We have outlined the contents and dynamics of elliptical galaxies, and we now interpret these observations by a sequence of theoretical models. We have to explain how a cloud of stars can be made and maintained so that:

(i) it has a density which is highest in the centre and which smoothly decreases outwards;

(ii) it looks like an oblate spheroid with radius about five kiloparsecs, and is never flatter than E7;

(iii) it is 1010 years old and contains some 1011 solar-type stars, but next to no gas or dust.

The average star-star distance in a galaxy with 1011 stars and a radius of five kiloparsecs is about 20 million stellar diameters. Any star moving with a speed of lOOkms-1 through such a sparsely-populated space has a probability of colliding with another star once in 1019 years, that is 108 stellar lifetimes. Imagine encounter¬ing only one neighbour in a hundred million human lifetimes! Accordingly, the cloud of stars that form a galaxy is said to be collisionless. Since the electric and magnetic fields carried by some stars are imperceptibly weak over distances of millions of stellar diameters, there is only one natural force to govern stellar motion, namely the force of gravity. The problem of describing an elliptical galaxy is thereby reduced to that of describing the behaviour of a large number of point-like masses, moving under gravity.

The laws of classical mechanics tell us that, on average, two stars must move past each other within about 100 stellar diameters before their gravitational interaction deflects them by more than 90° from their former paths. Such an interaction is strong enough to be considered as a collision, even if the stars do not actually touch. To a star in an elliptical galaxy, this kind of gravitational collision is expected to happen once in 1014 years, that is once in a thousand times the galaxy’s lifetime. Accordingly, ellipticals are collisionless with respect to gravitational interaction too. There¬fore the stars interact primarily with the average gravitational field of the galaxy, caused by the mean attraction of all distant stars. The attractions due to neighbours form but a small perturba¬tion on the motion in the average gravitational field. This estimate also shows that once the shape of an elliptical is established, it will change only on a timescale of 1014 years. We therefore conclude that the elliptical galaxies assumed their shape right at the time when they were formed, shortly after the beginning of the Universe.

Once an elliptical has settled to its final state, a very quiet period starts. Stars orbit in the galaxy, very few being able to escape: in order to attain the escape velocity, they must be accelerated by a close encounter, which for a given star has an average chance of occurrence of once in a thousand galaxy lifetimes. The absence of collisions also ensures that the galaxy does not collapse, because this can only happen when the stars suffer close encounters so frequently that many of them are knocked into orbits passing through the inner parts of the galaxy. The orbits traced out by the stars in their courses about an elliptical galaxy can be likened to a ball of string that is so loose that it never ties itself into a knot.

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