GALAXY FORMATION

Galaxy Formation A Personal View

John Gribbin

M

©J. R. Gribbin 1976 Softcover reprint of the hardcover 1st edition 1976

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First published 1976 by

THE MACMILLAN PRESS LTD London and Basingstoke Associated companies in New York Dublin Melbourne Johannesburg and Madras

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SBN 333 19367 9 (hard cover) SBN 333 19512 4 (paper cover)

ISBN 978-0-333-19512-3 ISBN 978-1-349-15657-3 (eBook) DOI 10.1007/978-1-349-15657-3

For my bro, molesworth 2

Introduction

No-one with an interest in science could fail to notice that astronomy is an area where great advances are being made; but the rapid progress and exciting developments occurring should not conceal the fact that we still have many more questions to ask than answers to give when it comes to dealing with the structure and origin of the Universe in which we live.

In keeping with the rapid development of knowledge about the Universe in the third quarter of the twentieth century, there have been many attempts to propose theories which can embrace all the evidence so far discovered. Some have fallen by the wayside, others have been modified in the light of later developments, but none has remained un­changed in the face of critical discussion and new observational evidence.

With this in mind I feel that there is a place for a book presenting a personal view of galaxy formation in the expanding Universe, giving something of the flavour underlying this activity in an area where the cement of scientific progress has yet to set. My intention is to provide a book which will be useful to the second-year student of physics -whether or not his course includes some mention of astrophysics speci­fically. I hope that I may also reach a wider audience, and that any scientifically literate person will be able to gain some idea of what this rapidly changing subject is about, and of the exciting debate which surrounds it.

This is not meant to be a conventional textbook; there are many better astrophysical texts than I could write already available. But as a journalist who has also been involved in astrophysical research I feel that the conventional textbook approach is not always the most apposite when it comes to putting across ideas. An occasional detour from the traditional path can do much to fill in details of the surrounding scenery not always visible from the high-road.

With this in mind, I have deliberately followed a path here which

(vii)

Introduction

reflects the development of my own interests, including an early flirta­tion with the steady-state theory as a rather unusual entrance into the realms of general relativity. The fact that, with regret, I can no longer accept the viability of this theory will serve, perhaps, as a cautionary tale for anyone who may be tempted to commit themselves to one or another of the many theories now prevalent.

John Gribbin

(viii)

Contents

Introduction 1. Stars and Galaxies 1 2. Cosmology: The Expanding Universe 7 3. The Traditional Approach: Turbulence and Gravitational

Instability 15 4. Layzer's Gravitational Clustering Hypothesis 23 5. Ambartsumian's Fragmentation Hypothesis 28 6. Continual Creation 32 7. Newtonian Cosmology and Jeans' Criterion 39 8. The Retarded Core Hypothesis 46 9. The Growth of Irregularities in an Expanding Universe 52

10. Evolution of Galaxies 58 11. Our Galaxy 64 12. The Present Balance and Future Prospects 68

References and Further Reading 13 Index 77

1 Stars and Galaxies

We are just about middle sized in the cosmic range of things, and the phenomena accessible to our senses are by and large middle range phenomena. At one extreme in the order of things we have atoms and sub-atomic particles; atoms typically have sizes of a few angstroms, that is a few X 10-8 em, or a few X 10-10 m. Down in that strange world the physical situation is far different from that we accept as normal. Parti­cles and waves are interchangeable, and it is not possible to say where an object is and where it is going, only that it is probably in a certain volume of space, and has a certain probability of responding in a certain way to a stimulus. In other words, we are in the realm of quantum physics.

At the other extreme, when we start to consider phenomena on a galactic or universal scale our commonsense view of the world -basically, the world view corresponding to Newtonian mechanics -again breaks down and we have to introduce such concepts as relativity theory to obtain a good description of what is going on. Our galaxy is about 25 kiloparsecs across- a parsec is just over 3.25 light years, and a light year is just about 9.5 x 1017 em, or rather less than 1016 m. So in going from an atom to a galaxy we traverse a range in size from 1 o-10 m to some 1018 m. Our everyday world involves objects perhaps as small as 10-3 m (1 mm), and certainly no bigger than the Earth itself, which is, in round terms, 107 m across. And this is indeed just about the middle ground, intermediate between the quantum mechanical world of the very small, and the relativistic world of the very big.

Of course, relativity and quantum mechanics are also important in other regimes - very high density situations and 'black holes', for example. This can be important for many areas of astronomy, including the problem of galaxy formation, and under these conditions even gravity may have to be treated from a quantum mechanical viewpoint. But leaving aside the question of high densities for the moment, and

2 Galaxy Formation

considering only linear dimensions, the world of the astronomer can be said to begin just about where the world of our everyday experience ends, at the boundary of the oblate 107 m spheroid that is our home. The astronomer must also have a thorough understanding of the world of the very small, since a knowledge of nuclear physics is essential to an understanding of how stars work; and the astronomer is not restricted to studies of our own Galaxy, of course. His world extends out to the most distant reaches of the Universe and overlaps with the area of study of the cosmologist. But naturally we know most about our own neighbour­hood, and before looking at how galaxies form and behave it makes sense to take a quick look at the present understanding of how the constituents of galaxies - stars- themselves form and evolve.

There are about 1011 stars in our Galaxy, and it is by no means the biggest galaxy there is. Most of these stars conform to the so-called 'main sequence' of stars, which have a clear relationship between their brightness- or rather, the amount of energy they radiate- and their surface temperature. Our own Sun is one of these main sequence stars, and as such its detailed properties provide a good guide to the galactic norm.

The Sun subtends about half a degree on the sky, which at its distance of some 1·5 x 1011 m from the Earth corresponds to a diameter of 14 x 108 m. Its mass is about 2 x 1033 g, giving a mean density of 1·4 g cm-3 , and its absolute luminosity is 4 x 1033 erg s-1• From geolo­gical and other evidence, we know that this luminosity has been maintained for at least 3 x I 016 s, and this tells us the first important thing about stars in general - there is some internal heat source which keeps them shining brightly.

Gravity alone can heat up a collapsing cloud of gas, but the gravita­tional potential energy stored in the Sun is only tGM 2 /R (where G is the gravitational constant, M is the mass of the Sun and R its radius) which provides 1048 erg, only enough to maintain the observed bright­ness for 1015 sat the very most. We now know, as a matter of course, that the power source of the Sun and stars is nuclear fusion, in which the nuclei of hydrogen atoms combine to produce helium nuclei with a release of energy. But it is worth recalling that this question of the source of solar energy caused more than passing difficulty to the physicists of half a century ago.

The gravitational potential energy we have already calculated corres­ponds to 5 x 1014 erg g -I, so this much energy must be produced inside the Sun to hold it up and prevent collapse. Since this heat energy corres-

Stars and Galaxies 3

ponds to thermal motion of the particles in the Sun, it is straightforward to calculate that the mean velocity of these particles - or nuclei - is about 300 km s-1, corresponding to a mean temperature of 5 x 106 K. At such a temperature and density the material making up the Sun is almost completely ionised, which is convenient since it must behave very much like a perfect gas, and that makes calculations simpler (see, for example, Sciama, 1971). But on the other hand, this temperature is not enough, according to simple nuclear physics, to encourage very much fusion of hydrogen nuclei into helium nuclei. The story goes that Eddington, told by the nuclear physicists that the Sun was not hot enough for nuclear burning, suggested that they should 'go and seek a hotter place'; he meant, of course, that since the Sun clearly does exist and has existed for so long, nuclear burning in its interior must be a reality and their calculations must need revision. And he was right. Partly through the stimulus of the astronomical information about the temperature inside the Sun, nuclear physicists soon came up with the concept of 'tunnelling', which corresponds to a small but significant probability that fusion can occur between two nuclei even when their kinetic energy is less than the amount required to surmount the potential barrier between them.

More recently, the Sun has provided another puzzle for nuclear physicists. According to their best theories, the nuclear reactions going on in the Sun should produce floods of the particles known as neutrinos, which should be detectable on Earth. So far, no solar neutrinos have been detected, and it may well be that once again the nuclear physicists must rewrite their theories. But that is really another story.

The rules which govern the behaviour of a perfect gas, and which seem so inappropriate to our everyday life, really come into their own when we study the Sun. For example, we can use Stefan's law (which tells us that the energy density of a radiation field at mean temperature Tis given by aT4 , where a is Stefan's constant) to derive the flux of energy crossing each square centimetre of a spherical shell centred on the Sun's centre. The flux is just

Xc !(ar4)

where c is the velocity of light, X is the wavelength of the radiation and r is the radius of the spherical shell. Since the energy needed to balance the Sun's self-gravitation depends on mass M and radius R, T depends only on these two parameters. In fact, Ta:.MfR (see Sciama, 1971 or

4 Galaxy Formation

standard astrophysics texts). This makes it possible to determine a simple relationship between luminosity L and mass,

L o:M3

that applies independently of radius, as Eddington discovered. A more sophisticated calculation brings out a slight dependence of luminosity on radius, but this law is very close to the observed properties of main sequence stars. That is sufficiently encouraging to suggest that the broad properties of stars can be determined from the same kind of simple, perfect gas approach, and that is indeed the case.

Before we look at other stars, though, let us just check that nuclear fusion is the complete answer to the energy generation problem. Taking the age of the Sun as 15 x 1016 s (5 x 109 yr) it has already used up 500 times as much energy as is available from gravitational sources during the gradual collapse of a gas cloud with the Sun's mass. But that energy- 30 x 1016 erg g-1 - still only requires the conversion of 5% of the Sun's hydrogen into helium, and that is a more than ade­quate margin of safety.

Eventually, however, the properties of the Sun must change as its hydrogen fuel is turned into helium. We can tell how stars evolve by looking at other stars which have already reached this state, and com­paring theories of nuclear burning with the reality of the images on our photographic plates.

As the hydrogen is exhausted, so that most of the Sun (or any star) is made up of helium, there will no longer be enough energy generated to hold up the mass of gas against the force of gravity. So it will begin to collapse - and that collapse will release potential energy in the form of heat. With enough heating from this source, nuclear reaction can continue, with helium nuclei being fused to give other products (mainly carbon) at a temperature of around 108 K. That definitely happens; but later stages of the evolution of stars are more of a mystery. Perhaps yet further stages of gradual nuclear burning occur, or perhaps an unstable situation is reached and we get a violent nova or supernova explosion. In either case, all the heavy elements are built up in stellar interiors and eventually are blasted into space in great explosions. There, the material eventually cools and condenses to form solid bodies, including planets, with some of it going into second and later generation stars.

Our Sun, our planet and ourselves all contain material which has been through this process of nuclear fusion inside stars. In the words of the song, we are, literally 'stardust ... billion-year-old carbon'. Not all

Stars and Galaxies 5

stars explode, however, and those which do not are just as interesting as those which do. If a star has no more nuclear fuel to burn, it has not exploded and it is not very big (no more than It times the mass of the Sun) it has a very quiet old age. It simply 'goes out', cools down and settles into first a white dwarf then a dark black dwarf state, with radius about 1% of that of the Sun but the same mass as the Sun, giving a density of 106 g cm-3• Quantum effects certainly become important at these densities, but an even more compressed state is possible.

No star could simply collapse to greater density than a white dwarf and remain a star, but in the explosions which scatter heavy elements across the galaxy tiny, superdense neutron stars can be created. In these stars, even the atoms have lost their identity and all that is left is a collection of neutrons - essentially one giant 'nucleus' - as massive as the Sun but contained in a radius of about 10 km. These are the objects believed to be associated with the so-called pulsars - sources of radio noise in our Galaxy which emit pulses of radiation with extreme regularity at periods from 33 ms up to a few seconds.

A more compact kind of object can, in theory, be formed. Any object more than a few times more massive than the Sun simply cannot be held up at all once nuclear burning has finished, and must collapse to a mathe­matical point. That collapse would take infinite time, according to an outside observer (we are now well into the realms of relativity!) but it has been suggested that such 'black holes' do exist in our Galaxy and elsewhere in the Universe - and the concept plays a big part in some theories of galaxy formation.

As well as all these kinds of stars - main sequence, stars at other phases of evolution, white dwarfs, neutron stars and (?) black holes -our Galaxy contains clouds and streamers of gas and dust, and a sleeting of cosmic rays, particles such as atomic nuclei whipping across space at speeds a good fraction of that of light. As far as we can tell, this is a pretty typical kind of situation. Galaxies come in many shapes and sizes, however, and astronomers have been driven by an urge to classify and explain them in the same way that stars have been classified and explained already.

This study of galaxies looked the logical next step on from the study of stars, but that has not proved to be the case. There is no 'main sequence' of galaxies, and no way to explain their observed properties, even in outline, by one unambiguous use of simple laws like those which apply to perfect gases. There are two principal types of galaxy, spirals

6 Galaxy Formation

and ellipticals. Spirals, as their name suggests, look like whirlpools of light, with distinct spiral 'arms' of gas, dust and stars. The pattern is strikingly similar to the whirlpool pattern of bubbles formed in a cup of coffee when it's stirred, or in bathwater going down the plug-hole. The similarity is so obvious that it has coloured a great deal of thinking about the problem of galaxy formation. 'Obviously' what we are look­ing at are whirlpools of gas and stellar material, dominated by viscous forces, gravity and angular momentum. But if that is so obviously true, what of the other galaxies - the elliptical, lens-shaped galaxies and the irregular galaxies with no well-defined structure? Do they form by some completely unrelated process or processes? That really does not seem very likely, although the possibility cannot be ruled out entirely. In any case, an alternative school of thought has developed about galaxy formation. Whereas the 'obvious' view is that the study of galaxies should hinge upon studies of how masses of gas as large as galaxies evolve under the influence of gravity, turbulence, fragmentation and so on, the alternative view seems almost to have been deliberately chosen to be as un-obvious as possible. Perhaps, far from being straightforward collapsing, swirling clouds of dust and gas galaxies are really expanding, or have expanded, from a very compact state.

The fact that such diametrically opposed schools of thought can co-exist shows just how much remains to be learnt about galaxies. That, of course, is what makes the problem so interesting and worth taking a detailed look at in a book like this. My view of the opposing theories is necessarily a personal one, and I do favour one of the two opposing schools of thought, as will become clear. But before we come to grips with the detailed theories of galaxy formation, we should perhaps take a look at the situation from the point of view of the cosmologist, whose interests, as I have said, overlap with those of the astronomer in the realm of the galaxies. To the cosmologist, galaxies mean no more (perhaps less) in terms of the structure of the U~verse than stars do in the structure of galaxies. But since some of the most intriguing ideas con­cerning galaxy formation are inextricably tied up with ideas about the nature of the Universe, a knowledge of cosmology is far more important to the study of galaxies than a knowledge of galaxies is to the study of stars.

2 Cosmology: The Expanding Universe

As long ago as the 13th century the Chinese philosopher nng Mu wrote (see Needham, 1959, p. 221):

'Heaven and Earth are large, yet in the whole of empty space they are but as a small grain of rice .... Empty space is like a kingdom and heaven and Earth no more than a single individual person in that kingdom. How unreasonable it would be to suppose that besides the heaven and Earth we can see there are no other heavens and no other Earths.'

With the entirely reasonable substitution of the modern term 'galaxy' for 'heaven' in the original, that could well be a modern statement about man's place in the Universe. But in fact the arrival of Western influences in China coincided with, or perhaps caused, a decline in the development of such philosophical ideas about the Universe, and the influence of the Jesuits who visited China at the end of the sixteenth and beginning of the seventeenth centuries helped to ensure that the heretical ideas of the Chinese did not gain wide currency in the West. As Matteo Ricci wrote from China at the turn of the sixteenth century, listing some 'absurdities' in contemporary Chinese thought (see Needham, 1959, p. 438):

'They say that there is only one sky and not ten skies; that it is empty and not solid. The stars are supposed to move in the void, instead of being attached to the firmament .... Where we say there is air between the spheres, they affirm there is a void.'

Some of these 'absurdities' did, indeed, reach the awareness of seven­teenth century astronomers in Europe, then struggling to make the crucial break with religious orthodoxy, just at the time when that same religious orthodoxy began to impose a stranglehold on the further development of Chinese thought. It is interesting to speculate how

7

8 Galaxy Formation

cosmology might have developed if Teng Mu's writings had been familiar to the eighteenth century cosmologist Thomas Wright, who in 1750 published a remarkable theory of the structure of our Galaxy (see Wright, 1971) but who just failed to make the next jump and appreciate that our Galaxy is but one of many in a much larger cosmos. But the real development of cosmology had to await the development of observational techniques which made it possible to probe into space beyond our Galaxy, and that is the principal reason why cosmology in its modern form began only in the present century.

