Anisotropies of galaxy ellipticity correlations in real and redshift space: angular dependence in linear tidal alignment model

Investigating intrinsic alignments (IAs) of galaxy shapes is important not only to constrain cosmological parameters unbiasedly from gravitational lensing but also to extract cosmological information complimentary to galaxy clustering analysis. We derive simple and useful formulas for the various IA statistics, including the intrinsic ellipticity–ellipticity correlation, the gravitational shear–intrinsic ellipticity correlation, and the velocity–intrinsic ellipticity correlation functions. The angular dependence of each statistic is explicitly given, namely the angle between the line-of-sight direction and the separation vector of two points. It thus allows us to analyse anisotropies of baryon acoustic oscillations encoded in the IA statistics, and we can extract the maximum cosmological information using the Alcock–Paczynski and redshift-space distortion effects. We also provide these formulas for the intrinsic ellipticities decomposed into E and B modes.