  We develop an analytic model for galaxy intrinsic alignments (IA) based on
the theory of tidal alignment. We calculate all relevant nonlinear corrections
at one-loop order, including effects from nonlinear density evolution, galaxy
biasing, and source density weighting. Contributions from density weighting are
found to be particularly important and lead to bias dependence of the IA
amplitude, even on large scales. This effect may be responsible for much of the
luminosity dependence in IA observations. The increase in IA amplitude for more
highly biased galaxies reflects their locations in regions with large tidal
fields. We also consider the impact of smoothing the tidal field on halo
scales. We compare the performance of this consistent nonlinear model in
describing the observed alignment of luminous red galaxies with the linear
model as well as the frequently used "nonlinear alignment model," finding a
significant improvement on small and intermediate scales. We also show that the
cross-correlation between density and IA (the "GI" term) can be effectively
separated into source alignment and source clustering, and we accurately model
the observed alignment down to the one-halo regime using the tidal field from
the fully nonlinear halo-matter cross correlation. Inside the one-halo regime,
the average alignment of galaxies with density tracers no longer follows the
tidal alignment prediction, likely reflecting nonlinear processes that must be
considered when modeling IA on these scales. Finally, we discuss tidal
alignment in the context of cosmic shear measurements.