The key piece of observational evidence which must be explained by any plausible theory of the Universe is the red shift in the light of the external galaxies. I almost said the recession of the external galaxies- but there are cosmologies which attempt to explain the red shift in non-Doppler terms. They are far from being the most plausible, however, and from here on I will ignore them, and accept that for galaxies at least the red shift is a Doppler effect indicating recession in an expanding Universe.

So in cosmological terms galaxies are just about the smallest aggre­gates of matter worth considering. They are effectively the 'test particles' by which astronomers can measure the expansion of the whole Universe - that is, of space itself. But in fact it was only just over 50 years ago, in 1924, that Edwin Hubble finally resolved the argument about whether or not the 'nebulae' visible in the sky were external galaxies at all. The breakthrough came both because of Hubble's prow­ess as an observer and because of the development of more powerful telescopes- in particular, the 100-inch reflector at Mount Wilson. With this instrument, Hubble was able to detect certain variable stars belong­ing to a family called the Cepheids in the Andromeda nebula and indeed in other nebulae as well. The importance of this is that the Cepheids vary in a regular way and that the period of any one Cepheid depends on its intrinsic brightness. So Hubble had a measure of the absolute brightness of the stars in the Andromeda nebula, and this made it a simple matter to work out the distance to the stars from their apparent brightness. These distances established that the spiral 'nebulae' are in­deed galaxies in their own right, hundreds of thousands of light years away from us.

The Cepheids provided just the first chain in a process by which distances to much further galaxies can be determined. Supergiant stars, for example, can be picked out at greater distances than Cepheids, and Hubble found that, as a reasonable rule of thumb, the brightest super-

Cosmology: The Expanding Universe 9

giants in all galaxies have about tll.e same absolute luminosity. The next step was to assume that all galaxies have the same absolute luminosity, and so obtain approximate estimates of the distances of galaxies so far away that not even supergiants can be resolved using Earth-bound telescopes.

That last step was pretty rough and ready, and since Hubble's time it has even been found that his understanding of the period-luminosity relationship for Cepheids was in error. So the actual numbers which Hubble produced when he first measured the distances to the external galaxies have now been considerably revised upwards, by a factor of five or so. But this in no way detracts from the achievement of Hubble in getting even a first approximate idea of these distances. Still less does it detract from the significance of the discovery of the expansion of the Universe, which provided the next step in the development of observa­tional cosmology.

It is no great trick to measure the Doppler shift effect produced in the spectra of nearby galaxies, and indeed such radial velocity measures were made before anyone knew with certainty that these objects were galaxies in their own right, and not aggregates of stars within our Galaxy. The first such observation was made in 1912 at the Lowell Observatory, and showed that the Andromeda galaxy is approaching us at about 200 km s - 1. This is about four times more than the fastest moving stars, so that result alone provided a strong hint that the Andromeda 'nebula' was something special. But by the early 1920s velocities had been mea­sured for several spiral nebulae, and these were, by and large, receding with velocities ranging up beyond 600 km s-1 .

Following Hubble's proof that these fast moving objects are external galaxies, it was discovered that our galaxy itself is rotating, and that the Sun is moving at 250 km s-1 because of this. So that effect had to be subtracted from the measured Doppler velocities to find how fast the other galaxies are moving relative to the centre of our own Galaxy. This reduces the Andromeda galaxy's velocity to a 'mere' 100 km s-1 ; but by then the velocity of that galaxy was far from being the most puzzling thing about the motions of the external galaxies.

By the end of the 1920s, Hubble's measurements of the distances to galaxies could be combined with Doppler shift measurements in a very simple law: the velocity of recession of a galaxy is proportional to its distance from our Galaxy. This is the famous 'red shift-distance relation'. Of course, this discovery in no way implies that our Galaxy is the centre of the observed expansion, any more than the fact that the

10 Galaxy Formation

horizon on Earth describes a circle around an observer means that he is at the centre of the world. With such a law of expansion (velocity pro­portional to distance) any observer in any galaxy will observe the same effect.

But on the other hand if we extrapolate backwards in time such an expansion law does, at first sight, clearly imply that the expansion started at some definite point in time, when all the galaxies were packed together. For the first time, astronomers had found a timescale which clearly had cosmological significance, as opposed to estimates of the ages of stars which are primarily of local significance.

Once again, the numbers determined by Hubble (the constant of pro­portionality in the velocity-distance relation) were thrown out by his errors in measuring the distances to galaxies. That caused a lot of con­sternation at the time, because as a result the 'age of the Universe' since the time when galaxies were crowded together came out as less than the accepted ages of the Sun and Earth. But these difficulties have been resolved as improving techniques had led to the modification of Hubble's constant. Now, even the most naive interpretation of the red shift­distance relation leads to an age for the Universe comfortably more than the age of the Solar System, and more or less the same as the ages esti­mated for the oldest stars in our Galaxy.

Over the past 20 years or so the development of radio astronomy has paved the way for ever deeper probes into the expanding Universe. First radio galaxies, then quasi-stellar objects (QSOs) have been discovered and studied. Two separate but possibly (according to some theoreticians) related puzzles are posed by these objects. First, in both radio galaxies and QSOs it seems that enormous amounts of energy are being liberated. Astronomers are used to large numbers - but when you start talking about explosions in which the mass-energy equivalent to annihilation of 1039 g of matter is occurring even astronomers are surprised. The other puzzle is the occurrence of very large red shifts in the spectra of QSOs. The most extreme cases known are two QSOs with red shifts close to 3-5, corresponding to velocities of recession well above 90% of the speed of light and implying correspondingly huge distances from our galaxy, using Hubble's law.

As a result, the validity of applying Hubble's law to QSOs has been questioned in some quarters. Perhaps, it is argued, the very processes which produce such violent outpourings of energy also affect the light from these objects, and physics as we know it on Earth simply does not apply under such extreme conditions. Some of these ideas are not un-

Cosmology: The Expanding Universe 11

attractive; but if you start from the ·basic assumption that our terrestrial laws of physics may not be universal then it is difficult to build any kind of testable model to explain the observations.

It seems to me that such extreme measures should only be adopted in descriptions of the real Universe (as opposed to mathematical abstractions) when all else has failed. And since 'conventional' physics has not yet failed, although it has to be pushed to the limits in describ­ing some of these phenomena, the time has not yet come for such drastic steps. The time may come to rewrite the laws of physics; for the present, however, I will accept that the red shift of QSOs is cosmological, and provides additional evidence of the expansion of the Universe. The nature of QSOs themselves, and their possible relationship to ordinary galaxies, will be discussed later.

So we have a Universe in which 'test particles' (galaxies and QSOs) are seen to be carried along by a universal expansion. Where did it come from? Where is it going? And how will it get there? Cosmology has in recent years made great strides in developing answers to all these questions - the only snag is, there are, in this case, more answers than questions. That is, several different 'model universes' can be constructed mathematically to account for the observed properties of our Universe. Only one can be 'correct' (although maybe none of them is!) but our limited observations of the Universe in both space and time make it impossible to point to one model and say with confidence 'that is an exact description of our Universe'.

With just the observation that the Universe seems to be expanding, there are two main theories of the basic nature of the Universe which have some philosophical appeal. If we just imagine running the Universe backwards in time, to get some idea of how it got into the present situation, then it is fairly clear that the observed expansion must be the result of something like an explosion from a very condensed state - a 'hot big bang'. This very definitely implies a beginning to the Universe as we know it, at some definite point in time. That is a worrying thought in some ways- apart from anything else, where did the mater­ial for the big bang come from, and what, if anything existed before the 'beginning'? Mathematicians can get round this by restricting their calculations to what happened after the big bang; or it is possible to envisage a situation in which the very compressed state of the initial explosion was produced by an earlier 'phase' of universal collapse, the opposite situation from that of the present. From there, it is a simple step (philosophically if not mathematically) to imagine that our present

12 Galaxy Formation

Universe might one day turn around into a collapsing state, become condensed, and bounce back into expansion. Such a cyclical universe could be imagined to go oscillating on indefinitely, removing the pro­blem of a definite beginning.

But the other basic theory of the Universe has even more philoso­phical appeal. Suppose that the Universe has always been expanding, with galaxies moving away from one another, but that new material is created in the gaps opened up, and forms new galaxies. Then, the Universe always looks, on average, much the same - it is in a 'steady state'. Of course, we now have the problem of accounting for the creation of new matter continuously to fill in the gaps - but in philosophical terms, is that any worse than having all the matter of the Universe created in one great event, at the beginning?

In the 1950s the two opposing basic theories aroused strong feelings for and against among the members of opposing cosmological camps. Today, the weight of the observational evidence suggests that at the very least the Universe is not in a genuine steady state, and that the properties of the average distribution of galaxies and other objects do seem to vary with time. But even dismissing all steady-state models (and a few diehards still refuse to do that) there is plenty of scope for choice among other models when trying to describe mathematically the behaviour of the Universe since the big bang. How fast has the expansion been? Was the 'bang' itself hot or cold? Is the expansion slowing down, and if so will it eventually turn over into a collapse? And so on, with at least a handful of possible (if not plausible) mathematical theories to be considered. But the situation is not really so chaotic. Einstein's theory of relativity produces naturally a set of equations which describe an ex­panding universe very much like the one in which we find ourselves, and just as there seems little point in choosing cosmologies which invoke new theories of physics at the present stage, so there seems little reason not to use these relativistic cosmologies as descriptions of the Universe. Einstein's theory may not be perfect, but it is the best theory of rela­tivity we have and as such it should not be lightly dismissed.

Indeed, relativity theory may in many cases be almost too powerful a tool to use in describing the Universe, although no-one seems to have realised this for several decades after the ideas of Einstein came to prominence at the beginning of this century. Newtonian theory can pro­duce much the same 'predictions' - including that of universal expansion. It is beyond the scope of the present book to go into the details of the various cosmological models here, especially since there

Cosmology: The Expanding Universe 13

are several excellent books on cosmology already available (such as Sciama, 1971). All that we need immediately to tackle the problem of galaxy formation is to know that the Universe is expanding, that if such expansion is extrapolated backwards in time then it implies 'creation' in some way at a definite point in time about 10 thousand million years ago, and that there is matter in the Universe, as the presence of galaxies shows.

This is where things become interesting. If the Universe started out from a point in space and time, then galaxies must have formed out of some intermediate state of matter. The simplest model (and unless there is pressing reason not to, it is always best in astronomy to apply Occam's Razor and take the simplest possibility) would be of a uniform, expand­ing gas cloud in which irregularities grow up and turn into galaxies. It has been known for many years that if irregularities arise in an initially isotropic and homogeneous expanding universe then under certain cir­cumstances they may grow as the expansion proceeds (see Lifshitz, 1946). But the rate at which inhomogeneities can grow is insufficient to account for the existence of galaxies at the present time, assuming that the original cause of inhomogeneity was statistical fluctuation, even if simple departures from isotropy are considered (see Zel' dovitch, 1963a, b and 1964; Lifshitz & Khalatnikov, 1964). It is just possible that bodies of stellar dimensions might form by the gravitational clustering mechanism proposed by Layzer (1954), but in order to form larger con­centrations of rna tter it would be necessary to postulate that nuclear reactions or some other mechanism then provides sufficient perturbation for star clusters and galaxies to form (Zel'dovitch, 1963a, b).

At the present time, it seems that the presence in the Universe of in­homogeneities as large as galaxies and clusters of galaxies is fairly con­clusive evidence that the universe has not evolved from a strictly iso­tropic and homogeneous Friedman universe- that is, the Universe must always have possessed a considerably larger degree of inhomogeneity than that provided by statistical fluctuations.

Since it is very difficult to deal with irregularities in general relativity, most theories of galaxy formation ignore this problem and postulate some inhomogeneous starting conditions, considering only the subse­quent evolution of these irregularities into galaxies, when it is hoped that general relativity may safely be ignored. In the extreme case the 'initial' conditions postulated are those existing now - a 'steady-state' universe in which irregularities are propagated by existing galaxies and clusters (McCrea, 1964; Roxburgh & Saffman, 1965).

14 Galaxy Formation

The theories which I will describe here are representative of the principal schools of thought about galaxy formation; naturally enough, I have taken care to include and emphasise the ideas which I consider to be of greatest relevance to the problem of the growth of irregularities in an expanding universe. This is still an area of science where personal pre­ferences must play a part, and I make no excuses for omitting, or dealing cursorily with, ideas which may have just as much solid physical basis as those I like.

3 The Traditional Approach: Turbulence and Gravitational lnstabi I ity

Many modern astronomers accept that galaxies must form from roughly uniform clouds of gas. Different authors use different values for the den­sity of such initial clouds, their estimates usually being based on 'reason­able physical arguments', but such estimates are always in the range 10-24 g em - 3 to 10-27 g em -3 (the lower limit is the observed mean density within a cluster of galaxies, and the upper the observed mean density within our own galaxy).

Apparently, Newton (see Brewster, 1855) was the first person to conjecture that a uniform unbounded medium consisting of gravitating particles would be unstable against fragmentation, but the first person to treat this idea mathematically was Jeans (1928). Although Jeans was at that time unaware of the expansion of the Universe, so that the observational basis of his theory is invalid, the 'Jeans Criterion' for the fragmentation of a self-gravitating gas cloud is still fundamental to many theories of galaxy formation, since the expansion of the Universe is often assumed to have no effect on the collapsing gas clouds other than to increase their separation from one another.

Turbulence

Almost thirty years ago, von Weizsiicker (1948 & 1951) and Gamow (1952) were responsible for bringing into serious contention among

15

16 Galaxy Formation

theories of galaxy formation the idea that galaxies might form from turbulent clouds of gas. The idea has recently been revived, in the con­text of the 'hot big bang' model of the Universe; although in its original form the theory is probably inadequate as a description of the galaxies we see around us in the real Universe, it is instructive to trace the development of von Weizsacker's ideas, and see just where they break down.

The initial conditions postulated are pregalaxies in the form of turbu­lent gas clouds, each of which forms a cluster of galaxies, and the physical basis for this assumption is that the rotational velocities of galaxies are observed to be of the same order as their linear velocities, as we would expect if galaxies may be treated as eddies in a turbulent flow. Subsequent evolution of such an eddy (assumed to have density roughly comparable with the present day intragalactic density) pro­ceeds by the conversion of turbulent motion into heat, so that energy is lost by radiation.

As a result of this loss internal energy is decreased and contraction takes place to a disc, in which differential rotation causes further turbu­lence and angular momentum is conveyed outwards. Thus a slowly rotating central region is formed, while the rest of the disc becomes progressively thinner and more extended, eventually disappearing completely as a result of mass loss from the periphery. Von Weizsacker identified the leftover central region with an elliptical galaxy, earlier stages in the evolution having had a two-component structure not unlike that of spiral galaxies. Since the timescale for the formation of stars from eddies within a galaxy is found to be only of order 5 x 106 yr it was necessary for von Weizsiicker to explain the existence of large

quantities of interstellar dust at the present time by saying that all stars formed at the same time, after which the presence of stars in some way inhibited further star formation, perhaps by radiation pressure. This is a most unsatisfactory argument, especially since it requires that stars normally thought of as young are in fact old stars which have been rejuvenated by accretion, a process unlikely to alter a star radically in any reasonable time($ 109 yr). There is no mechanism in the theory to account for the formation of binary stars and galaxies, and Layzer (1964) has shown that differential rotation cannot maintain turbulence for periods comparable with the collapse time of the cloud:

Assume that turbulent motions contain most of the internal kine­tic energy of the cloud, so that

v2 ~ GpD2 (3.1)

The Traditional Approach :Turbulence and Gravitational Instability 17

where Dis the cloud diameter, pits mean density and v a typical eddy velocity. An eddy of size A will have a lifetime of the order A./v, which is the time taken to travel its own length, and the time taken for such an eddy to contract in free fall under its own gravitation will be

I r=(GpYz

where p' is the density of the eddy. Equations (3.1) and (3.2) give

r ~ (p'liir~ D/v

(3.2)

and ifA <{D and 1 < P'lP < 10, as is likely for a typical eddy, then

T~ A.fv

that is, a typical eddy does not last for a sufficient time to contract appreciably by self-gravitation.

Thus it appears that the theory as originally put forward by von Weizsacker must be discarded - turbulence may be important at some stage of galactic evolution, but it is not adequate to explain the whole process.

