Intrinsic alignments (IA), correlations between the intrinsic shapes and orientations of galaxies on the sky, are both a significant systematic in weak lensing and a probe of the effect of large-scale structure on galactic structure and angular momentum. In the era of precision cosmology, it is thus especially important to model IA with high accuracy. Efforts to use cosmological perturbation theory to model the dependence of IA on the large-scale structure have thus far been relatively successful; however, extant models do not consistently account for time evolution. In particular, advection of galaxies due to peculiar velocities alters the impact of IA, because galaxy positions when observed are generally different from their positions at the epoch when IA is believed to be set. In this work, we evolve the galaxy IA from the time of galaxy formation to the time at which they are observed, including the effects of this advection, and show how this process naturally leads to a dependence of IA on the velocity shear. We calculate the galaxy-galaxy-IA bispectrum to tree level (in the linear matter density) in terms of the evolved IA coefficients. We then discuss the implications for weak lensing systematics as well as for studies of galaxy formation and evolution. We find that considering advection introduces nonlocality into the bispectrum, and that the degree of nonlocality represents the memory of a galaxy's path from the time of its formation to the time of observation. We discuss how this result can be used to constrain the redshift at which IA is determined and provide Fisher estimation for the relevant measurements using the example of SDSS-BOSS.
