So far, our calculations represent a controlled search through parameter space to examine how halo masses affect the properties of tidal tails in galaxy pairs, and we find generically that galaxies with massive halos produce short and low mass tails upon merging. As a final test of our results, we look at a more general case of a galaxy merger with unequal masses, inclined geometries, and a bound orbit. Using the structural and kinematic properties of the Milky Way and the Andromeda Galaxy, we present a possible merging scenario to explore whether the future merger of the Milky Way/Andromeda system will result in the spectacular tails seen in the Antennae, or merely a dull, amorphous merger.
To set up the merger, we must first adopt mass models for the Milky
Way and Andromeda. A variety of arguments suggest that the mass of
Andromeda, 
, is approximately twice that of the Milky Way, 
.
The flat portion of Andromeda's rotation curve has 
km s
\
(e.g., Braun 1991), and the B luminosity disk scale length is 
kpc (Walterbos & Kennicutt 1988). These values can
be compared to those for the Milky Way, 
km s
and 
kpc (Freeman 1987). Assuming that Andromeda is a scaled-up
version of the Milky Way, 
. The Tully-Fisher relation, 
with
, also predicts 
1.5 -- 2, (e.g., Raychaudury &
Lynden-Bell 1989).
Having fixed the mass ratio of the galaxies at 
, we now need
to set the
total mass of the galaxy pair. Various arguments suggest that
the total mass of the Milky Way and Andromeda is quite large. Perhaps
most convincingly, given the separation D= 700 kpc and radial
velocity 
km s
, the timing argument gives a total mass
for the system of 
M
for
a Universe age of 13 Gyr (i.e. 
km/s/Mpc, 
or
km/s/Mpc, 
).
This sets the mass of the Milky Way at 
M
,
similar to our Model D galaxy. For the Milky Way, we therefore adopt the
scaling parameters 
kpc and 
km s
for model D giving a
total mass, 
M
. For Andromeda, we adopt,
kpc and 
km s
giving a mass 
M
.
We also set up a low mass foil of this case using Model B as the base
model. With the same distance and velocity scalings the masses in this
case are 
M
and 
M
, values in accord with the lower bound
of the mass estimates of the Milky Way.
The final constraints on the merger are the orientations, separation,
and relative velocity of the galaxies. In Galactic coordinates, the spin
axis of Andromeda points in the direction 
(Raychaudury & Lynden-Bell 1989) while the Milky Way spin axis points
to the south galactic pole, 
by definition.
We adopt a separation D=700 kpc with Andromeda currently positioned at
and a radial velocity 
km s
.
Andromeda's transverse velocity 
is unknown; however, in
keeping with the spirit of this work, we choose 
such that the galaxies
can best build tidal tails. For Model D galaxies,
we use 
km s
, pointing towards
so the resulting orbit has 
kpc.
For Model B, we use 
km s
which also leads to 
kpc.
In these encounters, the disk of the Milky Way is inclined 23
to
the orbital plane, as closely aligned to prograde as the constrained
properties allow. The first part of the orbit is
uneventful so we advance the galaxies along a Keplerian orbit with the
given initial conditions until they are separated by 400 kpc and begin
the N-body simulation at this time. From this point, the time to impact
is only 
Gyr for both cases.
Figure 13
presents the time sequence of the interactions for the low and
high mass models from a view looking
down the North Galactic Pole. The orbital plane is inclined slightly with
respect to this line of sight. The smaller circular galaxy in the initial
frame of each sequence is the Milky
Way. Our expectations from the previous simulations of high mass models
are born out yet again.
In the low mass models, the encounter is very resonant and long tidal tails
are thrown off from both galaxies. Material is effectively ejected from
the Milky Way, and merging occurs shortly after the first pass.
In the high mass models,
the encounter velocity is too high on the first pass
to lead to a strong resonant response in either galaxy. Short tidal tails
(5 scale lengths) are thrown off both galaxies but quickly fall back in.
The secondary encounter which leads to the final merger also fails to
develop large tidal tails. Like the other experiments, the galaxies fall
together on a nearly radial orbit on the second encounter and merge together
without throwing off any significant tidal tails. It appears, therefore,
that if the large median
mass estimates of the Milky Way's halo from the timing argument
and satellite kinematics are correct, then the halo:disk+bulge mass ratio of our Galaxy must
be approximately 3 times that in galaxies with long tidal tails
such as the Antennae or Superantennae. On the other hand,
the merger of a low mass Galaxy with 
M
with a similar low mass Andromeda will resemble
the Antennae. A low mass Model B Galaxy is still consistent with the lower
bounds on the mass estimates from satellite kinematics.
Figure 13: Merger of the Milky Way and Andromeda galaxies using low and
high mass models for the system. All observed constraints are used to set
up the orbit though the unknown transverse velocity is chosen to give a
close, nearly prograde encounter to maximize the response in the disks.
The low mass model produces long tidal tails while the high mass model
fails in this regard, following the trend of the other simulations.