We now breathe some life into the PPN formalism by presenting a chapter full of metric theories of gravity and their post-Newtonian limits. This chapter will illustrate an important application of the PPN formalism, that of comparing and classifying theories of gravity. We begin in Section 5.1 with a discussion of the general method of calculating post-Newtonian limits of metric theories of gravity. The theories to be discussed in this chapter are divided into three classes. The first class is that of purely dynamical theories (see Section 3.3). These include general relativity in Section 5.2; scalar–tensor theories, of which the Brans–Dicke theory is a special case in Section 5.3; and vector–tensor theories in Section 5.4. The second class is that of theories with prior geometry. These include bimetric theories in Section 5.5; and “stratified” theories in Section 5.6. The theories described in detail in these five sections are those of which we are aware that have a reasonable chance of agreeing with present solar system experiments, to be described in Chapters 7, 8, and 9. Table 5.1 presents the PPN parameter values for the theories described in these five sections. The third class of theories includes those that, while perhaps thought once to have been viable, are in serious violation of one or more solar system tests. These will be described briefly in Section 5.7.

With the PPN formalism and its associated equations of motion in hand, we are now ready to confront the gravitation theories discussed in Chapter 5 with the results of solar system experiments. In this chapter, we focus on the three “classical” tests of relativistic gravity, consisting of (i) the deflection of light, (ii) the time delay of light, and (iii) the perihelion shift of Mercury.

This usage of the term “classical” tests is a break with tradition. Traditionally, the term “classical tests” has referred to the gravitational redshift experiment, the deflection of light, and the perihelion shift of Mercury. The reason is largely historical. These were among the first observable effects of general relativity to be computed by Einstein. However, in Chapter 2 we saw that the gravitational red-shift experiment is really not a test of general relativity, rather it is a test of the Einstein Equivalence Principle, upon which general relativity and every other metric theory of gravity are founded. Put differently, every metric theory of gravity automatically predicts the same red-shift. For this reason, we have dropped the red-shift experiment as a “classical” test (that is not to deny its importance, of course, as our discussion in Chapter 2 points out). However, we can immediately replace it with an experiment that is as important as the other two, the time delay of light.

Since the discovery by Hubble and Slipher in the 1920s of the recession of distant galaxies and the inferred expansion of the universe, cosmology has been a testing ground for gravitational theory. That discovery was thought at the time to be a great confirmation of general relativity for two reasons. First, general relativity, in its original form, predicted a dynamical universe that necessarily either expands or contracts. Of course, Einstein had later modified the theory by introducing the “cosmological constant” into the field equations in order to obtain static cosmological solutions in accord with the current, pre-Hubble observations. To his great joy, following Hubble's discovery, Einstein was allowed to drop the cosmological constant.

Second, was simply the fact that general relativity was capable of dealing with the structure and evolution of the universe as a whole, a capability not shared by Newtonian theory (unless special assumptions are made). However, this capability is more a consequence of the Einstein Equivalence Principle (alternatively of the metric-theory postulates) than a property of general relativity. Because of EEP, spacetime is endowed with a metric g which determines the results of observations made using nongravitational equipment (light rays, telescopes, spectrometers, etc.) and the motion of test bodies (galaxies). Via the field equations provided by each metric theory of gravity, the distribution of matter then determines the metric g, and thereby the entire physical spacetime in which observations are made.

Introduction

There will be no attempt in this book to describe the detailed physical properties of the interstellar medium (gas, dust, cosmic rays, magnetic field) in our own and other galaxies; that would require a whole book to itself. It is, however, necessary and desirable to discuss some of its properties for several reasons. In the first place I believe that galaxies were initially composed of gas alone, so that the process of galactic evolution is largely a process of conversion of gas into stars with the subsequent evolution of the stars. In the second place, if even five per cent of the visible mass of a galaxy is in the form of gas at the present time as we have seen to be true for our Galaxy, it is not really possible to discuss the structure of the galaxy whilst ignoring the gas. The gas content of galaxies will be discussed in this and the following two chapters.

Here I discuss the present structure of the gas disk in our Galaxy, with some comments about other galaxies and with some remarks about the possible past behaviour of the disk. In Chapter 7 I shall discuss the chemical evolution of galaxies, about which information is obtained by a study of the chemical composition of stars of different ages and of the present composition of the interstellar gas.

Introduction: the Hubble classification of galaxies

In the preceding chapter I have discussed in considerable detail the properties of one individual galaxy – the Galaxy. In this chapter I discuss other galaxies (external galaxies) and I compare and contrast their properties with those of the Galaxy. The easiest property of a galaxy to discuss is its visual appearance. Soon after the existence of external galaxies had been established in the early 1920s it was realised that galaxies of regular shape could be divided into two main classes, spiral galaxies and elliptical galaxies. Subsequently it was realised that the spirals should be subdivided into ordinary spirals and barred spirals and that a further class known as lenticular galaxies should be introduced. In addition there were irregulars, galaxies possessing no obvious symmetry. In the 1930s Hubble introduced his classification of galactic types which, with some modifications, is still used today.

