Since most of the mass of a spiral galaxy is in the form of old (Population II) stars, let us consider the stellar component first. As in the case of ellipticals, the stars form a collisionless system, so .that we expect the mass distribution to change extremely slowly. The evolution time turns out to be a thousand galaxy lifetimes, a fact which is hardly changed at all by the presence of gas. This can be seen by imagining a typical star like the Sun, tunnelling its way at a typical velocity of 200 km sec”1 through an interstellar gas with a typical density of one hydrogen atom per cubic centimetre. Such a star would at most intercept 500kg matter per second, or in other words, it would intercept a mass equal to its own after a billion galaxy lifetimes! Therefore, the way in which the stars are on the average distributed through a spiral galaxy must date from the galaxy’s birth, just as in the case of ellipticals.

The gas behaves in a very different fashion, because it is dominated by collisions. Since stars occupy only a minute fraction of the volume of a galaxy, the gas does not interact directly with them. The fate of interstellar gas on a large scale (kiloparsecs) is deter¬mined roughly by four processes: heating by starlight and cosmic rays, cooling by radiation, stirring and heating by blast waves from active stars (e.g. novae and supernovae) and gravitational interaction. The first three effects never quite balance, but roughly speaking they lead to the establishment of a galactic atmosphere with a mean density of a million atoms per cubic metre and temperatures between 100-5000K. This atmosphere is rather turbulent and tries to settle in the average gravitational field formed by the stars in the galaxy. The settling is governed by the inertia of the gas and its tendency towards equilibrium between the forces of gas pressure and gravity. Thus the gas seeks the points of lowest gravitational energy, thereby forming a very thin layer in the plane of the galaxy, that is, at right angles to the axis of the galaxy’s rotation. This is the origin of the disc of gas in spiral galaxies. The thickness of the gaseous disc is maintained at a few hundred parsecs by gas pressure and turbulence. The radial extent of the disc is determined by the balance between the inward pull of gravity and the centrifugal acceleration due to rotation. The rapid rotation of spiral galaxies causes the radius of the gaseous disc to be at least as large as that of the stellar disc, and often up to twice as large.

The typical disc structure of a rapidly rotating galaxy contain¬ing gas and stars has now been explained, but this is only the first part of the problem. The second part is to account for the origin and maintenance of SPIRAL STRUCTURE. The observations summarized in the previous section indicate that spiral arms survive for up to a hundred galactic years. This means that they cannot be permanent condensations, because these can only survive as a pattern if the whole galaxy rotates as a solid body. The rotational velocity of spiral galaxies never increases in direct proportion to the radius, except sometimes in their innermost parts, so that DIFFERENTIAL ROTATION rather than solid-body rotation prevails. Consequently any material structure in a galactic disc is wound up and entirely obliterated in only a few galactic years, and the spiral arms must therefore be a wave phenomenon: what we perceive as spiral patterns are not permanent ridges of matter, but instead comprise the locus of wave crests of a DENSITY WAVE. Therefore, the crucial problem is to show that the material in the plane of a spiral galaxy can oscillate in such a way that density waves are formed with a wave-crest pattern that looks like a trailing spiral and rotates as if it, were a solid body.

Waves occur as small perturbations of an equilibrium. In the case of waves on a pond, the ripples are the perturbations and the equilibrium state is the level surface of the water. The ripples move out from a disturbance, but the water in the pond oscillates in small ellipses, without outward motion. Spiral arms are density perturbations, and the equilibrium state is the simple rotating disc structure described above. The surface of a pond is in equilibrium between the pull of gravity and hydrostatic pressure. The disc of a galaxy is in equilibrium between the inward pull of gravity and the centrifugal effect of inertia. A water wave is formed when water particles oscillate around their equilibrium state in unison with neighbouring particles; similarly, a spiral density wave can only occur if there is a certain unison between the motions of the matter at neighbouring radii in the plane. The stars are expected to make up the bulk of the wave, because most of a galaxy’s matter is in the form of stars. Stellar orbits in a galaxy are rosette orbits , so it is not easy to visualize stars moving in some semblance of order; for greater clarity, let us pretend that the orbits are ellipses around the galaxy’s centre. When there is no unison between their oscillations, the orbits form a random collection, but when every orbit is related in a methodical manner to its neighbours, a pattern emerges.

In water waves, the ordering of neighbouring water particles is brought about by molecular forces. In spiral waves, the force of gravity between stars acts as the maestro for orchestrating the stellar motions. The resulting pattern is not fixed with respect to the stars but is rather a fleeting density enhancement, moving around the galaxy as a wave. As the shape of the spiral depends on the shape of the individual stellar orbits. Since we know that these orbits do not change appreciably during the galaxy’s lifetime, it is to be expected that the pattern in permanent as well.

This explanation would suffice to solve the problem of spiral structure, if it weren’t for the fact that waves are subject to decay. As we know from everyday experience, waves eventually die out; this is known as DAMPING. To the dismay of density wave theorists. it has been shown that these waves, if left to themselves, would decay within half a dozen galactic years. Consequently, the prob¬lem now to be considered is the way in which the waves are maintained ; this is a fascinating but as yet unsolved problem.

Because the gas is such a small fraction of a galaxy’s total mass its gravitational influence on a density wave is practically negli¬gible. Instead of acting itself, the gas is acted upon by the gravitational potential associated with the density wave. The response of the gas to the spiral potential well can be calculated with the methods of hydrodynamics. Here again, the fact that the gas is collision dominated has remarkable consequences. The wave moves with respect to the matter in the galaxy’s disc with a velocity of some 30 km sec-1 on the average (except certain special regions in the galaxy which are not considered here). For a star, which is a collisionless particle, this means that it feels a gravitational bump which merely deflects its orbit a little. A gas particle, however, is collision dominated, so that it follows not only the imposed gravitational field but also the pressure forces from the neighbouring gas. These forces propagate with the velocity of sound, about 10 km seer1 at most. Because the speed of the density wave is three times larger than the sound speed, the gas is forced to go faster than sound during part of its motion around the galaxy. The theory of hydro¬dynamics predicts that this must cause the formation of SHOCK WAVES near the spiral arms. Since these shocks are accompanied by a strong compression of the gas , and since inter¬stellar dust is swept along with the gas, the dust lanes seen in the spiral arms of many galaxies are thought to be the place where these cosmic sonic booms occur. Thus the presence of sharp dust lanes indirectly confirms the existence of a density wave.

Stars are formed from gas, and it is reasonable to expect that compression will make interstellar matter more liable to star formation. Hence theorists speculate that young, massive stars occur preferentially in spiral arms because they form more readily when the gas is compressed by a density wave. Too little is known about star formation to allow this guess to become a theory. More¬over, the occurrence of shock waves is a serious complication.

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