Discriminating Weak Lensing from Intrinsic Spin Correlations Using the Curl‐Gradient Decomposition

Abstract

The distortion field defined by the ellipticities of galaxy shapes projected\non the sky can be uniquely decomposed into a gradient and a curl component. If\nthe observed ellipticities are induced by weak gravitational lensing, then the\ndistortion field is curl free. Here we show that, in contrast, the distortion\nfield resulting from intrinsic spin alignments is not curl free. This provides\na powerful discriminant between lensing and intrinsic contributions to observed\nellipticity correlations. We also show how these contributions can be\ndisentangled statistically from the ellipticity correlations or computed\nlocally from circular integrals of the ellipticity field. This allows for an\nunambiguous detection of intrinsic galaxy alignments in the data. When the\ndistortions are dominated by lensing, as occurs at high redshifts, the\ndecomposition provides a valuable tool for understanding properties of the\nnoise and systematic errors. These techniques can be applied equally well to\nthe polarization of the microwave background, where it can be used to separate\ncurl-free scalar perturbations from those produced by gravity waves or defects.\n