Intrinsic alignment-lensing interference as a contaminant of cosmic shear

Cosmic shear surveys have great promise as tools for precision cosmology, but can be subject to systematic errors including intrinsic ellipticity correlations of the source galaxies. The intrinsic alignments are believed to be small for deep surveys, but this is based on intrinsic and lensing distortions being uncorrelated. Here we show that the gravitational lensing shear and intrinsic shear need not be independent: correlations between the tidal field and the intrinsic shear cause the intrinsic shear of nearby galaxies to be correlated with the gravitational shear acting on more distant galaxies. We estimate the magnitude of this effect for two simple intrinsic-alignment models: one in which the galaxy ellipticity is linearly related to the tidal field, and one in which it is quadratic in the tidal field as suggested by tidal torque theory. The first model predicts a gravitational-intrinsic ($GI$) correlation that can be much greater than the intrinsic-intrinsic ($II$) correlation for broad redshift distributions, and that remains when galaxies pairs at similar redshifts are rejected. The second model, in its simplest form, predicts no gravitational-intrinsic correlation. In the first model, and assuming a normalization consistent with recently claimed detections of intrinsic correlations, we find that the $GI$ correlation term can exceed the usual $II$ term by $>1$ order of magnitude and the intrinsic correlation induced $B$-mode by 2 orders of magnitude. These interference effects can suppress the lensing power spectrum for a single broad redshift bin by of order $\sim 10\%$ at $z_s=1$ and $\sim 30\%$ at $z_s=0.5$. We conclude that, depending on the intrinsic-alignment model, the $GI$ correlation may be the dominant contaminant of the lensing signal and can even affect cross spectra between widely separated bins. We describe two ways to constrain this effect, one based on density-shear correlations and one based on scaling of the cross correlation tomography signal with redshift.