Self-calibrating the gravitational shear-intrinsic ellipticity-intrinsic ellipticity cross-correlation

We extend the 3-point intrinsic alignment self-calibration technique to the gravitational shearintrinsic ellipticityintrinsic ellipticity (GII) bispectrum. While significantly decreased from using cross-correlations instead of autocorrelation in a single photo-z bin, the GII contamination persists in adjacent photo-z bins and must be accounted for and removed from the lensing signal. The proposed technique will allow the measurement and removal of the GII intrinsic alignment contamination from the cross-correlation weak lensing signal. We relate the GII and galaxy densityintrinsic ellipticityintrinsic ellipticity (gII) bispectra through use of the galaxy bias, and develop the estimator necessary to isolate the gII bispectrum from observations. We find that the GII self-calibration technique performs at a level comparable to that of the gravitational sheargravitational shearintrinsic ellipticity correlation (GGI) self-calibration technique, with measurement error introduced through the gII estimator generally negligible when compared to minimum survey error. The accuracy of the relationship between the GII and gII bispectra typically allows the GII self-calibration to reduce the GII contamination by a factor of 10 or more for all adjacent photo-z bin combinations at l > 300. For larger scales, we find that the GII contamination can be reduced by a factor of 35 or more. The GII self-calibration technique is complementary to the existing GGI self-calibration technique, which together will allow the total intrinsic alignment cross-correlation signal in 3-point weak lensing to be measured and removed.