Yet another factor which can influence the development of tidal tails
is the orientation of the disk plane to the orbital plane. Toomre &
Toomre (1972) showed that tails were best formed during prograde
collisions, but that highly inclined encounters were still effective
at creating tails. However, Toomre & Toomre considered point-mass
galaxies, which allowed for a good match between 
and
. In galaxies with extended mass distributions, like
those considered here, the higher relative velocities at impact appear
to inhibit tail formation in prograde encounters. In principle, the
situation could be somewhat better for inclined encounters, as the
orbital angular velocity of the perturber projected onto the disk
plane is reduced in such encounters.
One should note, however, that although the encounter may be more resonant,
the duration of the encounter is about the same for different disk
orientations and this may be the controlling factor.
To test this case using a specific example, we attempted to reproduce
the well-studied and often-modeled galaxy merger ``The Antennae" (NGC
4038/39) using our four different galaxy models. Barnes (1988) previously
modeled this system with fully self
consistent galaxies with halo:disk+bulge mass ratios of 4:1, and
was able to reproduce much of the tidal tail morphology of the galaxies.
Our new simulations extend his efforts to include galaxies having
much more massive halos. For each of the different galaxy models,
we set up a merger using Toomre & Toomre's (1972) disk orientations
for the encounter. The galaxies are each inclined to the orbital plane
by i=60
, with arguments of pericenter 
. The
galaxies are again placed on zero energy orbits, with impact parameters
. On these orbits, 
4 for the collisions, somewhat
smaller than Barnes' (1988) choice of 
. However, the differences
between our Model A merger and Barnes' model for the Antennae
proved relatively minor.
Figure 11 shows the four models projected onto the orbital plane
around the times when the galaxies exhibit the longest tidal tails.
Models A and B closely resemble Barnes' (1988) two simulations
with 4:1 and 8:1 halo:disk+bulge mass ratios . Models C and D again
show the difficulty in producing tidal tails in the high speed encounters
resulting from the massive halos of these galaxy models. As before,
the tails extend only to 
10 scale lengths before quickly
falling back into the galaxies well before the they actually merge.
Tails produced in the subsequent merging are even shorter and less
massive than those shown here (c.f. Figure 6).
Figure 11: Models of NGC 4038/9, the Antennae, as viewed in the orbital
plane. Time is measured relative to the point of impact in simulation
units. The width of each snapshot is 30 
or 120 kpc scaled to the
Milky Way.
The failure of Models C and D to reproduce the Antennae is further
emphasized by viewing the simulation from other directions. For
each simulation, lines of sight were chosen such that in projection
the galaxies looked most like the observed morphology of the Antennae.
Figure 12 shows the view in the orbital plane down lines of sight
80
, 70
, 60
, and 50
from the line of pericenter for
Models A, B, C, and D, respectively. Models A and B exhibit the long,
thin, curving tidal tails for which the Antennae is famous, but
as the halo mass is increased, as in Models C and D, the tails are
more like low mass, stubby ``plumes" than the tidal tails of the
Antennae.
Concerned again about the consequences of greater disk
heating in the massive halo models, we reran the Model D Antennae
using five times as many halo particles to reduce this disk heating.
Although the ``tails" are somewhat thinner and more well-defined
(Figure 12),
they are still extend to short distances when compared to both the
low mass halo models and the Antennae itself. This model demonstrates
again that these numerical affects do not significantly alter our major
conclusions.
Figure 12: Models of NGC 4038/9, the Antennae, viewed along directions to
resemble the observed galaxy. Lines of sight are in the orbital plane and
lie 80
, 70
, 60
, and 50
from the x-axis (or
line of periapse for the chosen orbit) for each of the Models A, B, C and D
respectively. The width of the snapshot is 24 
or 96 kpc scaled to the
Milky Way.