Some notes from one of the many films produced by Aarseth on the 380/196 using the FR80.
These films are based on a computer model of the expanding universe. We consider a spherical region of space containing 4000 galaxies initially at random. The starting velocities are directed radially outwards from the common centre at a prescribed rate. This corresponds to a stage when the universe had an age of about one billion years (109 yrs) which is generally believed to be the epoch of galaxy formation. The future evolution of this system is studied, by the N-body method where the mutual interactions of all the galaxies are included according to Newton's law of gravity and the motion of each member is integrate accurately. If no initial fluctuations were present, the galaxies would expand radially preserving a homogeneous system with the velocities being slowed down by the net inward attraction. However, the fluctuations which are present in any random distribution tend to grow with time. Regions, with a slight density excess are slowed down slightly with respect to the mean expansion, whereas low-density regions expand faster, thereby thinning out. The density contrast grows with time and at the end of the calculations quite large groups are formed.
The main aim of this work is to demonstrate that clusters of galaxies can form in both open and closed cosmological models. A closed model corresponds to the case when all the galaxies have sufficient initial velocities to just reach infinity if no clustering takes place, whereas in an open model the galaxies are expanding faster than this critical value. Hence given the present observed expansion rate we can deduce whether the universe is open or whether it will stop expanding and begin to contract. Unfortunately the actual mass density of the universe, is rather uncertain since there may be significant amounts of matter in non-luminous form; hence the need to study both models (although most astronomers' think the evidence favours an open universe).
The calculations are quite time-consuming. Typically it takes about 4 hours on the IBM 360/195 to complete one evolutionary model with 4000 interacting model galaxies. Analysis of the results suggest that the neglect of the more distant galaxies does not produce a significant effect; i.e. smaller systems show much the same behaviour.
The first two short sequences of the film show a projected view of the expanding spherical systems. In the first model the growth of clustering is considerably more pronounced than in the second model which represents an open universe. If the two final models are to represent the present epoch, it is necessary that the open model should reach a larger linear size. Typically the closed universe models increase by a linear factor of 10, whereas the open models expand by a factor of 20 or 30; this takes us from age 109 years to the present (about 15 x 109 yrs).
The three next sequences show models plotted in co-moving coordinates. In this representation the coordinates are scaled with respect to the outer system radius, thus showing as stationary points any galaxy which expands at a rate proportional to its central distance (i.e. obeying the so-called Hubble's law of universal expansion). Deviations from pure expansion can now be seen directly and the growth of clustering is easier to follow. Note that even some of the clusters merge together in larger units. Although this is a two-dimensional picture, it is clear that there are regions with a single galaxy far from any other; these are the so-called field galaxies. When analysed carefully in terms of the pair distributions the final pictures show a similar structure to. the corresponding distribution of the actual galaxies. As for the initial chain-like distribution in the last co-moving-model, this is a mathematical device used to represent a distribution which has less fluctuations on sma!1 scales than a random distribution and greater fluctuations on large scales. Analysis of the latter distribution does in fact show that the final clusters contain more members than in the corresponding case of a random distribution and is probably more like the real sky, if the universe is open.
In the last sequence the viewer rotates around the expanding system where the initial conditions are first shown enlarged. This enables one to discern a three-dimensional effect, Now it is very clear that the clusters previously seen in projection are really separate sub-systems. These groups are relatively stable except for the accretion of members and the internal dynamical effects, and can therefore be associated with observed clusters which are believed to be stable. The plotting points are shown with different intensities, representing their distances from the viewer who is moving slowly away from the system during the latter part in order to retain more of the system within the field of view. The very last part of this sequence shows the final distribution when the calculations stopped; this gives the viewer time to look at the system in more detail and ask whether the picture does in fact resemble the real universe.
