  The intrinsic alignments of galaxies are recognised as a contaminant to weak
gravitational lensing measurements. In this work, we study the alignment of
galaxy shapes and spins at low redshift ($z\sim 0.5$) in Horizon-AGN, an
adaptive-mesh-refinement hydrodynamical cosmological simulation box of 100
Mpc/h a side with AGN feedback implementation. We find that spheroidal galaxies
in the simulation show a tendency to be aligned radially towards over-densities
in the dark matter density field and other spheroidals. This trend is in
agreement with observations, but the amplitude of the signal depends strongly
on how shapes are measured and how galaxies are selected in the simulation.
Disc galaxies show a tendency to be oriented tangentially around spheroidals in
three-dimensions. While this signal seems suppressed in projection, this does
not guarantee that disc alignments can be safely ignored in future weak lensing
surveys. The shape alignments of luminous galaxies in Horizon-AGN are in
agreement with observations and other simulation works, but we find less
alignment for lower luminosity populations. We also characterize the
systematics of galaxy shapes in the simulation and show that they can be safely
neglected when measuring the correlation of the density field and galaxy
ellipticities.
