Joint constraints from cosmic shear, galaxy-galaxy lensing and galaxy clustering: internal tension as an indicator of intrinsic alignment modelling error

In cosmological analyses it is common to combine different types of measurement from the same survey. In this paper we use simulated DES Y3 and LSST Y1 data to explore differences in sensitivity to intrinsic alignments (IA) between cosmic shear and galaxy-galaxy lensing. We generate mock shear, galaxy-galaxy lensing and galaxy clustering data, contaminated with a range of IA scenarios. Using a simple 2-parameter IA model (NLA) in a DES Y3 like analysis, we show that the galaxy-galaxy lensing + galaxy clustering combination ($2\times2$pt) is significantly more robust to IA mismodelling than cosmic shear. IA scenarios that produce up to $5\sigma$ biases for shear are seen to be unbiased at the level of $\sim1\sigma$ for $2\times2$pt. We demonstrate that this robustness can be largely attributed to the redshift separation in galaxy-galaxy lensing, which provides a cleaner separation of lensing and IA contributions. We identify secondary factors which may also contribute, including the possibility of cancellation of higher-order IA terms in $2\times2$pt and differences in sensitivity to physical scales. Unfortunately this does not typically correspond to equally effective self-calibration in a $3\times2$pt analysis of the same data, which can show significant biases driven by the cosmic shear part of the data vector. If we increase the precision of our mock analyses to a level roughly equivalent to LSST Y1, we find a similar pattern, with considerably more bias in a cosmic shear analysis than a $2\times2$pt one, and significant bias in a joint analysis of the two. Our findings suggest that IA model error can manifest itself as internal tension between $\xi_\pm$ and $\gamma_t + w$ data vectors. We thus propose that such tension (or the lack thereof) can be employed as a test of model sufficiency or insufficiency when choosing a fiducial IA model, alongside other data-driven methods.