Although the idea of cosmic turbulence as at least a contributory factor in the development of galaxies in the early stages of the evolution of the Universe was given something of a new lease of life a few years ago, when several groups around the world developed the idea within the context of the hot big bang model of the Universe (for references see Jones, 1973), serious difficulties remain in attempting to reconcile the development of large density variations with the speed of viscous decay of the eddies. According to Jones, the theory might just be able to account for formation of spiral galaxies under favourable conditions. This seems, however, an inadequate basis on which to accept the theory when other ideas are also available, and I find that even in its modern form the concept of cosmic turbulence as explaining the origin of galaxies is unappealing.

A slightly more appealing possibility, due to Jones (1973), is that galaxies might form from density perturbations which themselves arise as a result of the decay of the initial turbulence in the expanding Universe. But as Jones points out, this idea too has its difficulties. I shall therefore not attempt to review the details of these ideas, which

18 Galaxy Formation

are readily available in recently published papers, but will move on to the theory of galaxy formation which next followed those of von Weizsiicker and Gamow in the early 1950s.

Gravitational Instability

In 1953, Hoyle put forward a theory of galaxy formation which postulated the existence of 'pregalaxies' at a density of 10-27 g cm-3 ,

and described in detail how such clouds might fragment into stars. To some extent, this begs the fundamental question of galaxy formation. One might well ask, where did Hoyle's pregalaxies come from? But setting this aside for the moment, Hoyle's ideas of some twenty years ago lead to some interesting results which might well be of relevance in our own and other galaxies.

Assuming that the mechanism by which the pregalaxy formed resulted in internal bulk motions with velocities greater than about I 0 km s-1,

there will be sufficient turbulent heating within the cloud to ionise the hydrogen of which it is made. As Hoyle pointed out, as the temperature of a hydrogen cloud is increased energy is radiated by the ionised atoms; but above 25 x l03 K (the temperature at which the cloud is fully ionised) the rate at which energy is radiated actually decreases slowly with rise in temperature, until a temperature of some 4 x 105 K is reached. Further increase in temperature then causes a slow rise in the rate of radiation of energy.

The only reasonable interpretation of this behaviour is that such a cloud can only exist in one of two stable regimes. Either it has a temper­ature in the range 104 to 2·5 x 104 K, or it has a very high temperature, in excess of 106 K. This is because it is very improbable that the energy available from bulk motions will lie in the small range corresponding to intermediate temperatures (see Figure 1).

Hoyle's original discussion of high temperature clouds was brief and highly speculative, being confined basically to expressing a hope that galaxies formed from such high temperature clouds might evolve into the kind of structures which cannot be accounted for by his proposed detailed model for the evolution of low temperature clouds. This kind of pious hope is not uncommon in astronomy, and indeed the scope for making such vague generalisations to account for all the phenomena which are not explained by any particular detailed model provides one of the main attractions of the subject for those, like myself, who some­times feel disinclined to attempt a thorough mathematical treatment of

The Traditional Approach: Turbulence and Gravitational Instability 19

all the problems. Indeed, Hoyle's 1953 model of the evolution of the low temperature clouds is only, as he put it, 'of a tentative nature'; and it does not really work entirely satisfactorily. So I shall outline it briefly only in order to point out the difficulties inherent in all models based on gravitational instability.

Any cloud in the lower temperature range will lose energy rapidly by radiation until the temperature is such that the power radiated is exactly

~ ·;: ::>

~

~ 2. ~ .2 "C e

J A

Low temperature regime

High temperature regime

T(K)

Fig. 1. Variation of radiated energy with changing temperature for a hydrogen cloud. Because of the energy involved in ionisation, there is a broad band of temperatures corresponding to a very small band of radiated power and any real cloud will be in either a high temper­ature (ionised) or low temperature (unionised) state outside this band (schematic only)

balanced by the rate of gain of energy by contraction, which occurs when the cloud is partially ionised at about 104 K. Once this temperature is reached contraction will take place isothermally, provided the cloud has a mass greater than 1·5 x 1010 M11H where Me is the mass of the Sun. (This condition is obtained by assuming that the cloud contracts if the total gravitational potential energy exceeds twice the thermal energy, a

20 Galaxy Formation

result which applies strictly to spherical clouds with negligible radiation pressure.) Hoyle then suggested that, long before the cloud has become so small that turbulence, shock waves and so on can destroy the homo­geneity of the cloud, subcondensations will form, each having the minimum mass necessary for contraction to continue independently now that the density has increased. The reason for considering such fragmen­tation is primarily that if the cloud does not fragment then galaxies and stars do not form, and there is no point in investigating the model further. Although, as Hoyle (1953) suggested, it is possible to argue that energy is more efficiently dissipated from a collection of small clouds thanirom one large cloud, this is not really a convincing argument in favour of fragmentation, since there is no reason to suppose that a more rapid loss of energy should be preferred. I would rather point out merely that fragmentation is possible, and consider the consequences if it does occur, without claiming that it is actually necessary for all clouds to fragment.

Starting from a density of 10-27 g cm-3 and a temperature of 104 K, Hoyle found that subcondensations (if they do form) will have mass close to 3·6 x 109 M0 , and may therefore be identified with galaxies. As contraction proceeds, the density of these subcondensations will rise until they too can fragment, and repeated contraction and fragmen­tation will continue until the fragments are opaque. Once that point is reached, contraction will proceed adiabatically rather than isothermally. The mass of the 'ultimate fragments' works out at between l-5M0 and 0-3Me, so Hoyle's theory gives a hierarchical structure, in which clusters of galaxies contain galaxies which in turn contain clusters of stars, and this is at first sight in good agreement with observation.

Unfortunately, as Layzer (1954) has pointed out, the fragmentation process should continue even after adiabatic conditions are reached, since at that stage most of the hydrogen is still not ionised! He has sug­gested that if fragmentation does occur then the ultimate fragments would have planetary rather than stellar mass, but he doubts whether fragmentation of this kind will occur at all in nature (Layzer, 1954 and 1963), and believes that any fragments which did form would be obliter­ated by tidal effects. I will describe Layzer's detailed arguments in the next chapter; but there are still other developments of the gravitational instability model which must be considered first.

The theory of fragmentation offered by Hoyle is unsatisfactory since so much that is fundamental to the theory is largely speculative - for example, the hierarchical structure discussed is shown to be 'not imposs-

The Traditional Approach: Turbulence and Gravitational Instability 21

ible' rather than a certain consequence of the initial conditions postulated.

More recently, Hunter ( 1962 and 1964) has considered a cloud in which the gravitational energy is much greater than the internal energy, and concludes that although bulk motions arise they are directed towards the centre of the cloud and do not tend to re-expand the gas by turbulent heating. In spite of criticism by Layzer (1963) Hunter remained convinced that subcondensations do form, but his treatment (1964) requires calculation of the perturbation to second order, which is some­what complex. The important result obtained by Hunter is that if in­homogeneities arising are of order op/p <: 0·01 then they will grow as the cloud contracts. Nakano (1966) has used Hunter's results in a pro­posed mechanism for the formation of star clusters from the interstellar medium, the irregularities contracting until stopped by rotational forces. Fragments formed on this model have an initial density of order 1 o-18

to 10-17 g cm-3 and mass comparable to the mass of the Sun, but further contraction is allowed if these fragments lose angular momentum in collisions with each other, the mean free path of a fragment being small until contraction has reduced it to roughly stellar dimensions. Although Nakano proposed no detailed mechanism for the loss in angular momen­tum it is natural to expect that in collisions fragments may (i) break up, giving sub-fragments with various angular momenta, or (ii) coalesce, giving a large fragment with angular momentum different from that of any of the fragments before collision.

An interesting speculation which Nakano did not consider is that after some contraction and further fragmentation by collision a system of floccules might arise, similar to that postulated by McCrea (1960) in his theory of the origin of the Solar System. The best that can be said about the gravitational instability model of galaxy formation is that no­one has been able to prove conclusively that it cannot work. So, like any astronomical theory which remains possible (if not probable) work on it continues from time to time. These theories seem to have become more and more complex as the years have gone by (see Simon, 1970; Zel'dovich, 1970; Press and Schechter, 1974) but without becoming any more satisfactory. As we will see, equally or more satisfactory results can be obtained by theories which do not even need to use relativity theory; so there seems little point in entering the realms of mathematical speculation at this stage.

By and large, the idea of galaxies forming from initially more or less uniform clouds of gas is unsatisfactory. Theories can be built up which

22 Galaxy Formation

are not definitely wrong, but that does seem to be begging the basic question (although it is enjoyable to do so sometimes). So what can be done in the way of radically different theories - if you like, working not from the outside inwards, but from the inside outwards?

4 Layzer' s Gravitational Clustering Hypothesis

The difficulty of constructing an adequate theory of galaxy formation based on the contraction of initially diffuse clouds of gas has encouraged several authors to put forward theories which are radically different in their approach to the problem. Some of the more recent theories are based on the existence of inhomogeneities in the universe, and these will be discussed later, but the first theory not involving collapsing gas clouds to achieve much notice was Layzer's theory based on the hypothesis of gravitational clustering, which assumes an initially homogeneous and isotropic universal matter distribution.

Layzer ( 1963) has pointed out the distinction between fragmentation processes and clustering processes. In the former a large mass divides into smaller ones, but in the latter initially non-interacting particles come to­gether to form bound aggregates (such as the formation of liquid drops in a vapour cooled below its critical temperature). It has been suggested that a fragmentation process is unlikely to be significant in a diffuse cloud of gas, since the long-range nature of the gravitational interaction will allow tidal forces from the whole cloud to overwhelm the relatively feeble self-gravitational forces of any small element which happens to achieve slightly greater density from statistical fluctuations. This argu­ment has to some extent been superseded by the work of Hunter ( 1962 and 1964), and it would also seem to conflict with an assumption made by Layzer later in the theory (see below), so the foundations of the clustering theory are not as solid as might be desired.

The hypothesis put forward by Layzer assumes that at some past epoch the Universe contained a distribution of matter which was uni­form apart from 'local irregularities', presumably arising from statistical

23

24 Galaxy Formation

fluctuations. As the Universe expands, these irregularities will grow until self-gravitating systems form, which may then be treated as particles in a new distribution so that the whole process is repeated. Thus it is ex­pected that planets and stars are formed at an early epoch, followed by successive clusterings which produce star clusters, galaxies, clusters of galaxies, and 'superclusters' ad infinitum. This process is the reverse of the evolution expected if the present day Universe were to contract, so a clear distinction is apparent between the reversible clustering model and the irreversible collapsing gas cloud models.

A rigorous mathematical treatment of this hypothesis would involve solving Einstein's equations with local irregularities in the matter distribution, which is a task of great complexity. The method suggested by Layzer is equivalent to a Newtonian approximation, and depends on the theorem that the gravitational potential inside a sphere of radius R embedded in a matter distribution which is only non-uniform on a scale small compared with R is the same as the potential which would exist if the sphere were embedded in empty space (strictly, the potential is only the same for r < R, since difficulties arise at the boundary). If it is assumed that random motions and the Hubble velocity associated with R are much less than the speed of light, then the evolution of irregular­ities within the sphere R may be adequately described using Newton's theory of gravitational potential. Although Layzer's clustering idea does not seem to be a good description of the way galaxies form in the real Universe, this use of the Newtonian approximation is worth more than passing interest, and will be met with again in other theories. Newtonian cosmological models began to be taken seriously in the mid-1930s, when Milne and McCrea ( 1934) developed them, and they have received some attention ever since (notably from McCrea and his proteges). The power of the approximation, of course, is that it makes intuitive reasoning on the basis of everyday experience rather more plausible. If a system obeys Newton's equations, then it really is rather like systems we have exper­ience of. But if it obeys Einstein's equations in ways which diverge from the predictions of Newtonian theory, then intuition becomes a very dangerous tool, except to the most accomplished mathematician. This intuitive (or, if you like, 'wishful thinking') aspect is clear in Layzer's theory.

Layzer claims that it is possible to define a kinetic energy per unit mass (Tm) and a potential energy per unit mass (Vm) such that

Tm + Vm ==Em== constant (total energy) (4.1)

Layzer's Gravitational Clustering Hypothesis

and the virial theorem holds in the form

2Tm + Vm = 0

25

(4.2)

Tm is defined in a frame co-moving with the expanding substratum, cos­mic pressure being assumed zero (dust-like matter), and Vm is defined as the difference between the specific gravitational energy of the non­uniform medium considered and the specific gravitational energy the medium would have if it were uniform (specific gravitational energy is found by considering a sphere large compared with any perturbations and treating it as if embedded in empty space).

Although Layzer does not offer a proof that equations ( 4.1) and (4.2) necessarily follow from the given definitions of Tm and Vm, these equations are certainly reasonable in a model using Newtonian theory, and if they are accepted then it follows that V m is constant.

Let Po be the mean density of the matter distribution, and consider fluctuations in density of wavelength A and amplitude ep0 . Considering departures from the mean, the excess mutual potential energy of two adjacent irregularities will be of the form

G (ep0 A3 ) 2/A

where A 3 represents the volume of an irregularity, ep0 A 3 the excess mass of an irregularity, and A is the distance between centres of adjacent irregularities. Thus the specific gravitational energy will vary as

so we may put

Vm-G€zPoA2

If R(t) is the length scale for the expanding Universe

Po~ R-3(t)

and it is reasonable to assume

(4.3)

since only waves satisfying nA = R are able to fit into a box of side R. Vm is constant (see above), so equation (4.3) gives

26

and

Galaxy Formation

1 e~R2

so that irregularities grow as the Universe expands. Unfortunately, the expression used in ( 4.3) does not seem to be in

agreement with the earlier definition of Vm, and I would prefer the following treatment, which is consistent with the rest of the theory.

The mutual potential energy of two adjacent uniform regions of size A is

G(p A3)2 v ~ 0 t A

and the mutual energy of the two irregularities discussed above is

V ~ G [(Po+ EPo)A3 ] 2

2 A so from Layzer's definition

v. ~ V2- V1 ~ G A6 (2ep~ + e2 p~) m PoA3 PoA4

and terms in e2 may be neglected if e is small. Therefore,

Vm ~ A2EPo

as before

so

and

But the essential dependence of eon R(t) is the same- fluctuations grow as the Universe expands. So this discrepancy does not affect Layzer's subsequent argument.

Although Layzer found this result pleasing, since it predicts that e = 0 at R = 0, that is, the initial matter distribution is perfectly uniform, he was unable to obtain any explicit results and could only justify the clustering hypothesis further by saying that 'when the cosmic density is low enough it seems reasonable to expect that the supply of gravitational energy will be sufficient for the formation of self-gravitating systems'. This expectation would seem to conflict with Layzer's earlier assump-

Layzer's Gravitational Clustering Hypothesis 27

tion that long-range tidal forces will disrupt irregularities, and although the densities considered now are much lower than those mentioned before this does show the danger present in such speculative assumptions.

The best way to test Layzer's theory would be to determine the time­scale required for the formation of galaxies, or the cosmic density to be expected when galaxies form, and although Layzer makes no attempt to calculate these parameters work by Zel' dovich ( 1963a, b and 1964) is applicable to the problem. Zel'dovich has shown that in any model starting from an initially uniform matter distribution it is not possible for bodies of greater than stellar dimensions to form in the time avail­able, assuming that the cause of irregularity is initially statistical fluctuations, unless some mechanism (nuclear reactions, for example) can provide a very large perturbation. Even with nuclear reactions it may still be impossible for irregularities of galactic sizes to form.

Observationally, the clustering model seems in difficulty since it pre­dicts that planets form before stars, and it is hard to reconcile this with the element abundances seen in stars and planets. Perhaps the funda­mental weakness of the model is its inability to explain why stars are still being formed in the Galaxy. Although Layzer says 'it is not known ... whether interactions ... can inhibit the gravitational contraction of prestars for long periods of time without disrupting them' this does seem to be a very unlikely occurrence, especially in view of Layzer's own comments about tidal forces, and reduces the theory to the level of speculation.

Clustering as a mechanism for the formation of the planets and so on after the stars and galaxies have formed seems a much more likely occurrence, and this possibility has received a great deal of attention (see, for example, Hoyle eta/., 1964; McCrea & Williams, 1965; Safronov, 1966; Urey, 1966).

5 Ambartsumian' s Fragmentation Hypothesis

Although Ambartsumian considers a fragmentation process, his approach is completely different from that of the 'traditional' hypotheses dis­cussed in previous chapters. The basis of the theory is the existence and form of the observed clustering of astronomical systems, ranging from binary stars to clusters of galaxies.

