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The distortion field defined by the ellipticities of galaxy shapes projectedon the sky can be uniquely decomposed into a gradient and a curl component. Ifthe observed ellipticities are induced by weak gravitational lensing, then thedistortion field is curl free. Here we show that, in contrast, the distortionfield resulting from intrinsic spin alignments is not curl free. This providesa powerful discriminant between lensing and intrinsic contributions to observedellipticity correlations. We also show how these contributions can bedisentangled statistically from the ellipticity correlations or computedlocally from circular integrals of the ellipticity field. This allows for anunambiguous detection of intrinsic galaxy alignments in the data. When thedistortions are dominated by lensing, as occurs at high redshifts, thedecomposition provides a valuable tool for understanding properties of thenoise and systematic errors. These techniques can be applied equally well tothe polarization of the microwave background, where it can be used to separatecurl-free scalar perturbations from those produced by gravity waves or defects.

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