  The statistical properties of the ellipticities of galaxy images depend on
how galaxies form and evolve, and therefore constrain models of galaxy
morphology, which are key to the removal of the intrinsic alignment
contamination of cosmological weak lensing surveys, as well as to the
calibration of weak lensing shape measurements. We construct such models based
on the halo properties of the Millennium Simulation and confront them with a
sample of 90,000 galaxies from the COSMOS Survey, covering three decades in
luminosity and redshifts out to z=2. The ellipticity measurements are corrected
for effects of point spread function smearing, spurious image distortions, and
measurement noise. Dividing galaxies into early, late, and irregular types, we
find that early-type galaxies have up to a factor of two lower intrinsic
ellipticity dispersion than late-type galaxies. None of the samples shows
evidence for redshift evolution, while the ellipticity dispersion for late-type
galaxies scales strongly with absolute magnitude at the bright end. The
simulation-based models reproduce the main characteristics of the intrinsic
ellipticity distributions although which model fares best depends on the
selection criteria of the galaxy sample. We observe fewer close-to-circular
late-type galaxy images in COSMOS than expected for a sample of randomly
oriented circular thick disks and discuss possible explanations for this
deficit.
