  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.
