Limitations on shapelet-based weak-lensing measurements

Aims: We seek to understand the impact on shape estimators obtained from circular and elliptical shapelet models under two realistic conditions: (a) only a limited number of shapelet modes are available for the model, and (b) the intrinsic galactic shapes are not restricted to shapelet models. Methods: We create a set of simplistic simulations, in which the galactic shapes follow a Sérsic profile. By varying the Sérsic index and applied shear, we quantify the amount of bias on shear estimates that arises from insufficient modeling. Additional complications from PSF convolution, pixelation, and pixel noise are also discussed. Results: Highly elliptical galaxy shapes cannot be accurately modeled within the circular shapelet basis system and are biased towards less elongated shapes. This problem can be cured by allowing elliptical basis functions. Another problem occurs for galaxies whose radial profile differs strongly from the Gaussian weighting function employed in both the circular and the elliptical shapelet bases. For galaxies with large Sérsic indices, shear estimates from circular shapelets are biased low even for small apparent ellipticities because of the preference for round models, and shear estimates from elliptical shapelets depend critically on accurate ellipticity priors. Independent of the particular form of the estimator, the bias depends on the true intrinsic galaxy morphology, but also on the size and shape of the PSF. Conclusions: As long as the issues discussed here are not solved, we question that the shapelet method can provide weak-lensing measurements for all observable galaxies (independent of their Sérsic index) with an accuracy demanded by upcoming missions and surveys. An accurate and reliable calibration, specific for the dataset under investigation, would be required but is difficult to infer consistently from the data.