Ambartsumian and others have done a great deal of work on assoc­iations of stars within our galaxy (for references see Ambartsumian, 1958a) from which the following conclusions may be drawn:

(i) The components of double and multiple star systems have a common origin.

(ii) Star formation continues in the Galaxy at the present time. (iii) The expansion of stellar associations implies that the disc popu­

lation consists of stars formed in groups which have now dispersed.

In an attempt to provide a unified theory of the formation of stars and galaxies Ambartsumian (1958a, b; 1960; and 1964) has considered the observed distribution of galaxies within clusters in comparison with that of stars within groups. Of fundamental importance are the obser­vations of systems with positive energy in our galaxy (Ambartsumian, 1958a, b), in particular the so-called 0 associations, which have densities much less than that required for stability against tidal effects. It is significant that the 'trapezium' type of system, where there are three components such that each is equidistant from the others, is dominant among 0 associations, since although this configuration is highly prob-

28

Ambartsumian's Fragmentation Hypothesis 29

able for an expanding system whose members have a common origin it is most improbable for any other system.

In spite of the usual difficulties of determining the distances between members in clusters of galaxies, Ambartsumian has shown satisfactorily that there is a high probability that the members of a given cluster of galaxies will also contain components in the 'trapezium' configuration; most of the multiple galaxies for which the separation of members could be determined were found to have this configuration. This implies not only that these clusters are expanding, but also that their ages are small compared with the rotation period of a cluster (as 0 associations are young compared with the rotation period of our galaxy) otherwise they would have dispersed- this is in agree­ment with other estimates of the ages of galaxies.

Accepting the evidence that clusters of galaxies are expanding, it is necessary to consider their origin in the light of this knowledge, which was not available when any of the theories so far discussed were formu­lated. Ambartsumian is well known for a suggestion that violent events are taking place in the nuclei of some galaxies; this idea overcame early objections to become widely accepted as the explanation of many radio sources, and now forms the basis of Ambartsumian's theory of galaxy formation. The most violent activity observed is the ejection of a blue jet ending in a bright central condensation (which Ambartsumian identifies with the nucleus of an embryo galaxy) from the nucleus of an elliptical galaxy. Less extreme events will give new systems which are bound to the nucleus, and these are tentatively identified with stellar systems such as globular clusters.

Thus the hypothesis presented by Ambartsumian states that the nuclei of galaxies contain matter at high density within a relatively small region. Up to half this matter may be ejected in a violent explosion, either by the nucleus splitting (as seems to be the case in the radio galaxy Cygnus A), or by the emission of small fragments in all directions. If a large piece of matter is ejected from the core at less than escape velocity, and if this fragment is itself unstable, then smaller fragments will be emitted from it as it moves outwards so that a jet forms behind it. Any rotational motion present will distort a bound jet into a spiral arm, and it is expected that globular clusters are formed by the emission of fragments which are too small to form jets or spiral arms.

An interesting galaxy which appears to be in agreement with this model is M51, which has a companion galaxy at the end of a spiral arm,

30 Galaxy Formation

and it is also noteworthy that Oort (1962) has pointed out that most spiral galaxies have two main arms, defined by 0 stars and gas, which can be traced from the periphery to the nucleus, which they join on opposite sides, indicating that the disc structure does in some way interact with the nucleus. Although Eggen, Lynden-Bell, and Sandage (1962) have interpreted the observed differences in eccentricity and other orbital parameters of halo stars and disc stars as implying that our Galaxy has collapsed from a gas cloud, the statistics used may well be interpreted as evidence that halo stars have been expelled from the nucleus with high velocity into elliptical orbits.

A major difficulty of this model is the problem of angular moment­um, as Ambartsumian himself points out. The observed rotation of spiral galaxies is large enough to preclude their having evolved from a state of higher density, but there is no evidence yet that elliptical galaxies are rotating at all. Perhaps the basic structure of all galaxies is the 'elliptical type' nucleus plus halo, and the rotating disc of spirals is caused by accretion of matter from the intergalactic medium. But Ambartsumian also points out that many pairs of spiral galaxies, which are presumed to have formed from a single nucleus, are observed to have very small net angular momentum, since the constituent galaxies have opposite rotation relative to each other, and it is also observed that if two galaxies are physically connected by a 'bridge' then they always rotate in the opposite sense to each other, so that much of the force of the above argument is removed.

The distinction between disc and halo populations is recognised by Ambartsumian, while Hoyle and Narlikar ( 1966a) have considered this from a different viewpoint. The results obtained by Hoyle and Narlikar show that condensation of gas and dust from the intergalactic medium onto galaxies of various ellipticity could indeed give rise to the range of galaxies - spiral, elliptical, and mixed - observed today.

The most important objection to Ambartsumian's hypothesis is that it does not seem possible to have sufficient mass concentrated in a small enough region of a galactic nucleus. A mass of 1011 Me contained in a volume just greater than that of its Schwarzschild sphere (see p. 47) has a density of about 10-4 g cm-3 , which hardly seems suitable for events of the violence observed. The density of the matter in atomic nuclei is ~ 1015 g cm-3 , which is only exceeded by bodies of less than a few score times the solar mass, assuming contraction within the Schwarzschild radius cannot occur. Of course, the existence of a cloud of objects in the nucleus, each with mass~ 20 Me might be desirable for the ejection of

Ambartsumian's Fragmentation Hypothesis 31

fragments, as well as providing the large densities which seem necessary, but it is difficult to see how associations large enough to form new nuclei could then occur. If the theory is to be taken any further it seems necessary to abandon some of the ideas of 'normal' physics and to consider either the continual creation of matter in the nuclei of galaxies, an idea similar to that put forward by McCrea (1964), or the existence of singularities in an expanding Friedmann universe (see below). These two possibilities are not dissimilar conceptually, since matter which 'emerges' from a singularity is to all intents and purposes 'created' in the external world. As we will find, even fairly complex pro­blems related to these possibilities can be discussed on a worthwhile basis simply using Newtonian mechanics. But there is one particular theory which requires more than Newtonian mechanics- and, indeed, rather more than Einstein's relativity theory - in its most sophisticated form. That theory is also completely different from those discussed so far, since it makes a fundamentally different assumption about the significance of the expansion of the Universe. I refer, of course, to the steady-state theory, in the elaborate form developed by Hoyle and Narlikar about ten years ago. Since parts of that theory can be applied to other ideas which I wish to develop, this is the best time to take a closer look at it.

6 Continual Creation

If I had been writing this chapter even a year or so earlier, I might well have begun it somethiRg like this:

'The idea of a steady-state Universe in its simplest form now seems untenable, since observational evidence suggests that the Universe is evolving. But there remain applications of the idea of continual creation in local regions which could be of relevance to the real Universe and might provide a model universe which varies in form without having an origin in time.'

Such an excuse for introducing the idea of continual creation into a more or less sober discussion of the question of galaxy formation might still be deemed necessary by many cosmologists. Recently however Narlikar (1973) has published a lucid defence of the steady-state theory which leads to the conclusion that 'until the observational situation clarifies further it is premature to write off the steady-state theory'. Of course, Narlikar has long been associated with the steady-state idea, particularly in its more exotic forms, and his interpretation of the evid­ence is not the only one possible. But the fact remains that such an interpretation is possible, and it is as well that there are such people around to point this out.

I have long felt that both the disciples of the steady-state and the adherents of the straightforward 'big bang' are dealing too much in black and white, either/or issues. Both extreme groups have had to develop and modify their ideas to counter attacks from the others, and this is certainly a good thing since it encourages the rapid development of cosmological ideas. But the truth probably lies somewhere in between -I can put it no better than to echo Narlikar's succinct statement (1973) that 'my own belief is that the structure of the Universe is much more interesting and sophisticated than that suggested by either the big bang model or the steady -state model'.

32

Continual Creation 33

I have already discussed the observations of the expanding Universe which seem, naively, to imply creation at one point in time, presumably in a big bang. But there is another explanation of the observed expan­sion, and this was formulated almost thirty years ago.

The philosophy behind the steady-state theory is very simple. When we look at the Universe we find that, on a large scale, it is uniform. As far as we can see, any region containing many galaxies would be indistinguishable from any other in overall properties, just as one litre of hydrogen gas at a certain temperature and pressure is exactly the same as any other. So cosmologists formulated a 'principle', known as the 'cosmological principle' which says simply that the Universe is indeed uniform on the large scale. This provided a satisfying philoso­phical tenet on which cosmologists based many possible relativistic cosmologies during the 1920s and 1930s. But in the 1940s Bondi and Gold (1948) and Hoyle (1948) took things a step further, both philosophically and mathematically.

It is implicit in the cosmological principle that the Universe is the same throughout space; but why, if that is the case, should it not also be unchanging in time, provided long enough stretches of time and large enough volumes of space are considered? That, in essence, is the 'perfect cosmological principle' - the Universe is uniform in time as well as space - and three decades ago it really stirred up quite a controversy.

There is, of course, only one way in which the perfect cosmological principle, or steady-state theory, can be squared with the observed expansion of the Universe. New matter must be continually created to fill in the gaps between galaxies as they move apart. And this new matter must somehow evolve into the form of new galaxies, on a time­scale short enough to maintain the observed density of galaxies in the Universe. The amount of matter needed is very small, and below the limits that could be detected in a terrestrial laboratory, assuming that it is spread uniformly through space, but the emotional resistance to abandoning the 'law' of conservation of matter provided a powerful incentive for much of the cosmological work of the 1950s and 1960s. This is not the place to go into the details of the steady-state/big bang controversy again, especially since it has been so amply covered else­where (see particularly Narlikar, 1973, and other contributions in the same book). But before moving on tq the more exotic and intriguing ideas of non-uniform creation, it is relevant to look at how even the simplest, philosophical ideas of the steady-state theory provided new scope for explaining the formation of galaxies.

34 Galaxy Formation

The great thing about galaxy formation, like everything else in a steady-state universe, is that there is no longer any problem in explain­ing where the first galaxies came from. There simply never were any first galaxies, and the problem becomes one of explaining how galaxies might form in the Universe as we see it today. That means that we are dealing with properties of the Universe and physical conditions we can observe, not with conditions extrapolated from observation; all that we need is a model for the continuation of the existing population of galaxies in much the same form as we see them today.

This leads to a neat model in which galaxies moving through the gas of intergalactic space cause new galaxies to be 'born'; the intergalactic gas itself, of course, is replenished by the continual creation of new matter from the vacuum by a process, the details of which can be ignored for the galaxy formation model.

In outline, the process is very simple. As a galaxy moves through the intergalactic gas (or, from the frame of reference of the galaxy, as gas streams past the galaxy) the focussing effect of the gravitational field of the galaxy causes gas to be concentrated 'behind' it. If the density con­centrated behind the galaxy is great enough, then the gas will continue to be further concentrated by its own gravity, as the parent galaxy moves away. In other words, a new galaxy will have been created from the intergalactic gas.

Sciama has described many of the details of such a process of galaxy formation in an expanding steady-state universe (see, for example, Sciama, 1959), and he came up with some intriguing numerical results. It turns out, in particular, that only galaxies with masses around 1043 to 1044 g give 'birth' to new galaxies in the same mass range; if any more massive galaxies (up to some 1050 g) had ever existed, their descendants would be less massive in each 'generation' until self-propagating galaxies of some 1044 g were left. This ties in very well with the observed mass distribution of galaxies. Further, since sometimes the 'parent' will remain gravitationally bound to its offspring, there is i mechanism in the model to explain how clusters of galaxies grow up, and since clusters are dyna­mic systems in which energy can be exchanged between individual members there is a mechanism for individual galaxies to 'boil off into intercluster space, starting the process by which another cluster can be gradually built up (for further details and references, see Roxburgh & Saffman, 1965).

So far so good. But it turns out that in fact there are difficulties in reconciling the estimated ages of the galaxies we observe with the

Continual Creation 35

distribution of ages that would be expected according to this model; and quite apart from any other difficulties, I have a prejudice against such models because they pull the continual creation on which they depend out of the hat - 'let there be matter' seems to be the limit of their consideration of this rather important aspect of the model. So I prefer to concentrate on the versions of the steady-state theory in which there has at least been an attempt to describe the creation in mathe­matical terms, and indeed more or less within the framework of general relativity. I find this approach more aesthetically appealing, and it certainly provides a more constructive insight into what can be done to produce mathematically complete models, leaving aside for the moment the question of just how accurately this particular model might describe the real Universe.

The model of matter creation which I particularly like involves irregular creation (see McCrea, 1964); McCrea has linked this possibility with the ideas of Ambartsumian and the fragmentation hypothesis, but the only complete mathematical description of a possible mechanism for such a process is that of Hoyle and Narlikar ( 1966a and b) involving the C-field ('creation' -field).

The equations of relativistic cosmology have been discussed fully by many authors during the past fifty years or so. Sciama (1971) gives a particularly good account from the point of view of the cosmologist, and Misner, Thorne and Wheeler ( 1973) have now produced what seems to be destined to become the classic description of relativity from a mathematical point of view. So I shall simply describe briefly how the idea of the C-field can be grafted onto the framework of relativity theory. Since I could never write such a good introduction to relativity and cosmology as Sciama, and in any case such a thorough treatment would be outside the scope of this book, I shall not attempt to cover the ground where he has already beaten such a broad path. Those readers unfamiliar with these ideas are advised to start with Sciama's book; alternatively, they can just skip the seemingly complex equations on the next couple of pages, as long as they are prepared to accept my written explanation of what the equations mean.

The C-field has its source in the 'beginning' or 'end' of world lines of particles, but the terms 'beginning' and 'end' are, of course, without any distinct meaning, and could be interchanged with an appropriate reversal of the direction of time. In terms of the geometry of space-time, the C-field has the effect of contributing an energy-momentum tensor to

36 Galaxy Formation

Einstein's equations, which become

Rik - ~ gikR = -81T G [Tik - f( qck - !KikqCI.)]

Here, the speed of light (c) has been defined as unity for convenience, andfis a coupling constant which provides a means of adjusting the strength of the theoretical C-field to account for whatever observational phenomenon is being investigated. Other terms in the equation, and in those that follow, conform to the standard notation of relativity and tensor theory, and a full discussion can be found in Misner, Thorne and Wheeler (1973).

Taking the divergence of the modified Einstein's equations yields

Tik ;k = [Cick ;k

where ; denotes covariant differentiation. The C-field then contains energy which we may write as

CkCk =m2

for 'free space', that is at large distances from any concentration of matter,M, say. At a distanceR from the massM, we have (see Hoyle and Narlikar, 1966a)

CkCk = m2 (1- 2~Mr1 (c = 1)

and fairly obviously the condition for the creation of a particle or particles of mass m0 must be that

CkCk ~m6

In other words, for a C-field with a universal energy density too low for creation of particles, we may still have creation of particles of mass m0

within a distance R 0 of a body of mass M such that

So far, the equations contain plenty of room for flexibility, especially in the choice of the parameters f and m. So it is no surprise to discover that Hoyle and Narlikar ( 1966a) were able to produce results in good agreement with the observed distribution of matter, by assuming that (i) the particles created are hydrogen atoms, and (ii) as the mass M grows through the creation of new matter, a point is reached where fragmentation occurs, more or less as suggested by McCrea ( 1964)

Continual Creation 37

within the context of Ambartsumian's fragmentation hypothesis. This prevents the process from running wild, which would certainly happen if the original mass M could increase its mass to appreciably more than 2M before fragmentation.

But this is far from being the end of the story. Hoyle and Narlikar (1966b) took these ideas a step further in an attempt to explain the energy observed in radio sources and cosmic rays. At first, it looked as if the theory might have to be abandoned, because it could not explain the observed energies. But by adjustment of the coupling constant f Hoyle and Narlikar came up with a model that provided a radically different view of the Universe, and which could not be disproved by the observations.

According to this new model, the basic 'steady state' of the Universe is one with a mean density of matter of about 10-9 g em - 3• However, there is a daunting disagreement between this figure and the observed matter density, which is smaller by a factor of about 1021 • But there is a way to resolve theory and observation: it is possible, as Hoyle and Narlikar have shown, that if the C-field were to die away temporarily on a small scale then there would be regions of the Universe in which the density fell as expansion proceeded. In time, the C-field will propa­gate into these 'holes' at the speed of light from surrounding regions, so that they will be 'filled in', and the Universe does indeed present a steady-state picture in the long-term view. In other words, we may be living in a region of space which just happens to have little or no C-field at present, and is therefore described very accurately by Einstein's equations. The expansion we observe should not be extrapolated back to infinite density and a big bang, but merely to 10-9 g em -J, when our local C-field fluctuation occurred.

