The effect of imperfect models of point spread function anisotropy on cosmic shear measurements

Current measurements of the weak lensing signal induced by large-scale structure provide useful constraints on a range of cosmological parameters. However, the ultimate success of this technique depends on the accuracy with which one corrects for the effect of the point spread function (PSF), in particular the correction for the PSF anisotropy. With upcoming large weak lensing surveys, a proper understanding of residual systematics is necessary. In this paper, we examine the importance of the adopted model for the spacial variation of the PSF anisotropy using images of fields with a large number of stars. A wrong parametrization of the PSF anisotropy leads to a residual signal in the data, affecting the cosmic shear measurements. We use data taken with the Canada-France-Hawaii 12k (CFH12k) camera, and note that some of the results might not be valid for other instruments. We select a random subset of stars which are used to characterize the PSF and to correct the shapes of the remaining stars. The ellipticity correlation function of the residuals is studied to quantify the effect of residual PSF anisotropy on cosmic shear studies. In order to single out the effect of the parametrization, we assume a perfect method for the actual correction of galaxy shapes. The PSF anisotropy is typically modelled for each individual chip of a mosaic; consequently, the residuals are coherent on small scales. As a result, the systematic signal decreases rapidly with increasing angular scale. Separation of the signal into 'E' (curl-free) and 'B' (curl) components can help to identify the presence of residual systematics, but in general, the amplitude of the 'B' mode is different from that of the 'E' mode. The study of fields with many stars can be beneficial in finding a proper description of the variation of PSF anisotropy, and consequently can help to improve the accuracy with which the cosmic shear signal can be measured significantly. We show that such an approach can lead to an appreciable reduction in systematics. The results suggest that the prospects for accurate measurements of the cosmic shear signal on scales larger than similar to10 arcmin are excellent.