  Intrinsic galaxy alignments constitute the major astrophysical systematic of
forthcoming weak gravitational lensing surveys but also yield unique insights
into galaxy formation and evolution. We build analytic models for the
distribution of galaxy shapes based on halo properties extracted from the
Millennium Simulation, differentiating between early- and late-type galaxies as
well as central galaxies and satellites. The resulting ellipticity correlations
are investigated for their physical properties and compared to a suite of
current observations. The best-faring model is then used to predict the
intrinsic alignment contamination of planned weak lensing surveys. We find that
late-type galaxy models generally have weak intrinsic ellipticity correlations,
marginally increasing towards smaller galaxy separation and higher redshift.
The signal for early-type models at fixed halo mass strongly increases by three
orders of magnitude over two decades in galaxy separation, and by one order of
magnitude from z=0 to z=2. The intrinsic alignment strength also depends
strongly on halo mass, but not on galaxy luminosity at fixed mass, or galaxy
number density in the environment. We identify models that are in good
agreement with all observational data, except that all models over-predict
alignments of faint early-type galaxies. The best model yields an intrinsic
alignment contamination of a Euclid-like survey between 0.5-10% at z>0.6 and on
angular scales larger than a few arcminutes. Cutting 20% of red foreground
galaxies using observer-frame colours can suppress this contamination by up to
a factor of two.
