Intrinsic alignments in the cross-correlation of cosmic shear and cosmic microwave background weak lensing

We demonstrate that the intrinsic alignment of galaxies with large-scale tidal fields sources an extra contribution to the recently detected cross-correlation of galaxy shear and weak lensing of the microwave background. The extra term is the analogy of the 'GI' term in standard cosmic shear studies, and results in a reduction in the amplitude of the cross-correlation. We compute the intrinsic alignment contribution in linear and non-linear theory, and show that it can be at roughly the 15 per cent level for the Canada-France-Hawaii Telescope Stripe 82 redshift distribution, if the canonical amplitude of intrinsic alignments is assumed. The new term can therefore potentially reconcile the apparently low value of the measured cross-correlation with standard Lambda cold dark matter. We discuss various small-scale effects in the signal and the dependence on the source redshift distribution. We discuss the exciting possibility of self-calibrating intrinsic alignments with a joint analysis of cosmic shear and weak lensing of the microwave background.