Barnes, 1988
In Encounters between Disk/Halo Galaxies, Barnes used prototype
bulge/disk/halo model galaxies. These models consisted of a central
bulge, a thin rotating disk and an optional spherical extended
halo. The exact details of the simulated encounter which would
produce the observed features of NGC 4038/9 followed those of Toomre
and Toomre; the initial conditions corresponded closely to those used
in Galactic Bridges and Tails, although some modifications were
necessary to account for the presence of the massive dark halo.
The main characteristics of the model galaxies were as follows:
|
Mass Ratio of Components | 1:3:16 |
|
Total Mass of Components |  |
|
Inverse Scale Length of Exponential Disk |  |
Circular orbital period at radius  |  |
All these quantities were measured in arbitray units with
G=1. Scaling to our galaxy, these numbers correspond to a
length of 40 kpc, a time of 250Myrs and a mass of
.
The galaxies were started on elliptical orbits with an eccentricty of
e=0.5; their pericentric separation was 
and the time to
pericentre was 
. Both galaxies were inclined at 
to
the orbital plane with a pericentric arguement of 
.
These particular initial conditions will lead to a slow symmetric
prograde encounter with the two disks inclined so as to sling tidal
tails high above the orbital place where they will eventually be seen
in projection crossing each other. The configuration used is shown
in figure 4.
Figure: Figure 1 of Encounters of Disk/Halo Galaxies.
Figure: Figure 2 of Encounters of Disk/Halo Galaxies.
Whereas Toomre and Toomre's test particle model galaxies followed
quasi-Keplerian trajectories, the orbits of Barnes' self consistent
model galaxies quickly decayed. The tidal coupling of orbital to
internal motion was so effective that the relative orbit decayed in less
than one initial orbital period. This was due to the presence of the
massive dark halo which effectively soaked up the energy and angular
momentum. Barnes noted that at the time when TT's model most closely
matched observations, his models had already merged. However, his
models do produce a configuration that resembled observations but at a
much earlier time - t=1.8 in his arbitrary time units, corresponding
to roughly one quarter of the initial orbital period after
pericentre.
Further analysis of the encounter revealed several interesting
features:
-
the interaction slewed the inner galactic disks by
counterclockwise, almost edge on to our line of sight, indicating the
presence of powerful torques on the disks during the encounter.
-
distinct peaks in the dark matter distribution were observed to
coincide with the luminous nuclei, ``like a dark, distended body
surrounding a luminous spine''.
-
the visible tails were confined to within the halo; this is a
consequence of dark matter, which initially shared phase space with
the luminous matter, tagging along to the present stage.
-
the more curving left hand tail of the model matches closely the
appearance of the south western tail as revealed in both deep optical images
(Schweizer, 1978) and high resolution HI mapping (Mahony, Van der
Hulst and Burke, 1987). Barnes was keen to stress that the asymmetry
between the two tails was not due to any macroscopic asymmetry in the
initial conditions but was instead due to
fluctuations in
the galaxies which are swing amplified by the disk and sheared out by
tidal forces during the encounter, thus further populating one of the
resulting tidal arms.
Reviewing this particular simulation, Barnes considered both the positive
and negative aspects of the result; the model encounter successfully reproduced:
-
the narrowness of the tidal tails. This demonstrated the requirement
for relatively cold disks at encounter. Previous attempts to self
consistently model encounters of this kind, such as those of Negroponte (1987),
produced stubby tails, clearly at odds with observation.
-
the proximity of the hulks. This is a distinct improvement on TT's
model; although TT foresaw the importance of orbital decay due to
tidal friction, they certainly could not have anticipated the
magnitude of the decay. By following the bulges (which trace the
dynamical centres of the galaxies) Barnes was able to observe that
these bulges barely separated after pericentre, plunging back together
after one third of an orbiral revolution.
However, the model result was not without its shortcomings:
-
The model galaxies, as shown in figure 5, are approaching one another
along the line of sight with velocities comparable to the circular
velocity of each disk. However, studies in HII (Rubin, Ford and
D'Odorico, 1970) and HI (Mahony et al) indicate only a small
line of sight difference -
. Thus the model fails to
match the observed kinematics of the main hulks.
-
Conceptually there are problems associated with the very existence of
this e=0.5 orbit. Due consideration would seem to suggest that the
galaxies experienced a close parabolic encounter - but such encounters
do not result in configurations such as the one observed in the Antennae.
In conclusion, Barnes noted that the model of NGC 4038/9 came
subjectively close to matching the appearance of the Antennae;
based on this observation, it was felt, with some confidence, that the
basic elements of the encounter were correct. He did caution, however,
that the quality of the match was somewhat enhanced by the presence of
chance fluctuations which could grow to macroscopic proportions
at the right time and place to produce assymetric tails - and so it
would be neither possible to infer precise properties of the
progenitors nor to establish the uniqueness of a solution.
Chris Power
