  We use a 380 h-1 pc resolution hydrodynamic AMR simulation of a cosmic
filament to investigate the orientations of a sample of ~100 well-resolved
galactic disks spanning two orders of magnitude in both stellar and halo mass.
We find: (i) At z=0, there is an almost perfect alignment at a median angle of
18 deg, in the inner dark matter halo regions where the disks reside, between
the spin vector of the gaseous and stellar galactic disks and that of their
inner host haloes. The alignment between galaxy spin and spin of the entire
host halo is however significantly weaker, ranging from a median of ~46 deg at
z=1 to ~50 deg at z=0. (ii) The most massive galaxy disks have spins
preferentially aligned so as to point along their host filaments. (iii) The
spin of disks in lower-mass haloes shows, at redshifts above z~0.5 and in
regions of low environmental density, a clear signature of alignment with the
intermediate principal axis of the large-scale tidal field. This behavior is
consistent with predictions of linear tidal torque theory. This alignment
decreases with increasing environmental density, and vanishes in the highest
density regions. Non-linear effects in the high density environments are
plausibly responsible for establishing this density-alignment correlation. We
expect that our numerical results provide important insights for both
understanding intrinsic alignment in weak lensing from the astrophysical
perspective and formation and evolution processes of galactic disks in a
cosmological context.