There are obvious problems in accepting this theory as a valid description of the Universe. Primarily, why bother with such a compli­cated model when all it seems to do is to put in an extra term to Einstein's equations and then takes it out again when applying those equations to any part of space that we can see? The adapted C-field model is by definition indistinguishable from a standard Friedmann model of the expanding Universe, and so the Friedmann model, being less mathematically complex, must be preferable.

But there is more to introducing the adapted C-field model here than setting it up simply to knock it down again. In the course of their investi­gation of what happens as a local region of space expands from a density of 10-9 g em -J, Hoyle and Narlikar (1966c) developed a description of

38 Galaxy Formation

the formation of galaxies which would obviously be directly relevant to the expansion of a Friedmann universe from the same density. So this mechanism could provide a link between any original irregularities pres­ent in the Universe (assuming a big bang origin) and the galaxies observed today. Hoyle and Narlikar present this model within the framework of general relativity, as they must in order to have scope for the C-field to be introduced and then discarded. But if we ignore the C-field alto­gether, there really is no need for anything more elaborate than Newtonian mechanics.

First, though, before taking a look at the Newtonian version of Hoyle and N arlikar' s ( 1966c) ideas on the growth of galaxies from pre-existing irregularities in an expanding universe, it might be appropriate to see how well 'Newtonian cosmology' works within the more conventional framework of an expanding Friedmann, or big bang, universe.

7 Newtonian Cosmology and Jeans' Criterion

Most of the basic results of relativistic cosmology also emerge from an equivalent treatment using Newtonian theory, although there is one stratagem that has to be used right at the beginning, because Newtonian gravitational theory cannot cope with infinities. But once used, matters become fairly simple for the Newtonian cosmologist.

The necessary stratagem is to apply all the calculations to a finite, but very large, region. In dynamical terms, the problem is essentially that of understanding the evolution of a large gas cloud, in which such objects as galaxies and QSOs are equivalent to the particles of the gas. With an infinite cloud, the gravitational potential anywhere in space would be infinite, according to Newtonian theory. So we may choose to consider a finite cloud which just happens to be larger than the volume of space we can see (rather reminiscent of the 'hole' in Hoyle and Narlikar's high density C-field universe). Then, although there is, strictly speaking, a unique centre to the cloud (which there is not in the infinite case) the problem can be solved, and the solution interpreted to provide an insight into the behaviour of the real Universe.

Provided the cloud is uniform and isotropic - as the Universe is as far as we can tell - then any point within the observable volume of space can be treated as the centre. And in that case, for anyone moving with the cloud, the velocity of any particle (galaxy or QSO) at a distance r must simply be given by

v = f(t)r (7.1)

where f is only a function of time, or the cloud would no longer be uni­form and isotropic. So immediately we have derived Hubble's law of

39

40 Galaxy Formation

expansion, without any advanced mathematics at all. The next step, using the one equation we have, is to integrate, giving

r =R(t)r0 (7.2)

(since v = r, the dot denoting differentiation with respect to time), which describes the position of the particle being studied at time t, with

1 • -R= f(t) R

(7 .3)

The constant r0 represents the position of the particle at the arbitrary zero of measurement of time, that is

R(t0 ) = 1

and with these equations the only motions possible are those of uniform expansion or contraction. And all this without even introducing Newton's laws of motion or gravitation!

When Newton's laws and other straightforward physical constraints are introduced, it is simple to build up a detailed cosmology (see, for example, Bondi, 1960). If the density of the 'gas' is p(t), then continuity of mass and momentum implies that

ap . ap 0 =-+V' .Pr =- + 3p(t)f(t) at at (7.4)

and with equation (7 .3) and R (to)= l, the integral of (7 .4) becomes

p(to) p(t) = R3(t)

The amount of matter interior to r (= R(t)r0 ) is simply

(7.5)

(7.6)

Since we are assuming spherical symmetry, the net gravitational potential due to matter 'outside' r is zero, so the force on mass m at r is

-m GM(r) r

r2 I r I (7.7)

and since this force can be equated with mr, from Newton's third law, it

Newtonian Cosmology and Jeans' Criterion 41

is a simple matter to derive the basic equation of motion describing the Newtonian model universe:

.. R ~ G (Ro)3 r = R r = - '! 1f Po R (7.8)

where G is the Newtonian gravitational constant. This equation - or rather, its relativistic equivalent - caused some

consternation some SO years ago, because it is immediately obvious that a static universe (R = R = 0) can only exist if the density p is zero. Because this equation was known before the expansion of the Universe was discovered, some attempt was made to rectify the apparent conflict with observation by introducing a cosmological constant' into the equations. This constant provides a means for zero Rand R with non­zero p; but since the Universe is now known to be expanding I see little point in elaborating on such models. Rather, it is better to consider that theory predicted the non-static nature of the Universe, which was then confirmed by observations.

Even so, there are different possible model universes implied by the basic equation (7 .8). Integrating gives an equation in R, which tells us something about the rate of expansion or contraction:

R2 = ~ 1f G p (to) _ k 3 R (7.9)

where k is a constant of integration. This is exactly the same as the result obtained by doing the equivalent calculation using relativity theory, so it seems reasonable to interpret the possibilities as indicating something about the nature of the Universe we live in.

First, there is the possibility that k = 0. If so, R tends to zero as R tends to infinity (specifically, integration gives R a: t~) and the Universe becomes more and more like a static universe as time goes on (this is essentially the Einstein-de Sitter model of relativistic cosmology).

Second, k may be greater than zero. Then, the cloud expands out to some maximum size at a time when R = 0, and then collapses in a con­tracting phase which is the reverse of the expansion. There is some difficulty in understanding what the physical meaning of the end of this collapse is, since it should proceed to a singularity; but some cosmologists have suggested that at some point before the singularity is reached there might be a 'bounce' which pushes the universe back into an expanding phase, so that the cycle can repeat.

Finally, we may have a negative value of k, and in this case there are

42 Galaxy Formation

again more than one possible models. R tends to infinity as R tends to some positive, non-zero value - that is, the cloud is still expanding even when it has become infinitely spread out. The equation cannot be inte­grated as easily as for the case k = 0, however, and all we can do is look at the limits of large and small t. At small t, we find the same behaviour

as in the k = 0 case, that is R(t) a: tl and for large t we find R a: t which implies steady expansion. The study of the further implications of these equations for cosmology and our understanding of the Universe is itself a fascinating and rewarding exercise - but rather a digression from my main theme of galaxy formation, and in any case the subject has been thoroughly discussed by, for example, Bondi (1960) and Sciama (1971). So having sketched the outline of the cosmological picture, I shall return closer to my main theme.

I mentioned in Chapter 2 the existence of 'Jeans' Criterion' for the fragmentation of a self-gravitating gas cloud, but although I pointed out that this criterion is fundamental to many theories of galaxy formation, I neglected to derive it. That omission can now be rectified - within the framework of Newtonian cosmology.

Jeans' formula was derived within the framework of Newtonian dynamics by Bonnor (1957). He took the example of a large mass of gas which obeys an equation of state

p = q(p)

and is stationary except for a small velocity u(r, t) due to wave motion related to the passage of a sound wave. If p and p are only allowed to deviate slightly from equilibrium (by an amount of the same order as u),

and squares and products of small quantities and their derivatives are neglected, then the hydrodynamical equations

au I -+(u.v)u=F--Vp at P (7.10)

and

ap at+V .{pu)=O (7 .11)

become

au 1 -=F--vp at P (7 .12)

Newtonian Cosmology and Jeans' Criterion 43

and

~~ + V' . (pu) = 0 (7 .13)

where F is the body force (due to gravity) on a unit mass. Since the gas is in equilibrium except for small perturbations

I Fo =- V' Po

Po

where the suffix zero denotes the equilibrium value. With

and

Poisson's equation gives

F=Fo+Ft

p =Po + w (Ft. w both small)

V'. F0 = -4nGp0

V'. F 1 = -4nGw

and from equations (7 .I2) and (7 .I4)

(7.14)

(7 .1 S)

(7 .16)

where we are taking the equilibrium value of dp/dp. Equations (7 .IS) and (7 .I6) then give

a 2 (w dp) -v.u=V'.Ft-V' --at Po dp

= -4nGw -v2 ( w dp) Po dp

(7 .17)

and by differentiating equation (7 .I3) and neglecting second order terms we obtain

(7 .18)

Bonnar now introduces the concept of a condensation s defined by

s = w/p 0

44 Galaxy Formation

and finds

32s+(V'Po) .(au)= 4 1rGsp +v2(s3p) 3t2 Po 3t 0 3p

(7.19)

Taking p0 as constant then giv,es the simple expression

~s= 41TGp0 s +\7 2 (s dp) 3t2 3p

(7.20)

which is the same as that derived by Jeans himself (1928) at the equiva­lent point in the calculation. The obvious snag about this step is that if p0 is constant, and therefore p 0 is constant, F0 must be zero, and the effect of gravity seems to have been entirely removed. The way round this difficulty is to say, in a rather vague fashion, that if we have an in­finite mass of gas then there can be no preferred direction for F 0 and so it must be zero. This argument breaks down as soon as we want to apply the result to a finite mass of gas, which is exactly what we do want to do, so in practical terms, as far as galaxy formation is concerned, there is no getting away from the fact that the philosophy behind the equations leaves something to be desired. That said, I will proceed to use the result without a further qualm. The equation which has become known as Jeans' criterion follows easily from (7 .20). We take a wave of length A which propagates in the x direction and look for solutions of the form

s = h(t) cos (27rx/A)

With dp/dp constant,

d2h = (47rGpo- 41f2 dp)h dt2 A2 dp

and the disturbance grows exponentially with time if

A>(__!!_ dp)t Gp0 dp

(7 .21)

So any mass of gas which has linear dimensions exceeding this limit will allow such disturbances and will be unstable. And that is Jeans' criterion for the stability or instability of a mass of gravitating gas against small fluctuations in density.

As Bonnor (1957) has shown, Jeans' formula (7.21) can also be derived within the framework of an expanding universe, and thus can be said to predict the occurrence of galaxies in a universe which is initially

Newtonian Cosmology and Jeans' Criterion 45

homogeneous. But it turns out that it is rather difficult to account for the presence of irregularities as large as the galaxies we see today, assum­ing that the Universe started from a homogeneous big bang some 1010 yr ago, unless we consider models in which the cosmological constant is non-zero (see p. 41 ). Since the best evidence, for extrapolating the observed expansion of the Universe backwards in time, is that the Uni­verse is indeed about 1010 yr 'old' (that is, about 1010 yr ago all the matter we observe was concentrated in a monobloc), this raises some considerable difficulties. One could argue that it provides a case for considering models with a non-zero cosmological constant in detail; I prefer, however, to argue that this timescale difficulty suggests that the Universe has not evolved from a perfectly homogeneous situation within the past 1010 yr. As I shall show, this approach leads to a persuasive view of galaxy formation within a framework which takes account of the presence of unusual active galaxies and even such exotic objects as QSOs.

8 The Retarded Core Hypothesis

In most ways, the hot big bang model of the universe is a good explan­ation of what we see around us. But if the Universe began from initially homogeneous and isotropic conditions, galaxies could not have formed in the time available. There is no reason why we should expect the initial condition of the Universe to have been one of perfect homogeneity and isotropy; it is quite permissible to postulate that the inhomogeneities which have given rise to the galaxies we see today were present at the very earliest stage of the exploding Universe. The latest discussion of this possibility is provided by Zel'dovich and Novikov (1974), and the problem is also mentioned by Misner, Thorne and Wheeler (1973).

Although we can postulate any amount of initial irregularity we need, some cosmologists argue that if initial perfect homogeneity has failed to explain the presence of galaxies in the Universe, we should next consider perfect inhomogeneity - that is, a random situation of universal chaos. I do not share this view, and I see no reason to expect the initial conditions to be 'perfect' in any sense. But fortunately it seems that this raises no problem. Several people have studied how a universe might evolve from initial chaos, and it looks likely (although it cannot yet be proved) that within a few seconds after the initial big bang such a universe will have smoothed itself into a nearly homogen­eous and isotropic situation very much like the Universe we live in. So whether we take initial chaos, or whether we say that there may have been some lesser degree of initial inhomogeneity, provided that we consider only events from a few seconds after the big bang the models are essentially the same. In either case, what we have now to consider is how galaxies might grow from irregularities which have been present since very early on in the evolution of the Universe.

46

The Retarded Core Hypothesis 47

Some ten years ago, Novikov (1964) discussed a model Friedmann universe which contained inhomogeneities in the form of 'cores' of delayed expansion. The idea is that such cores would themselves be expanding from a singular state, in much the same way that the Uni­verse itself is expanding, but at different rates. At about the same time in the mid-1960s, Ne'eman also considered the same kind of model universe (Ne'eman, 1965), and the model has many attractive features.

Many people have considered the possibility of gravitational collapse as the energy source for quasars and radio galaxies, the most energetic objects in the Universe (see especially Hoyle et al., 1964). When any diffuse cloud of matter condenses, energy is released. This energy comes from the gravitational potential energy of the cloud, and such a process of energy generation is potentially the most efficient possible. For a cloud of mass M, the ultimate collapse which could be observed from the outside world would be to a radius of r = 2GM/c2 , where G is the constant of gravitation and c is the speed of light. Once this situation is reached, the 'cloud' has become so dense that light cannot escape from it - the escape velocity exceeds the speed of light - and we have a black hole. This radius, which corresponds to the so-called Schwarzs­child limit, marks the limit beyond which the collapse takes the matter out of visible contact with the outside Universe, and if a diffuse cloud collapses to the Schwarzschild radius then the energy released is !-Mc2 -

that is, 50% of the rest mass energy of the cloud. The physical singularity associated with indefinite collapse occurs at a mathematical point (or in some cases a line) where literally infinite densities must be produced if the collapse does not halt. The Schwarzschild limit marks another kind of singularity in the mathematics; for a fair-sized collapsed mass a physical object - even a living person - could cross this limit without harm. But once crossed, in an inward direction the limit could never be recrossed - no object or radiation can escape once it has reached this part of the Schwarzschild 'throat'.

Now, !Mc2 is far more energy than any thermonuclear process, and the only way more energy could be obtained would seem to be by the com­plete annihilation of matter, which would be possible if it came into contact with antimatter. The sort of energy needed to power a QSO or a powerful radio galaxy is 1062 erg, and that energy could, in theory, be produced by the complete collapse of only 108 solar masses - a 'mere' 1 o-4 or so of the mass of a galaxy.

There are snags with this model, and in particular it is not easy to see how the energy would be converted into the observed spectrum of radio-

48 Galaxy Formation

frequency and cosmic ray emission. The plausibility of the detailed model was not helped when Hoyle et al. ( 1964) invoked the negative energy C-field to produce oscillations in their model QSOs, which con­flicts with general relativity, where only 'one way traffic' is allowed through the Schwarzschild 'throat' (Kruskal, 1960). But it provides an important reminder that on the large scale gravity is the most important force, and the most important energy source, in the Universe - indeed, it is gravity that drives the Universe itself.

In any case, though, as more evidence is gathered from observations of violent objects in the Universe, the more it seems that these are involved in violent expansion- explosions- and not in collapse. So it seems natural to look at the reverse of the gravitational collapse model, and to consider monotonic expansion from local singularities which can occur within the framework of the overall expansion of the Universe from its own initial singularity. Such expanding objects could explain the presence of QSOs in the Universe and, at a later stage, might form the massive objects required for galaxy formation on Ambartsumian's hypothesis.

For simplicity, consider an expanding Friedmann universe which is homogeneous except for certain spherical regions which were 'delayed' and failed to expand for some time with respect to the rest of the universe. It is important to notice that if such a core expands at some later time then an external observer will be able to see the entire expansion process, starting from a point, and not just that part of the expansion which takes place outside the Schwarzschild sphere. As is explained by Novikov and Ozernoi (1963), for a collapsing object light rays emitted while inside the Schwarzschild radius can never reach an external observer, but rays from the external universe can penetrate to the object. Time reversal of this process implies that rays from the object can reach an external observer for an expanding object, but until reaching its Schwarzschild radius the object cannot 'see' the external universe.

