Density‐Ellipticity Correlations, Galaxy‐Galaxy Lensing, and the Importance of Non‐Gaussianity in Intrinsic Alignment

We compute both the extrinsic (lensing) and the intrinsic contributions to the density-ellipticity correlation function, the latter by using current analytic theories of tidal alignment. The gravitational lensing contribution has two components, one analogous to galaxy-galaxy lensing, and the other arising from magnification bias: gravitational lensing induces a modulation of the galaxy density, as well as the ellipticity. On the other hand, the intrinsic alignment contribution vanishes, even after we take source-clustering corrections into account, which suggests that the density-ellipticity correlation might be an interesting diagnostic with which to differentiate between intrinsic and extrinsic alignments. However, an important assumption commonly adopted by current analytic alignment theories is the Gaussianity of the tidal field. The inevitable non-Gaussian fluctuations from gravitational instability induce a nonzero intrinsic density-ellipticity correlation, which we estimate. We also argue that non-Gaussian contributions to the intrinsic ellipticity-ellipticity correlation are often nonnegligible. This leads to a linear scaling, rather than a quadratic scaling, as is commonly assumed, with the power spectrum on sufficiently large scales. Finally, we estimate the contribution of the intrinsic alignment to low-redshift galaxy-galaxy lensing measurements (e.g., the SDSS) due to the partial overlap between foreground and background galaxies, and we find that the intrinsic contamination is about 10%-30% at 10'. Uncertainties in this estimate are discussed.