It we were to be really pedantic we could assert that a normal galaxy is an abstraction: all galaxies, when inspected sufficiently closely, deviate from the norm. Most of the peculiarities are minor, but there are quite a few puzzling ones. An important class of PECULIAR GALAXIES are those which were originally normal but have been disturbed by a collision with a neighbour . The probability of a GALAXY COLLISION can be estimated just as it was for stars. A representative 1011Mo galaxy with a diameter of 50 kpc moves typically with a random velocity of a few hundred kilometres per second. The mean distance between these galaxies is about 3000kpc, so that it follows that a galaxy can be expected to collide with a similar one once in 1013 years, that is once in a hundred galaxy lifetimes. On the average, therefore, the collision probability is quite low. But in regions where the galaxies have clumped together (such as clusters of galaxies), average distances can be as small as 500kpc, while random velocities of 1000kms-1 and above occur. The mean time between collisions accordingly reduces to 15 billion years, so that a galaxy has a better than even chance to collide with a neighbour once in its lifetime.

Not many of these encounters are expected to have spectacular consequences. Usually the galaxies stay far enough apart for their internal structure to remain undisturbed. Even so, close en¬counters are astronomically useful because they make it possible to measure the masses of the galaxies. By observing the relative velocities and distances, and by application of the laws of mechanics, it is found that the masses so determined agree rather well with those derived from rotation curves. The interacting-galaxy method is especially important for elliptical galaxies, whose rotation curves are virtually unobservable. These mass determinations show that the mass/luminosity ratio is about five for spiral galaxies and some ten times larger for ellipticals. The pair en¬counters indicate that spiral galaxies probably have no massive low-luminosity haloes. If they did, either the observed masses should be at least a factor 10 higher, or we must assume that the haloes of the interacting pair interpenetrate. In the latter case, the inner motions of the galaxies should be much more disturbed than is actually observed.

The derivation of masses from encounters illustrates how an interaction can serve to probe the colliding objects. In a few cases, the observed collision leads to spectacular disturbances which enable astronomers to probe even deeper into the internal constitution of the galaxies. A method which has been used with consider¬able success in recent years is a form of model building: with the aid of computers, a number of collisions is simulated until the end result looks like an interaction which is actually observed. Be¬cause the interaction picture is only a snapshot, the model building is necessarily ambiguous for lack of data; even so, relatively simple models have yielded striking results. In this approximation, two massive point-like bodies are sent on a close-encounter course. Each of these has an attendant cloud of test particles which initially move on bound circular orbits. These particles are allowed to move in the gravitational field of the two massive bodies; the mutual attractions between the test particles are neglected. During an encounter, every particle has its orbit distorted , and together the particle clouds often form the BRIDGES and TAILS characteristic of many observed galaxy collisions In some cases, it is suspected that the tidal distortions induced by the encounter strongly influence the formation of spiral structure but here further studies are necessary in which the test particles are allowed to interact with each other.

The tidal forces that occur during a collision have the largest influence on the most weakly-bound particles, that is the ones in the outskirts of a galaxy. Usually these particles are torn away-, and the majority is captured by the more massive of the two galaxies. Thus small galaxies orbiting near larger ones are stripped of their outer layers. Such TIDAL LIMITING is observable by measurement of the way in which the surface brightness of a galaxy decreases outwards; for example the, outer brightness profile of M31 is due to interaction with the Andromeda Nebula, M 31.

The most spectacular results of all are to be expected in the rare ease where two galaxies collide head-on. Then all stars, including the innermost ones, experience such a rapidly changing gravitational field that a situation arises that is comparable to the collapse stage of galaxy formation. Unless the colliding galaxies go so fast that their interaction time is too short, the encounter leads to an actual merging of the galaxies. This is expected to occur most effectively when the collision velocity is of the order of the random velocity of the stars, say a few hundred kilometers per second. For in that case, stars from one galaxy find it relatively easy to follow the gravitational field of the other: they are, as it were, at a loss to determine to which galaxy they belong! The violent relaxation due to the changing gravitational field smoothes the stellar distribution, so that the merged product comes to look like a single galaxy.

The fate of the interstellar gas during a galaxy collision is almost entirely unknown. The approximations which hold for the stars are not applicable to the gas, which is collision dominated. For ex¬ample, an orbital cross-over could never happen in gas flow. Thus, full hydrodynamic computations are necessary, which present such formidable obstacles that this aspect of the encounters between galaxies is only just ginning to be studied.

Two-galaxy collisions are rare, and encounters between three galaxies are correspondingly rarer. But SMALL GROUPS OF GALAXIES are observed, in which the distances between the members arc only a few tens of galaxy diameters . Our Local Group is one of these. The relatively large number of such groups can only be explained if the galaxies in them are held together by their mutual gravitational attraction. It could be argued that the group’s arise when galaxies happen to stand close together in the sky but have a large separation along the line of sight. Calculations show, how¬ever, that such projection effects do occur, but too infrequently to explain all groups.

Small groups of galaxies are rather loose structures. Their members are typically half a megaparsec apart, moving with a few hundred kilometers per second relative to the centre of mass of the group. Under these circumstances, collisions are rare: one collision per galaxy per hundred billion years.

The small groups are interesting because the motion can be studied exactly with computers. It is found that the small groups usually contain up to twice as much mass as can be accounted for by adding the masses of the individual galaxies, assuming normal mass-to-light ratios. To explain this finding, we must assume either that the groups are not bound together, which conflicts with the fact that there are so many of them ; or that the galaxies have massive haloes, which conflicts with other mass determinations; or that the extra matter is in between galaxies, which is problematic because it must be in such a form that it could hitherto have escaped direct detection.

The HIDDEN or MISSING MASS PROBLEM has not been solved yet, but the study of the dynamics of small groups has yielded some interesting results about their appearance. It had been known for a long time that there exist chains of galaxies . At first sight, these alignments seemed rather enigmatic. But numerical calculations showed that a gravitationally bound group of five galaxies assumes an apparent chain configuration about five per cent of the time. Consequently, unless it can be shown that they are held together by other forces, the existence of chains indirectly proves that small groups of galaxies must be gravitationally bound : for the chances that a random encounter would yield such a configuration are entirely negligible.

We have now concluded our rather lengthy review of the properties of normal galaxies. We have devoted a relatively large amount of space to these topics because we believe that the main thrust of astrophysical research between now and the end of the century will be among the realms of the wheeling galaxies.

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