  Accurate measurements of the cosmic shear signal require a separation of the
true weak gravitational lensing signal from intrinsic shape correlations of
galaxies. These `intrinsic alignments' of galaxies originate from galaxy
formation processes and are expected to be correlated with the gravitational
field through tidal processes affecting the galaxies, such as tidal shearing
for elliptical galaxies and tidal torquing for spiral galaxies. In this study,
we use morphologically selected samples of elliptical and spiral galaxies from
the IllustrisTNG simulation at z=0 and z=1 to test the commonly employed linear
(tidal shearing) and quadratic (tidal torquing) models for intrinsic
alignments. We obtain local measurements of the linear and quadratic alignment
parameters, including corrections for large-scale anisotropies of the
cosmologically small simulation volume, and study their dependence on galaxy
and environmental properties. We find a significant alignment signal for
elliptical galaxies (linear model), that increases with mass and redshift.
Spiral galaxies (quadratic model) on the other hand exhibit a significant
signal only for the most massive objects at z=1. We show the quadratic model
for spiral galaxies to break down at its fundamental assumptions, and
simultaneously obtain a significant signal of spiral galaxies to align
according to the linear model. We use the derived alignment parameters to
compute intrinsic alignment spectra and estimate the expected contamination in
the weak lensing signal obtained by Euclid.