If a sphere of gravitating matter is considered it is apparent that it may either expand to infinity, or expand to a size less than the gravitational radius and then contract, just like the whole Universe. For the latter case, an external observer will see only the early stages of expansion- from their viewpoint the co-moving space is semiclosed. A detailed discussion of such semiclosed spaces is given by Zel'dovich ( 1963a, b). The reason for the delay in expansion of the cores may be considered as part of the boundary on the origin of space-time as we

The Retarded Core Hypothesis 49

know it, but Lifshitz, Sudakov, and Khalathikov (1963) have also con­sidered a contraction of the Universe prior to the expanding phase observed today, such that inhomogeneities in the earlier phase cause the delay in expansion of cores in the current phase. It is sufficient for the present purpose, however, to postulate the existence of delayed cores and consider the physical appearance of such cores to an external observer, disregarding events prior to the time when the density of the core considered was infinite.

Novikov (1964) has considered a model in which the cores are sur­rounded by spherical regions of empty space, so that the external universe produces no net gravitational field in the 'vacuole' (the vacuole model was discussed by Einstein and Strauss (1945)). The expanding object behaves much as the expanding universe in a Friedmann model, but once it has expanded beyond its Schwarzschild radius the expanding matter may interact with infalling matter attracted by the object's gravity, such infalling matter possibly arising from the ejection of successive shells by the core. Both Novikov and Ne'eman point out that such conditions are highly favourable for the emission of intense radiation, so that a mechanism is readily available for the transfer of gravitational energy into other forms.

The immediate appeal of this model, in an intuitive way, is obvious. Together with Ambartsumian's ideas, it offers the basic framework of a unified theory explaining the formation of QSOs, galaxies and all other objects in the Universe in terms of the formation of the Universe itself. As Novikov has mentioned, we have no definite knowledge of any object that is in a state of gravitational collapse, but we do know of at least one system- the Universe itself- which is in a state of anti-collapse; so it could be argued that, other things being equal, anti-collapse is a more plausible explanation of astronomical and cosmological phenomena than collapse.

So the picture of the Universe which appears now to offer the best hope of explaining the existence of galaxies and other irregularities such as QSOs seems to me to be what might be called the 'lumpy' relativistic model. The only major conceptual difficulty is the presence of delayed cores of expansion, since the rest follows easily from their presence. So perhaps it is worth digressing slightly to provide a 'physical reasonable­ness' argument for their existence, before looking at details of how galax­ies might grow up around them.

If it is accepted that the Universe is inhomogeneous then the existence of delayed cores as described above follows inevitably in a universe

50 Galaxy Formation

which expands from infinite density. Consider contraction, from which the expanding model is obtained by time reversal. Let the average density of a region A be p A, and let there be regions B and C inside A such that PB > Pc (see Figure 2). A sphere of given radius has mass pro­portional to the density within the sphere, and the radius of the Schwarzschild sphere associated with a mass m is given by

2Gm R =--am s c2

that is

Rs cx:p

so if

PB >Pc

then

assuming B and C each have the same radius. If A now contracts homo­logously then region B will reach its Schwarzschild radius before region C, so an observer in C will see B disappearing 'inside' its Schwarzschild radius. Time reversal implies that in the expanding universe observers in regions of less density will see the 'emergence' of regions of greater

A

Fig. 2. Representation of a region of the universe A which is uniform in density except for the two spherical regions B and C, B having greater density than C

The Retarded Core Hypothesis 51

density from 'within' their Schwarzschild spheres at times correspond­ing to the densities of the constrained regions. Kruskal (1960) has pro­duced a rigorous mathematical treatment describing this kind of expansion; in the equivalent contracting case a given region will tend asymptotically to the Schwarzschild limit, and for expansion the process is equivalent to expansion from the limiting situation starting at time t = - co. (It is worth noting in passing, however, that one of the more exotic suggestions of Hoyle and Narlikar (1967) is that the sign of the gravitational constant changes at the Schwarzschild radius. That would, of course, invalidate the above argument).

So both mathematically and in terms of physical reasonableness we can understand the existence of irregularities at an early stage in the expansion of the Universe. The obvious question still to be answered is: will these irregularities develop into anything like the galaxies we see around us? The answer seems to be yes, but in order to find it we must turn once again to a more rigorous mathematical argument.

9 The Growth of Irregularities in an Expanding Universe

As I have already mentioned, Hoyle and Narlikar considered the forma­tion of galaxies in their modified steady-state model. Since this model involves expansion from a denser state and is essentially indistinguishable from an expanding Friedmann model, the same arguments should apply to the case of expansion from a hot big bang, provided that the exist­ence of massive inhomogeneities is postulated. These could well be the retarded cores discussed in Chapter 8, but any compact, massive inhomogeneity will suffice, whatever its origin. Provided that we con­sider in detail only what happens in the delayed cores after they have completed the first stage of their expansion and have grown beyond their Schwarzschild radii, we may once again simplify the calculations by using the Newtonian equations- specifically, the Newtonian analogy to the Einstein-de Sitter model universe.

So for a homogeneous expanding cloud of massM we have

•2 2GM r =-­r

Ideally, the calculation should be carried through with some mass - the retarded core - kept within some confine (presumably its Schwarzschild radius) at the centre of the cloud from the start of expansion. But that involves a full mathematical treatment, and a simpler calculation in the Newtonian approximation may suffice to indicate the broad outlines of what is going on. The trick is to allow a mass J.1 to appear at the origin of rat a time when r = r0 • As it stands, that assumption can be as accurate

52

The Growth of Irregularities in an Expanding Universe 53

as we wish, since we have not yet spe·cified either p. or r0 • And if such a mass does appear then subsequent expansion will obey the equation

r2 = 2G (M + p.)/r- 2Gp./ro

so that the cloud expands to a maximum radius given by

Tmax =(1 +M/p.)ro -(M/p.)ro (M~p.)

and then falls back. Since M is the mass interior to r, the outer regions expand to greater maximum radius than the inner regions.

In the Einstein-de Sitter cosm~logy with spherical symmetry we have

where

S a: T' and c = 1

Transforming to locally flat space-time (for an observer at R = 0) gives ds2 = dt 2 - dr2 - r 2 d.Q2 +(local gravitational effects) and the local gravitational effects may be included as a fourth order term such that

(9.1)

where M is the mass interior to r, proportional to r 3 for uniform density. Equation (9.1) is the Newtonian result to first order, and the effect of a mass p. at r = 0 may be included by writing

ds2 = dt2 [1 - 2G (M + p.)/r] - dr 2 - r 2 dil2

where M is now the mass of the cloud interior to r and not the total mass (cloud+ core) interior tor.

It is possible to represent the solution of the local gravitational pro­blem by a power series in the dimensionless parameter 2G(M + p.)/rc 2

which is small for a local problem. The first term in the series is the Newtonian solution for the effect of p. and may be used to good approximation provided that the second term in (GM/rc 2 ) is smaller than the first order term in (Gp./rc 2 ) that is, if

2 Gp./(rc 2 } > [2GM/rc 2 ] 2

This must hold for all r, including r = r0 , so

To> (M/p.) 2GM/c 2

54 Galaxy Formation

if the problem is capable of solution by the Newtonian approximation. This corresponds to

(9.2)

The argument here comes close to being circular, but seems fairly plausible. What we have found is that if the Newtonian approximation is valid, then the maximum radius reached by the expanding cloud with a retarded core at its centre satisfies inequality (9.2). Now, the whole purpose of this calculation is to come up with a mathematical descrip­tion of something which looks like a galaxy, so we can put a typical galactic radius- say 3 x 1022 em- into inequality (9.2) as the value of Ymax· If that is done, the inequality holds with a central mass J.1 of 109 Me acting to retard the expansion of a cloud of mass M = 1012 Me With those figures, we can also set a limit of 3 x 1019 em on r 0 .

Putting all these figures together, we can say that for such a mass (109 Me) the value of r 0 is much greater than the appropriate value of r8 • And, most important of all, we do indeed find that for galaxy-like objects the assumption that J.1 ~M is plausible.

All this does not, of course, prove that there must be collapsed objects at the centres of galaxies. But it suggests that the idea is not unreasonable and that is the best that can be hoped for for many astronomical ideas. Since the theory assumes that the mass J.1 is only present for r;;;;. r 0 some modification would be necessary for an accurate description of the 'real' situation when J.1 is present from the start of the expansion; this is unlikely to affect the overall argument, but suggests that no real confidence should be placed on the exact value of J.1 found above.

The important conclusion is that a mass of reasonable size can restrain a cloud with mass comparable to that of a galaxy. If r 0 is less (and r0 would presumably be the Schwarzschild radius of the mass J.1 in a rigorous treatment) then less than 109 Me is required to restrain a cloud of mass 1012 Me within a radius of 3 x 1022 em.

But that, of course, is not the full story. What will the clouds restrained within these limits actually look like? In order to investigate this aspect further, I assume that stars form in the cloud of gas expand­ing about the central mass. From equation (8.2)

I M =constant (J.12 Ymax)"! (9.3)

where taking the equality in equation (9.2) implies that we are con­sidering the minimum radius within which the mass J.1 can restrain mass M

The Growth of Irregularities in an Expanding Universe 55

Because of the symmetry of the cloud, the outer layers have no gravitational influence on events near the centre and the mass interior tor may be found by setting 'max= r in equation (9.3).

I M, =constant X r'J

The mass contained in a shell of thickness drat distance r is thus

Mr+dr- M, = (M, + (~) dr)- M,

and the volume of the shell is

_2 =constant x r 3 dr

4rrr 2 dr =constant x r 2 dr

so the mean density at r is _2

r 3dr _ s Pr = constant x - 2-- ex r 3

r dr

and if all stars have the same luminosity function then the emissivity per unit volume at r is

To an external observer, the intensity distribution will be seen as .s.

I,= r I, ex: r-3

for a spherical distribution. This result agrees very well with observations of galaxies. The

standard astronomical rule of thumb for the intensity distribution was derived by Hubble from observations, and is simply an inverse square law,

I, ex: ,-2

In fact, the (-5/3) law derived above is in even better agreement with observation than this rule of thumb (see, for example, Liller, 1960). The theory breaks down, of course, in the central regions where relativistic effects must be considered, and we do not see infinitely bright centres to galaxies, although very bright spots are observed at the centres of most elliptical galaxies.

Deviations from the Einstein-de Sitter expansion may be repres­ented by imposing a rate of strain tensor and a rotation of the cloud

56 Galaxy Formation

about the mass 11· Hoyle and Narlikar (1966a, b and c; 1967) have looked into this problem within the framework of their model, and us­ing the full relativistic treatment; there seems little point in reproducing their calculations here, but the basic results are as follows.

For the rate of strain, Hoyle and Narlikar obtain

or

Ymax = r0 ( ~) (1 -AiM t) -I in direction i (i = 1 ,2,3)

where the A.i are constants. This is the same as the unstrained result except for the factor (1 - A.iMtr1 . Rotation is in fact negligible, since it is a second order effect, and would be swamped by the rate of strain term. 1

If the A.iM7> term is negligible, then the spherical case discussed above I

is recovered. A.iMti ~ 1 implies that the cloud is dissipated in at least I

one direction, but the most interesting case is AiM" ~ 1, when it is found that stable galaxies of various forms are possible. These forms were discussed in some detail by Hoyle and Narlikar (1967), who con­cluded that in general an ellipsoidal form with unequal principal axes will result, the axial ratio depending on A.iMi.

Motion of the object 11 relative to the substratum will modify the shape of the resulting galaxy. If 11 moves in the direction x 1 then in the x 2 and x 3 directions the effect is analogous to rotation and may be neglected. In the x1 direction a strain term appears, with opposite sign for the +x 1 and -x 1 directions, so that the radius is increased in one of

I these directions and decreased in the other by a factor (1 + I Ail M 7>r 1 ,

changing the total extension of the galaxy along x 1 by a factor (1 -A.] M!r1, with J1 no longer in the geometrical centre of the observed optical distribution.

This provides an overall picture of a system of galaxies very similar to the elliptical galaxies which are observed in the Universe (see, for example, Shapley, 1972). So far this model offers no explanation for the existence of spiral galaxies, since their angular momenta preclude the possibility that they have formed by expansion from more com­pact structures. But there is no reason to suppose that some form of condensation could not take place, since the model allows the presence of large quantities of matter in the region between the original inhomo-

The Growth of lnegularities in an Expanding Universe 57

geneities. Thus spiral galaxies could form by some other process, although it seems reasonable that condensation will take place more readily onto the elliptical galaxies already present, assuming that the radiation pressure from these galaxies is not so strong as to prohibit this, which could occur for the very large elliptical galaxies observed to be intense radio sources. Such mixed spiral/elliptical galaxies will have an overall structure depending on (i) the mass of the elliptical compon­ent relative to that of the disc, and (ii) the shape of the elliptical component, and its orientation relative to the disc.

Condensation onto a spherical galaxy may be expected to form a system of the Sa-Sc type, with the disc tending to force the spherical component into rotation and hence oblateness. Condensation onto prolate elliptical galaxies could occur with the angular momentum vector of the disc parallel to the long axis of the ellipsoid, in which case there will again be a tendency for the ellipsoid to be changed in shape through a spheroid to oblateness, or the condensation could occur with the angular momentum vector perpendicular to the long axis, giving a barred spiral structure.

Two tests of this model are immediately apparent. First, if elliptical galaxies are found to have rotation then the theory is obviously not applicable to the real Universe, but this test is very difficult observa­tionally. Second, and more susceptible to observation, study of our own Galaxy should be able to yield evidence for or against there being a definite two-component structure. As an extension of this approach, it also seems desirable to investigate the possibility that QSOs, violent galaxies and quiet galaxies like our own might form some kind of evolutionary sequence related to the outburst of a retarded core, its assimilation into the Universe around it, and the quiet respectability of its old age.

10 Evolution of Galaxies

Galaxies come in a wide variety of shapes and sizes. Until now, it has not really mattered for the purposes of this book just how galaxies differ from one another - we have been primarily concerned to account for their existence, and have considered them as 'test particles' which enable us to observe the expansion of the Universe. But if we are to find out any more about the nature of galaxies and how they evolve -which is, after all, part of the story of how the galaxies we see today have formed - then we must now take a closer look at the different basic types of galaxies.

Our own Galaxy is a spiral, a member of one of the two most common classes of galaxy. Spiral galaxies, as their name suggests, have a spiral structure which makes them look rather like whirlpools of light on astronomical photographs. They have a central condensation of stars, around which spiral arms of dust, gas and stars are wound, and in general the stars in the arms are younger (so-called Population I) while the stars of the central condensation are older (Population II).

Of course, not all spiral galaxies are the same. The family includes both tightly wound and loose spirals, and intermediate cases, and there are also barred spirals, in which the central condensation or nucleus forms a bar between two spiral arms which extend on opposite sides of the nucleus. Such galaxies only have the two spiral arms. It is possible to break down these groups still further, on the basis of the degree to which the arms are developed and so on, but basically spirals divide into the two categories - regular and barred - and the most significant feature about them, apart from their shape, is the two-component nature of their stellar populations.

The other principal category of galaxies is the ellipticals. These are lenticular, so they look elliptical on the sky, which gives them their name. It is generally accepted that most low-mass galaxies are elliptical, and it is even possible that there is a smooth gradation between the

58

Evolution of Galaxies

smallest of these galaxies and the globular clusters of stars which are found in large galaxies.

59

By contrast to this, however, the biggest and brightest galaxies known are also ellipticals - giant ellipticals - and these may be several times as massive as our Galaxy, which has a mass of some 1011 M ~. So the range in size of ellipticals is far greater than the range in size of spirals; and there is another important difference - elliptical galaxies contain only old, Population II stars. In other words, ellipticals are in some respects like spirals without any arms, or alternatively spirals are like ellipticals with arms.

That comparison raises the 'chicken and egg' problem which con­fronts anyone trying to trace an evolutionary path between the different kinds of galaxies. There are even a few galaxies which seem to fill the gap between spirals and ellipticals, and these are called SO systems. They have flat discs with no spiral structure, surrounding spherical or elliptical nuclei. But which way should the evolutionary path, assuming that it exists, be traced?

There has from time to time been support for the view that the open spirals are at the beginning of a sequence in which the arms become more tightly wound and the stars age until we are left with first an SO and then an elliptical galaxy (see, for example, Oster, 1973, p. 303). But as Oster also points out there are very old stars at the centres of all galaxies, and even on this evolutionary interpretation the ellipticals may simply have developed more rapidly than the spirals from the same time at which formation began.