The simplest version of the Hubble classification is illustrated in fig. 33. At the time that Hubble introduced the classification, he thought that it might represent an evolutionary sequence with galaxies possibly evolving from elliptical to spiral form but, as we shall see later, that is not believed to be true today. There are alternative classifications of galaxies in use but the Hubble system is essentially adequate for the present book. There is one important group of galaxies which was not known to Hubble because its members are rare and the nearest one is a very large distance from the Galaxy.

Introduction

It is not really possible to consider the formation and early evolution of galaxies without also considering cosmology, that is the structure and evolution of the whole Universe. The reason for this is that, as I have mentioned earlier in Chapter 3, we have no clear evidence for more than one epoch of galaxy formation and that epoch appears to have been shortly after the origin of the Universe, if we believe that the Doppler shifts in the spectra of distant galaxies indicate expansion of the Universe from an initially dense state. I am supposing that the galaxies have formed out of intergalactic (or more accurately pregalactic) gas in much the same ways as stars have formed out of the interstellar gas. However, there is one important difference. Once a galaxy has formed, its distance from other remote galaxies increases because of the expansion of the Universe, but there is no reason for believing that the galaxy itself expands. Thus, whereas star formation can be assumed to take place in a system of gas which is stationary apart from internal motions within a galaxy, the formation of a galaxy takes place against a background of general expansion of the pregalactic gas.

It is important to know when condensations of galactic size were first established, because this influences how much gravitational energy was released in galaxy formation.

This book is in effect a second edition of the book Galaxies: Structure and Evolution published by Wykeham Publications in 1978. When copies of the original edition were exhausted, the publishers were unwilling to reprint it. I am grateful to Dr Simon Mitton of the Cambridge University Press for agreeing to take the book over and for encouraging me to undertake the necessary task of revising the text.

The problem of the structure and evolution of galaxies is central to astronomy. On the one hand a galaxy is composed of stars, whose individual properties are known at least in broad outline. However, the process of star formation, which is crucial to the evolution of galaxies, is not at all well understood. On the other hand galaxies and clusters are the main constituents in the Universe and their properties provide important information about the origin and evolution of the Universe. In addition both the origin and present structure of galaxies are influenced by the possibility that the major form of matter in the Universe is not luminous stars but invisible weakly interacting particles.

In this book I discuss in general terms what is known both about the present structure of galaxies and about their past life history. Most of the detailed discussion refers to our own Galaxy. Although the subject is treated precisely where that is possible it will be apparent that, while the main ideas appear to be well-established, there are very considerable detailed uncertainties.

Introduction

In this chapter I shall consider that a galaxy consists of stars alone. To a first approximation this is true of a real galaxy apart from the possibility of hidden mass in the form of weakly interacting elementary particles; in what follows the gravitational field of any hidden mass is assumed to be added to that of the stars. For most of the life history of a galaxy the mass in the form of stars is much greater than the mass of the interstellar gas and the stars exert a much stronger gravitational influence on the gas than the reverse. Although there is a continual mass exchange between the stars and the gas, this occurs slowly compared to the time taken by individual stars to travel about the galaxy, certainly once the formation phase of the galaxy is completed. To a large extent in what follows I shall refer to the Galaxy, but it may be regarded as typical of other galaxies.

The first point to be made about the Galaxy, if it is considered as a system of stars, is that to a good approximation stars may be regarded as point masses. Except in the densest regions of galaxies, stellar separations very much smaller than 1016 m are rare, whilst only the very largest stars have radii greater than 1010 m.

Introduction

A study of the chemical composition of stars in our Galaxy indicates that this composition varies from star to star and that the variation is not random. In particular, there is some correlation between:

1. (a) Stellar chemical composition and stellar age, and

2. (b) Stellar chemical composition and stellar position or, more accurately, place of origin.

The correlations are in the sense that the oldest stars and the stars formed in the halo region of the Galaxy have a lower heavy element content than the youngest stars and those formed in the disk. It is not completely clear whether this is one correlation or two. To the accuracy to which stellar ages are known all halo stars could be older than all disk stars and their low heavy element content could just be a consequence of their time of formation. There is, however, also some evidence that halo stars of similar age have very different heavy element content, with those halo stars which were formed furthest from the galactic centre being most deficient in heavy elements. The present estimates of stellar age are not accurate enough to decide whether time of formation is the major factor determining stellar chemical composition or whether there have always been important variations of composition with position.

Introduction

This chapter contains a description of the properties of the Galaxy. It is concerned mainly with obervations, although as I have mentioned on page 18 many of the observations require a considerable amount of interpretation before they are very useful. The Galaxy is primarily a system of stars and I start this chapter by summarising some of the properties of stars of different types. As I shall explain later, there is some considerable uncertainty about the total mass of the Galaxy and about the masses of its individual components. In particular we shall learn that much of the mass of our own Galaxy and other galaxies may be invisible. Although this hidden matter might be very low luminosity stars or dead stellar remnants, there is a general belief that it is composed of weakly interacting elementary particles. At present I shall concentrate attention on the visible components. For them it may not be too far wrong to suppose that 95 per cent of the mass is stellar (including dead remnants) and about 5 per cent is in the form of interstellar gas and dust. In addition the Galaxy contains cosmic rays, very high energy charged particles, which contribute very little to the total mass but whose total energy is very important in discussions of the structure of the interstellar medium, as we shall see in Chapter 6.