  Weak gravitational lensing has become a powerful probe of large-scale
structure and cosmological parameters. Precision weak lensing measurements
require an understanding of the intrinsic alignment of galaxy ellipticities,
which can in turn inform models of galaxy formation. It is hypothesized that
elliptical galaxies align with the background tidal field and that this
alignment mechanism dominates the correlation between ellipticities on
cosmological scales (in the absence of lensing). We use recent large-scale
structure measurements from the Sloan Digital Sky Survey to test this picture
with several statistics: (1) the correlation between ellipticity and galaxy
overdensity, w_{g+}; (2) the intrinsic alignment auto-correlation functions;
(3) the correlation functions of curl-free, E, and divergence-free, B, modes
(the latter of which is zero in the linear tidal alignment theory); (4) the
alignment correlation function, w_g(r_p,theta), a recently developed statistic
that generalizes the galaxy correlation function to account for the angle
between the galaxy separation vector and the principle axis of ellipticity. We
show that recent measurements are largely consistent with the tidal alignment
model and discuss dependence on galaxy luminosity. In addition, we show that at
linear order the tidal alignment model predicts that the angular dependence of
w_g(r_p,theta) is simply w_{g+}*cos(2*theta) and that this dependence is
consistent with recent measurements. We also study how stochastic nonlinear
contributions to galaxy ellipticity impact these statistics. We find that a
significant fraction of the observed LRG ellipticity can be explained by
alignment with the tidal field on scales >~10 h^-1 Mpc. These considerations
are relevant to galaxy formation and evolution.