But I do not find this kind of evolutionary picture attractive. Why should some galaxies - with identical masses - evolve faster than others? And if ellipticals and globular clusters contain primarily old stars, surely,it is more sensible to consider spiral structure as an addition which has become tacked on to some galaxies? In that case, the evolu­tionary pattern becomes more naively intelligible. Globular clusters and associations right up to the size of giant ellipticals formed first, and those galaxies lucky enough to gather in a good crop of dust and gas from intergalactic space then grew spiral arms containing younger stars. That is certainly the direction of evolution which appeals to me, and since our understanding of galactic evolution is so poor I am free to con­centrate on such models until something comes up to prove that they do not work. But I should stress that this is a personal choice, and that I am not here attempting to prove that this evolutionary path is prefer­able to the reverse, or even that the different kinds of galaxy do form

60 Galaxy Formation

an evolutionary sequence at all. I am merely saying that evolution of the kind I wish to discuss is not impossible, and has some intuitive appeal.

There is one more class of galaxies to be mentioned before moving on to paint the details of this evolutionary picture, and that is the large irregular galaxies. Objects such as M82 show evidence of gigantic explosions which have occurred at their centres, hurtling matter out­wards and destroying any structure the galaxy may have had. Other objects show evidence of equally energetic but more organised activity, such as a jet or spike apparently being shot out from the nucleus in one preferred direction. Of these energetic galaxies, two kinds are particularly worthy of note. TheN-type galaxies are seen on photographs as bright, star-like objects with very faint envelopes; and the Seyfert galaxies are rather similar looking objects which can be clearly seen to possess spiral arms. These are both classes of strong radio source, and in some cases have been identified at x-ray and infrared frequencies. Clearly, they represent systems where violent events are occurring at the centres.

It is probably fairly obvious, even on the limited evidence presented here, where my supposed evolutionary sequence lies. If we start with QSOs and progress through N-galaxies and Seyferts to ordinary quiet galaxies we have a sequence in which the neighbours at any point are virtually indistinguishable from one another, as several people have pointed out. On the other hand, we could argue that QSOs are simply the same kind of event, occurring in a galactic nucleus, as that which produces N-type and Seyfert galaxies. That idea has become even more attractive recently, with the discovery of evidence that the object BL Lac may be a normal galaxy with a QSO at its heart (Oke and Gunn, 1974). But whether you argue in favour of an evolutionary sequence, or whether you say that all galaxies have the potential to be N-type, Sey­fert or QSO, and that they exercise this potential from time to time, the same fundamental concept of all galaxies, QSOs and so on as related phenomena- part of the same family - is implied. The reason why they look so different from each other on the surface is because of violent events associated with their nuclei and so the nucleus ought to be the place to look to unravel secrets of the evolution of galaxies.

Once again, I will not try to cover comprehensively all the relevant ideas about galactic nuclei, but over the past few years several people have considered the possibility that there might be black holes at the centres of some or all galaxies- including our own (Lynden-Bell, 1969). I will take one such study as an example, repr~ducing some of

Evolution of Galaxies 61

the arguments used by Wolfe and Burbidge (1970) in a paper on 'Black Holes in Elliptical Galaxies'.

Wolfe and Burbidge start with the basic observational evidence, that the average mass of a bright elliptical is 8 x 1011 M0 and the mass-to­light ratio, in terms of the solar equivalent, is about 70. It is fairly straightforward to work out from this, using astronomers' knowledge of stars in our own Galaxy, that the stars responsible for the light from these ellipticals can only account for about 25% of the mass; the miss­ing mass, it is suggested, must be present in the form of diffuse matter, very low mass dim stars, evolved dead stars, or black holes.

A black hole (see Chapter 8) is just a collapsed object from which light cannot escape, and this could be a dead star about twice as massive as our Sun, or even the whole Universe, if the latter is 'closed'. A lot of nonsense (and a smaller amount of sense) has been written about black holes in recent popularisations, but that need not concern us here. We need only accept that any sensible theory of gravity (including Newton's) requires that a sufficiently dense body will have an escape velocity greater than that of light, and will be invisible to an outside observer- it will be a black hole. Wolfe and Burbidge present plausible arguments that the black hole explanation is the least un­likely account of the missing mass in bright ellipticals, and they point out that although there is no comparable mass-to-light problem with spirals, there is sufficient leeway to allow for a few per cent of the mass of such galaxies to be locked up in a black hole or holes. It is when they look at the implications of this that the story starts to become interesting.

The explosive events which I have already mentioned seem to occur in the nuclei of both spirals and ellipticals, and the most powerful explosions, generally in elliptical galaxies, produce radio sources which can only be explained in terms of an energy of 1061 erg, equivalent to the mass energy (mc2) in 107 Suns. Such energy generation must involve gravity, and must involve concentrations of mass within a few parsecs at the nuclei of galaxies. Since the outbursts seem to be recurrent, the energy available must be more than the minimum needed to explain one outburst, so the total mass needed is likely to be around 109 M0 , or more.

In terms of its mass, the Schwarzschild radius of an object (in em) is given by

62 Galaxy Formation

so for a core of mass 109 to 1011 M 0 we are talking about radii in the range 10-4 to 10-2 pc. If the appropriate mass lies within the appro­priate value of Rs, then we are talking about a black hole.

According to Wolfe and Burbidge, 'on the basis of conventional theory, it must be argued that ellipticals which have given rise to radio sources contain black holes' simply because of the energy requirement which implies that such large masses are indeed concentrated within such small distances from the centres of such galaxies. Starting from the observed distribution of stars in such galaxies, Wolfe and Burbidge find that the mass of any central black hole must in general be less than 1010 Me, and if they assume that the system of stars which makes up such a galaxy is relaxed, the upper limit on the mass of the black hole is 109 Me. This calculation, which is just the reverse of the calculation presented in Chapter 9 (seep. 54), has produced exactly the same answer. Previously, we found that a central 'retarded core' of less than 109 Me is sufficient to restrain a galaxy of 1012 M0 and produce a distribution of stars like that observed; Wolfe and Burbidge show that such a distribution of stars, together with the evidence of violent out­bursts, implies the presence at the centre of a black hole of mass up to some 109 Me.

So this provides a powerful new argument in favour of the presence of collapsed objects at the centres of galaxies. But these objects need not, in fact, be black holes in the conventional sense. It is far easier to understand the association of such radio galaxies and other energetic sources with the outward flow of matter that is observed if we stick to the retarded core hypothesis. In that case, it is more sensible to talk about these superdense regions as 'white holes' - objects which were collapsed, but are now expanding, perhaps not smoothly but in a series of outbursts, and pouring matter out into the Universe.

This, in itself, is a sort of matter creation, and there is still Gust) room for theories which take the process a step further and say that matter is indeed created in the nuclei of galaxies, but this seems to me an unnecessary complication of what is in essence a very simple idea.

So we have a situation in which either a simple evolutionary picture or a repeated outburst model can apply. QSOs are simply the strongest outbursts of retarded cores, and galaxies form, perhaps, from the matter ejected in these outbursts but restrained by the gravity of the core. Less violent, but still dramatic, explosions in the cores of galaxies could pro­duce the diversity of radio sources, Seyferts, N-galaxies and the like, and in between outbursts we would see ordinary ellipticals and spirals,

Evolution of Galaxies 63

gathering strength for the next explosion. In some cases, perhaps the core has exhausted its capacity for violence, and we see galaxies which really have settled down into respectable old age.

And we should not forget Ambartsumian's ideas - globular clusters, and even new galaxies, could be formed from bits ejected from the core (along jets?); in that case, it would be tempting to identify this process with the formation of Population II stars, and 'conventional' collapse of dust and gas clouds with the formation of Population I stars as found in spiral arms, although it is possible that the arms themselves might define the 'wake' of something ejected violently from the galactic nucleus.

That kind of speculation on the basis of slender (but appealing) evidence shows why the study of galaxy formation is so fascinating, but it would be stretching the evidence too far to attempt a more detailed explanation of the observed varieties of galaxies at this stage. So perhaps it is time to move from the general to the specific, and take a look at our own Galaxy, where we certainly know more about events on the stellar scale, even if it is not always easy to see how these relate to the more general question of galaxy formation.

11 Our Galaxy

Although spiral arms form such prominent features in photographs of many galaxies, their apparent importance exaggerates their true relation­ship with the rest of the galaxy being studied. The Population I stars which trace the spiral arms are very hot, bright bluish-white giants, some as much as 100000 times as bright as our Sun. The Population II stars which characterise central regions of spirals, and make up the whole of ellipticals, may be only I% of the brightness of such typical Population I stars, so it needs a lot of Population II stars to produce a display as impressive as the appearance of even a scarcely populated spiral arm. The other prominent feature of our own and other galaxies is provided by the globular clusters - dense, spherical concentrations of up to 100 000 Population II stars. These clusters are themselves distributed throughout a spherical volume of space centred on the nucleus of the galaxy.

It was only in the 1940s that Walter Baade's work showed that the spiral structure of the Andromeda galaxy is outlined by a relatively few bright blue stars, and not until 1951 that optical astronomers armed with this information first used Population I stars to trace part of the spiral structure of our Galaxy. It now seems that the straightforward classification into two Populations was rather naive, and there should in fact be a handful of Populations. But that kind of refinement is definitely taking us into the realm where we would not see the wood for the trees, so in terms of the basics of galactic structure there is still some merit in keeping close to the concept of just two stellar populations.

The optical astronomers were only just in time when they started out to study the spiral arms of our own Galaxy a quarter of a century ago, because the then new science of radio astronomy was soon turned to the same problem, and provided a wealth of data in the form of maps of the 21-cm hydrogen emission from clouds of gas and dust within the

64

Our Galaxy 65

Galaxy. There is still something of a dispute about how conflicting evidence from the optical and radio studies should be resolved. But enough is known to describe the layout of the Galaxy in general terms.

Our Galaxy is a flattened disc about 80 000 light years across, and about 5 000 light years thick, with a bulge at the centre about 15 000 light years thick. The whole system is rotating, but not as a solid disc, and the Sun, for example, takes about 200 x 106 yr to complete an orbit around the centre. The spiral arms seem to be fairly tightly wound around the centre, and are almost circular according to the best models -by which I mean, of course, the models that I like best! There are three or four loops of the spiral between the Sun and the galactic centre, and although for a time there was wide support for the theory that these arms are permanent features fixed by the pattern of the Galaxy's magnetic field, it now looks as if they are more ephemeral phenomena, like waves on the sea, formed by gravitational forces.

Between the arms of our Galaxy, as in other spirals, there is no dust and little or no gas; the Population I stars have formed by collapse of locally dense regions within the great sweep of gas and dust which is in fact the dominant feature of spiral galaxies. Hydrogen gas in a thin disc in the plane of the Galaxy expands outwards at speeds of up to l 00 miles a second, and at least one major feature of outward moving material has been christened the 'expanding arm', moving outwards at 30 miles a second over a front lO 000 light years wide. This implies movement of an amount of matter equivalent to the mass of the Sun out from the centre each year, or 200 x 106 M8 during one rotation of the Galaxy. This is a lot of matter even for a galaxy, and there is an obvious question: where does it come from? It has been argued that the outward flow is balanced by an inward trickle of new gas falling onto the nucleus from all directions, but I do not find this idea attractive. Rather, it seems to me that we must look for a mechanism in the nucleus itself.

During the past few years it has become very clear that the nucleus is the site of unusual astrophysical processes. The infrared emission, for example, is so strong that it is on a par with that from the bright nuclei of Seyferts, and this must be taken as a strong hint that all galaxies have such energetic nuclei. One of the most intriguing possibilities was put forward by Lynden-Bell (1969), who suggested that there might be a QSO at the centre of our Galaxy, albeit possibly a dead one. Lynden­Bell started out from an estimate of the numbers of QSOs in the sky, which showed that there is a good chance of finding one in the local

66 Galaxy Formation

group of galaxies. So, he argued, where in the Local Group is the best place to look? Assuming that a dead QSO must be a massive object which would soon collapse inside its Schwarzschild radius, it would be detected only because of its gravitational field. But that gravitational field could well attract so much material to the resulting black hole that a swirling mass of dust and gas would surround it. In that swirling cloud, we might well expect stars to form. In other words, the dead QSO should be at the centre of a spiral galaxy.

This picture is plausible since matter cannot fall into the plughole of the black hole until it has lost angular momentum, essentially, on Lynden-Bell's model, by the frictional twisting of the magnetic field in the gas cloud, and ultimately by the acceleration of fast particles. In the outer part of the resulting whirlpool, accelerated particles become cos­mic rays, but in the inner regions collisions convert the energy of the particles into heat and the kind of intense radiation that we do indeed observe coming from the galactic nucleus. In order to explain the observed intensity of the infrared source at the nucleus, only w-s M6

need disappear into the plug-hole each year, although appropriately faster rates would be needed to account for the radiation from Seyfert nuclei.

That idea is reasonable, as far as it goes, and the idea that QSOs are at the centre of most or all 'normal' galaxies is now even more plausible since the discovery of evidence that BL Lac is a QSO embedded in an elliptical galaxy (Oke and Gunn, 1974). But it does not quite tie in with all the evidence of expansion and outward flow of matter discussed above. The data used by Lynden-Bell can also be accommodated within a model for our Galaxy which does indeed have a QSO at the centre, but in which the QSO is, or was, a retarded core. The globular clusters and central regions of the Galaxy could then have formed by a process similar to that outlined in Chapter 9, and the spiral arms by one of two possible mechanisms.

First, we could indeed have some kind of accretion of intergalactic material onto the dead QSO, retarded core, or whatever. But I prefer the second alternative- that violent outbursts associated with the retarded core (perhaps the very same kind of outbursts that are now being observed in active QSOs) have flung out chunks of collapsed matter along with other material. These pieces of primeval core could leave a wake of matter behind them, and in time rotation would wind such a jet into a spiral form. It would be natural to expect such a pro­cess to produce jets like those observed in some QSOs and peculiar

Our Galaxy 67

galaxies, and we might also expect that symmetric outbursts would be common, giving rise to the kind of expanding double source which is found to be so common by radio astronomers.

That is certainly moving us into the realms of speculation. There are probably few astronomers who would go along with such a model of our Galaxy in its most naive form, but they might, perhaps, be hard pressed to justify fully their objections to this kind of model of galaxy formation. Bearing in mind the detailed knowledge we have of our particular galaxy, however, it is perhaps better to move out again to take an overview of the general situation in order to see just where the study of galaxy formation stands today, and just where it is likely to be going in the immediate future.

12 The Present Balance and Future Prospects

We have seen how simple ideas of conventional physics can be applied to the problem of a self-gravitating gas cloud, and that under certain conditions such a cloud will fragment into subsystems not unlike star clusters. But it has proved very difficult to show that the kind of 'reasonable assumptions' needed to make the process work actually apply in the Universe at large. Perhaps the fragmentation would proceed rapidly on beyond the stage corresponding to the existence of objects the size of stars; on the other hand, it may proceed so slowly that stars could not yet have formed by this process in our Universe. Present developments along these lines bear all the characteristics of being an astronomical dead end. The theories become ever more complex with­out actually proving their case; all that can be said in their favour is that it has not yet proved possible to say conclusively that they are wrong.

This situation is reminiscent of the status of the steady-state theory of cosmology. By juggling with various factors and 'tweaking up' the theory whenever it shows signs of faltering it is possible to build an ever more complex version of the theory to explain all observations. But this is particularly futile since the steady-state theory was originally introduced chiefly because of its conceptual beauty and simplicity; these properties have long since fallen by the wayside during the tweaking-up process.

The same sort of philosophy of simplicity runs strongly counter to the collapsing gas cloud theories of galaxy formation. As I have mentioned, we do not actually know of any large collapsing objects in the Universe, whereas expansion is a fundamental property of the Universe itself, and therefore immediately a more plausible hypothesis to apply to the problem of galaxies and galaxy formation. This, to me,

68

The Present Balance and Future Prospects 69

is a strong argument against such ideas as Layzer's gravitational cluster­ing hypothesis (Chapter 4). I have no objection to the idea of clustering as a process important for the formation of planetary sized bodies after the formation of stars and galaxies, but both on aesthetic grounds and because of nagging doubts about the time required for clustering to pro­duce objects as large as galaxies in the time available I cannot accept Layzer's ideas as a true explanation of the presence of galaxies in our Universe.

