}$ arcsec$^{2}$, or the Stokes parameters to $1.9\times10^{-3}$ arcsec$^2$. This testable requirement can now form the basis for future performance validation, or for proportioning the requirements between subsystems to ensure unbiased cosmological parameter inference.