  Intrinsically aligned galaxy shapes are one of the most important systematics
in cosmic shear measurements. So far theoretical studies of intrinsic
alignments almost exclusively focus on their statistics at the two-point level.
Results from numerical simulations, however, suggest that third-order measures
might be even stronger affected. We therefore investigate the (angular)
bispectrum of intrinsic alignments. In our fully analytical study we describe
intrinsic galaxy ellipticities by a physical alignment model, which makes use
of tidal torque theory. We derive expressions for the various combinations of
intrinsic and gravitationally induced ellipticities, i.e. III-, GII- and
GGI-alignments, and compare our results to the shear bispectrum, the GGG-term.
The latter is computed using hyper-extended perturbation theory. Considering
equilateral and squeezed configurations we find that for a Euclid-like survey
intrinsic alignments (III-alignments) start to dominate on angular scales
smaller than 20 arcmin and 13 arcmin, respectively. This sensitivity to the
configuration-space geometry may allow to exploit the cosmological information
contained in both the intrinsic and gravitationally induced ellipticity field.
On smallest scales (l ~ 3000) III-alignments exceed the lensing signal by at
least one order of magnitude. The amplitude of the GGI-alignments is the
weakest. It stays below that of the shear field on all angular scales
irrespective of the wave-vector configuration.
