  The topic of this paper is a generalisation of the linear model for intrinsic
alignments of galaxies to intrinsic flexions: In this model, third moments of
the brightness distribution reflect distortions of elliptical galaxies caused
by third derivatives of the gravitational potential, or, equivalently,
gradients of the tidal gravitational fields. With this extension of the linear
model mediating between the brightness distribution and the tidal gravitational
fields and with a quantification of the shape of the galaxy at third order
provided by the HOLICs-formalism, we are able to compute angular spectra of
intrinsic flexions and the cross-spectra with weak lensing flexions. Spectra
for intrinsic flexions are typically an order of magnitude smaller than lensing
flexions, exactly as in the case of intrinsic ellipticity in comparison to weak
shear. We find a negative cross correlation between intrinsic and extrinsic
gravitational flexions, too, complementing the analogous correlation between
intrinsic and extrinsic ellipticity. After discussing the physical details of
the alignment model to provide intrinsic flexions and their scaling properties,
we quantify the observability of the intrinsic and extrinsic flexions and
estimate with the Fisher-formalism how well the alignment parameter can be
determined from a Euclid-like weak lensing survey. Intrinsic flexions are very
difficult to measure and yield appreciable signals only with highly optimistic
parameter choices and noise levels, while being basically undetectable for more
realistisc flexion measurement errors.
