In the previous chapter we gave an outline of the measurements astronomers can make to find out the properties of stars. Most off the mass of a galaxy is in stars of one type or other This chapter shows how mathematicians, physicists and theoretical astronomers have used the observations in order to deduce how stars work. One of the greatest achievements of astronomy m the first half of the twentieth century was the elucidation of the mechanisms that keep the Sun and other stars shining. We start our description of the workings of a star with an illuminating extract from the writings of the very distinguished Cambridge astrophysicist, Sir Arthur Stanley Eddington. He may fairly be said to have established the theory of stellar interiors. This extract from ‘The Internal Constitution of the Stars’ published in 1926 predates modern nuclear physics, and yet it shows a remarkable grasp of the basic behavior of atomic particles inside a star and the possible source of sub¬atomic energy.

‘The inside of a star is a hurly-burly of atoms, electrons and aether waves (photons). We have to call to aid the most recent discoveries of atomic physics to follow the intricacies of the dance. We started to explore the inside of a star; we soon find ourselves exploring the inside of an atom. Try to picture the tumult! Dishevelled atoms tear along at 50 miles a second with only a few tatters left of their elaborate cloaks of electrons torn from them in the scrimmage. The lost electrons are speeding a hundred times faster to find new resting-places. Look out! There is nearly a collision as an electron approaches an atomic nucleus; but putting on speed it sweeps round it in a sharp curve. A thousand narrow shaves happen to the electron in 10-10 of a second; sometimes there is a sideslip at the curve, but the electron still goes on with increased or decreased energy. Then comes a worse slip than usual; the electron is fairly caught and attached to the atom, and its career of freedom is at an end. But only for an instant. Barely has the atom arranged the new scalp on its girdle when a quantum of aether waves (a photon) runs into it. With a great explosion the electron is off again for further adventures. Elsewhere two of the atoms are meeting full tilt and rebounding, with further disaster to their scanty remains of vesture.

‘As we watch the scene we ask ourselves, can this be the stately drama of stellar evolution ? It is more like the jolly crockery-smashing turn of a music hall. The knockabout comedy of atomic physics is not very considerate towards our aesthetic ideals; but it is all a question of time-scale. The motions of the electrons are as harmonious as those of the stars but in a different scale of space and time, and the music of the spheres is being played on a keyboard 50 octaves higher. To recover this elegance we must slow down the action, or alternatively accelerate our own wits; just as the slow motion film resolves the lusty blows of the prize –fighter into movements of extreme grace and insipidity .And what is the result of all this bustle ? Very little .Unless we have in mind and extremely long stretch atoms are repaired as are smashed: just as many bundles of radiation are sent out as are absorbed; just as many electrons are captured as are exploded away. The atoms and the electrons for all their hurry never get anywhere; they only change places. The aether waves (photons) are the only part of the population which do actually accomplish something; although apparently darting about in all directions without purpose they do in spite of themselves make a slow general progress outwards. This flow would if uncompensated lead to a gradual change in the whole state of the star, very slow, but yet, we believe, too fast to accord with observational evidence. It is therefore necessary to assume that sub-atomic energy of some kind is liberated within the star, so as to replenish the store of radiant energy. This also involves a gradual transformation of the material of the star which, however, scarcely concerns the present discussion. The point which we wish here to explain is why this clash of atoms, electrons and aether waves is of practical con¬cern to the astronomer, seeing that for each portion of radiation absorbed an equal quantity of radiation is being emitted ?’

‘We may think of the star as two bodies superimposed, a material body (atoms and electrons) and an aetherial body (radiation). The material body is in dynamical equilibrium, but the aetherial body is not; gravitation takes care that there is no outward flow of matter, but there is an outward flow of radiation. If there were no interaction between the two bodies, the whole store of radiation would diffuse away in a few minutes; it is because it is tied to the material body by the processes of absorption and emission that it is restrained to a slow rate of diffusion. Absorption followed by emission, although it leaves the quantity of radiation unaltered, has this effect: radiation with a slight outward bias is taken from the aetherial body; it is quickly restored again with the outward bias removed. The quicker the succession of these transformations the more strictly the outward flow is curbed. That is in accordance with the conclusion we had already reached that the factor which resists the outward flow of radiation is the absorption coefficient or opacity of the material of the star.

In our reading of the writings of Eddington we must recall the stage of development of physics at that time. The Bohr theory of atomic structure, the old quantum theory, the theories of special relativity and general relativity and the theory of black-body radia¬tion had all been recently developed. Eddington was able to bring together these new fields of physics for the first time in order to pro¬vide science with a unified picture of the structure of a star. With great insight he realized the importance of a sub-atomic source of energy about which little was then known. He rebuffed his critics, who suggested that stars were not hot enough for this sub-atomic process, with the retort ‘go and find a hotter place’! Amazing as it may seem, Eddington was able to construct a detailed theory of how a star works, without knowledge of the exact nature of any nuclear energy processes. It remained for Hans Bethe and Carl von Weizsacker to propose, in 1939, two possible nuclear fusion factions to explain stellar energy production.

There has always been much interplay between physics and the theory of stellar structure. After the development in the nineteenth century of the theory of thermodynamics, which explains certain aspects of the behaviour of matter and heat energy, the work of J.H.Lane, A.Ritter, Lord Kelvin and R.Emden followed. These pioneers of stellar theory treated a star as a mass of gas that is held together by its own gravity. They investigated the mechanical properties, due to the balance of gravity and internal pressure forces, while also incorporating as much of the thermodynamic theory as possible. The thermal, or heat balance and heat flow aspects of stellar structure were developed by Karl Schwarzschild and Eddington himself, following in the wake of the momentous quantum theory. Eddington’s ‘The Internal Constitution of the Stars’ in 1926 was a milestone in the development of astrophysics. It was later followed in 1939 by S.Chandrasekhar’s detailed mathematical theory of the inside of stars, and the filling in of the nuclear physics details, also in 1939, by Bethe and von Weizsacker.

More recent work on stellar structure theory has concentrated on the detailed physical process occurring inside stars and on the evolution of a star in time. This has been made possible both by a deeper understanding of the various branches of physics involved and also by the use of high-speed computers, which are capable of solving the complex mathematical equations that describe a star. The major reason, however, why so much progress has been made in studying the inside of a star, which has properties quite unlike that of ordinary matter, is that the laws governing its behaviour are the few basic laws and forces in nature. These fundamental laws, such as those of thermodynamics and the quantum theory, are now well understood. Indeed they form the backbone of any college-level course in basic physics. In other branches of astronomy, such as planetary theory or the structure of galaxies, many physical processes probably interact in a complex manner. For this reason it is not possible for us to describe the entire life history of a planet or a galaxy in anything like the detail which we can give for a star.

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