Of the three main lines of attack suggested during the past 20 years or so that leaves the models based, more or less, on Ambartsumian's fragmentation hypothesis. But these models do not come to the fore merely by default, as a result of the deficiencies of the other two types of model. To my mind, these models are intrinsically more satisfying -and they have the great merit that detailed calculations indicate that expansion from retarded cores, within the framework of the overall expansion of the Universe, can produce systems very like the galaxies we see in the heavens, within timescales comparable to the age of the Universe.

Even without invoking a steady-state model of the Universe, con­tinual creation could play a part in these models of galaxy formation. It depends exactly how you care to define matter 'creation', since some of the most intriguing models involve outbursts of matter from singularities (in the form of white holes) where the matter has previously been, to all intents and purposes, out of reach of the rest of the Universe.

Part of the fascination of the study of galaxy formation is that just about all of the theories discussed here (and others!) remain at least possible, if not quite plausible. So if you like to play around with the equations of, say turbulent flow and magnetohydrodynamics applied to a collapsing gas cloud you could justify it (if justification were necessary) by saying that you were investigating possible models of galaxy formation. But as it happens some of the most exciting work in terms of mathematics applied to the Universe that is going on today brings us right back to the concepts of black and white holes, and introduces some intriguing new twists which can be followed up by the next generation of research students.

The idea of white holes as constituents of the Universe today recently ran into some heavy weather, when Eardley (1974) produced calculations showing that if a retarded core did exist in the early Universe then the 'white hole' would rapidly be converted into a black hole by matter falling onto it from outside. But these calculations came

70 Galaxy Formation

as no real surprise. Indeed, they simply bear out the 'common-sense' view of such a situation, as a little thought will make clear. The answer to this dilemma is, however, equally simple. When we talk about delayed cores of expansion, what we mean in mathematical terms is some kind of constraint or boundary condition on the expansion of the Universe itself from a singular state. Common sense certainly breaks down when we are dealing with singularities, and it is quite justifiable to argue that retarded cores are produced by special conditions at the origin of the space-time of our Universe, and that these conditions are not amenable to investigation by the conventional approach of general relativity.

That is not quite such a cheat as it looks at first - I can imagine the cries of 'hypocrite' coming from those who say that I am now doing with retarded cores just what I object to Hoyle and Narlikar doing with the steady-state theory, making a special case to remove any embarrass­ing objections. But in fact all cosmologies (except the steady-state!) run into problems with boundary conditions at the origin of the Universe. If you really want to work things out from a beginning at time zero you have to make a few assumptions, because general relativity just does not produce unambiguous answers to the questions you want to ask. That may, of course, be a sign that we need a better theory, and a better theory may or may not allow retarded cores to exist - that is one of the problems for the next generation. In the meantime, I feel no qualms about claiming the initial behaviour of such cores, the fact that they are 'delayed' at all and the trigger for their outburst, are all boundary condition problems and therefore outside the scope of the present discussion.

Another possible product of the very beginning of the Universe - the first microsecond or so - is a family of 'mini' black holes. Hawking (1971) seems to have been the originator of this idea; his suggestion has been lucidly discussed by Rees (1974) and elaborated by Hawking him­self as well as by others (see Carr and Hawking, 1974). Because the radius of a black hole is proportional to its mass, tiny black holes would be even more bizarre than larger ones. A black hole of the same mass as the Earth would be a few millimetres across; but a black hole the size of a proton would contain some 1015 g of matter. In spite of their mass, such black holes would be fairly stable in some respects, since the size of their Schwarzschild 'throats' would be so small that new matter could be funnelled into them only very slowly. One of these objects could pass right through the Earth and remain unaffected; according to

The Present Balance and Future Prospects

one theory (not widely accepted) the mysterious Tunguska meteorite which blasted trees in Siberia early in this century without leaving an impact crater might have been such an object.

71

Hawking has also been a leader in investigations of the ultimate fate of such bizarre objects. Using quantum theory, he finds that black holes are not really black, in the sense of being perfect absorbers. Particles can be created in pairs in the strong gravitational field of a black hole, and as a result radiation is produced which can escape into space (Hawking 1974). Although this means that any black hole must eventually evaporate by losing its mass-energy in radiation, the operative word here is 'eventually'. For a black hole as massive as a star, this process takes 1040 times longer than the age of the Universe, and in any case these objects would gain mass from accretion faster than they lost it by radiation.

But for mini black holes the picture is rather different. They could dissipate their energy in a time shorter than the age of the Universe and, intriguingly, such an object might eventually disappear in a violent out­burst of energy- 1035 erg emitted in less than a second.lt is tempting to speculate that these outbursts might be related to some of the phenomena observed in our galaxy, but most people take the concept as an intriguing mathematical toy rather than as something directly relevant to our Universe.

Another idea, more relevant to this book, is that if black holes formed early in the history of the Universe grew as the Universe expanded they might today be big enough to form the nuclei onto which galaxies condense. The present state of play seems to be that mini black holes definitely do not grow in this way, and that if such objects ever formed then black holes with masses of I o-s g and upwards might be around today (Carr and Hawking, 1974). But this is very much an active area of present research, and some factor may be found which changes this conclusion. One thing, however, is beyond doubt, and that is the importance of studies of this kind. As Rees (I 974) puts it 'one of the most outstanding theoretical developments in relativity during the last few years [has] undoubtedly been the proof that singularities are inevitable, even in situations possessing no special degree of symmetry'. Theorists are now beginning to move towards studies of quantum gravity, and relativity and black holes must attract increasing attention in future, both from observational astronomers and from theorists and physicists. It seems inevitable that the study of such phenomena will be the 'big physics' of tomorrow, since our theories and understanding of

72 Galaxy Formation

the Universe have reached a point where only very limited progress can be made by studying the middle range of phenomena observable on Earth, at low densities and in weak gravitational fields.

This is in striking contrast to the situation when we look at the other routes which have been taken in the search for the answer to the riddle of origin of the galaxies. More than ever they look like played out dead ends, and more than ever it looks as if, unlike the situation with stars, the nature and origin of galaxies is intimately tied up with phenomena quite unlike those we can reproduce, even in small measure, on Earth.

To me, the way ahead is clear. There is already enough evidence, both observational and theoretical, to show that galaxy formation is a pro­cess which is related to the presence of singularities and energetic out­bursts rather than to collapse of great clouds of gas. In addition, studies of this kind of phenomenon are just those studies likely to be at the forefront of research in the next decade or two, just as nuclear physics was the forefront of research in the 1930s. Within ten years, we may be much closer to a real understanding of these processes, although I am sure that it will take much longer than that to thrash out all the details. To some extent, this is a personal belief based on my acceptance of the idea of outbursts as fundamental processes in galaxy formation. My acceptance is based more on personal appeal than on entirely logical and mathematical grounds, but to those who find such an idea outrageous, rather than at least entertaining, I have one other argument to offer; in the tradition that one picture is worth (at least) a thousand words, if you just cannot accept the idea of great outbursts of matter from super­dense states which are now the nuclei of galaxies, take another look at the cover picture of this book!

References and Further Reading

Ambartsumian V. A., {1958). In Report on II th Solvay Conference. -, (1958). Observatory, 75, 72. -, (1960). Quarterly JL R Astr. Soc., 1, 152. -, (1964). In Report on 13th Solvay Conference. Bondi H., (1960). Cosmology, Cambridge University Press. Bondi H. & Gold T., (1948).Mon. Not. R. Astr. Soc., 108,252. Bonnor W., (1957).Mon. Not. R. Astr. Soc., 117, 104. Brewster (1855), see Newton, I. Carr B.J. & Hawking S.W., (1974). Mon. Not. R. Astr. Soc., 168, 399. Eardley D.M., (1974). Phys. Rev. Lett., 33, 442. Eggen 0. J., Lynden-Bell D. & Sandage A. R., (1962). Astrophys. J.,

136,748. Einstein A. & Strauss E. G., (1945).Rev. Mod. Phys., 17, 120. Gamow G., (1952).Physical Review, 86,251. Gribbin J. R., (1967). 'Galaxy Formation', M.Sc., Dissertation, University

of Sussex, England. Hawking S. W., (1971). Mon. Not. R. Astr. Soc., 152, 75. -, (1974). Black Holes Aren't Black,

Gravity Research Foundation. Hoyle F., (1948).Mon. Not. R. Astr. Soc., 108,372. -, (1949). ibid., 109,396. -, (1953). Astrophys. J., 118, 513. Hoyle F., Fowler W. A., Burbidge G. & Burbidge E. M., (1964).

Astrophys. J., 139, 909. Hoyle F. & Narlikar J. V., (1966a).Proc. R. Soc., A290, 143. -, (1966b). ibid., A290, 162.

73

74 Galaxy Formation

Hoyle F. & Narlikar J. V., (1966c). ibid., A290, 177. -, (1967). ibid., A299, 188. Hunter C., (1962).Astrophys. J., 136,594. -, (1964). ibid., 139,570. Jeans J ., ( 1928). Astronomy and Cosmogony, Cambridge University

Press. Jones B., (1973). Astronomical J., 181,269. -, (1964).Ann. Rev. Astr. Astrophys., 2, 341. Kruskal M.D., (1960).Phys. Rev., 119, 1743. l.ayzer D., (1964). Astronphys. J., 59, 170. -, (1954). Astronomical J., 137, 157. Lifshitz E. M., (1946). J. Phys. (USSR), 10, 116. Lifshitz E. M. & Khalatnikov I. M., (1964). Sov. Phys. Uspekhi, 6, 495. Lifshitz E. M., Sudakov V. V. & Khalatnikov I. M., (1963). Sov. Phys.

JETP, 16, 732. Liller W., (1960).Astrophys. J., 132,306. Lynden-Bell D., (1969).Nature, 223,690. McCrea W. H., (1960). Proc. R Soc., A256, 245. -, (1964).Mon. Not. R. Astr. Soc., 128,335. McCrea W. H. & Williams I. P., (1965).Proc. R. Soc., A287, 143. Milne E. A. & McCrea W. H., (1934). Quart. 11. Mathematics, S, 73. Misner C. W., Thorne K. S. & Wheeler J. A., (1973). Gravitation,

W. H. Freeman, San Francisco. Nakano T., (1966).Prog. Theor. Phys., 36,515. .

*Narlikar J. V ., (1973). In Cosmology Now, Laurie John, ed., BBC Publications, p. 69.

Needham, J. (1959). Science and Civilization, Vol. 3, Cambridge University Press.

Ne'eman Y., (1965). Astrophys. J., 141, 1303. Newton 1., (1855). (Letter to Dr Bentley), see, e.g., Brewster D.,

Memoirs of Sir Isaac Newton, Edinburgh. Novikov I. D., (1964). Sov. Astr. AJ, 8, 857. Novikov I. D. & Ozernoi L. M., (1963). Sov. Phys. Doklady, 8,

580. Oke J. B. & Gunn J., (1914).Astrophys. J. Lett., 187, L5. Oort J. H., ( 1962). In Distribution and Motion of Matter in Galaxies,

L. Woltjer, ed., Benjamin, New York, p. 234. *Oster L., (1973). Modem Astronomy, Holden-Day, San Francisco. Press W. H. & Schechter P., (1974). Astrophys. J., 187,425. Rees M. J., (1974). The Observatory, 94, 168.

References and Further Reading

Roxburgh I. W. & Saffman P. G., (1965).Mon. Not. R. Astr. Soc., 129, 181.

Safronov V. S., (1966). Sov. Astr. AJ, 9, 987. *Sciama D. W., (1959). The Unity of the Universe, Faber & Faber. * -, (1971 ). Modem Cosmology, Cambridge University Press. *Shapley H., (1972). Galaxies, 3rd edition, revised by P. W. Hodge,

University of Harvard Press. Simon R., (1970). Astron. Astrophys. J., 6, 151. Urey H. C., (1966).Mon. Not. R. Astr. Soc., 131, 199. Weizsiicker C. F. von, (1948). Die Naturwissenschaften, 35, 188. -,(1951).Astrophys. J., 114,165. Wolfe A.M. & Burbridge G. R., (1970).Astrophys. J., 161,419.

75

Wright T., (1971).An Original Theory of the Universe, facsimile reprint by Macdonald, London, of 1750 edition.

Zel'dovich Ya. B., (1963a). Sov. Phys. JETP, 16, 732. -, (1963b). ibid., 16, 1395. -, (1964). Sov. Phys. Uspekhi, 6, 478. -, (1970). Astron. Astrophys., 5, 84. Zel'dovich Ya. B. & Novikov I. D., (1967). Sov. Astr. AJ, 10,602. -, (1974). Relativistic Astrophysics, Vol. 2, University of Chicago Press.

References marked with an asterisk are particularly suitable for further reading; in addition, the following books would be of more than passing interest to anyone beginning to study astronomy:

Frontiers in Astronomy (Scientific American reprints; W. H. Freeman, San Francisco, 1970);

The New Cosmos by Albrecht Unsold (Longmans, 1969); Modem Cosmology by Jagjit Singh (Penguin, 1970); and, of course, I cannot miss the opportunity to mention Our Changing Universe by John Gribbin (Macmillan, 1976).

Index

Ambartsumian theory, 28, 63 Andromeda nebula, 8, 9, 64 Atoms, size, 1

BL Lac, 60, 66 Black dwarf, 5 Black holes, 1, 5, 47, 60, 61, 66,

69, 70 Bonnor formulae, 42 Burbidge theory, 61

Carbon, 4 Cepheids, 8 C-fie1d, 35, 48 Oouds

high temperature, 18 low temperature, 18, 19

Clustering See Gravitational clustering

Condensation in galaxies, 56

Cosmic rays in galaxies, 5, 37, 48, 66

Cosmological constant, 45 Cosmological principle, 33 Cosmology, history, 7 Cygnus A, 29

Doppler effect, 8-10 Dust, in galaxies, 5, 59, 64-66

77

Earth, size, 1 Einstein theories, 12, 24, 36, 52

Fragmentation, 20-23, 28, 68 Friedmann model, 31, 37

Galaxies age, 10, 29, 34 clusters, 23, 28, 34, 59, 64,

66 cores in, 47, 49, 52, 62, 66 distances, 8, 29 elliptical, 6, 16, 29, 30,

55-59 evolution, 58 formation theories

clustering, 23, 28, 69 collapsing gas, 2, 5, 18, 30,

47,68 continual creation, 34 expanding, 7 fragmentation, 18, 28, 42,

68,69 retarded core, 46, 52, 66,

70 turbulence, 15

irregular, 60 luminosity, 61 N-type, 60 nuclei, 29, 30, 60, 65

78

Galaxies (continued) radio, 10, 29, 47, 60 Seyfert, 60, 65 size, 1, 65 SO systems, 59 spk~,5,6,8, 16, 17,30,

56-58, 64 types, 5, 58 velocity, 9, 16, 39

Gas, in galaxies, 5, 15, 24, 34, 54, 59, 64-66.

Gravitation~ clustering, 23, 28 Gravitational instability, 18 Gravitational potential, 24, 39,

47 Gravity, 1, 2

Hawking theory, 70, 71 Helium, 2-4 Hoyle theories, 18, 30, 31, 56 Hubble theories, 8, 39, 55 Hunter theory, 21 Hydrogen, 2-4, 18, 64, 65

Infrared, 60, 65, 66

Jeans' criterion, 15, 42

Layzertheory,20, 23 Light year, 1 Lynden-Bell theory, 65

M51, 29 M82, 60

Nakano theory, 21 Narlikar theory, 30-32, 56 Neutrinos, 3 Newton theories, 12, 15, 24, 31,

39,52

Index

Nova, 4 Novikov theory, 49 Nuclear fusion, 2-4, 13 Nuclei, atomic, 5

0 associations, 28

Particles, subatomic, 1 Planets, formation of, 27 Pregalaxies, 16, 18 Pulsars, 5

Quantum mechanics, 1 Quasistellar objects, 10, 39, 45,

47,48,57,60,62,65

Radiation emission, 5, 49 Red shift, See Doppler effect Relativity theory, 1, 21 Ricci, Matteo, 7

Schwarzschild sphere, 30, 47, 48, 50,52,61, 70

Sciama theory, 34 Solar System, age of, 10 Stars

binary, 16, 28 disc, 30 explosion, 4, 5, 10 formation, 2, 13, 16 halo, 30 luminosity, 9 neutron, 5 population I, 58, 63-65 population II, 58, 63, 64

Stefan's law, 3 Subcondensations, 20, 21 Sun

age, 4

Sun (continued) gravitational potential

energy, 2, 4 luminosity, 2, 4 nuclear fusion, 3, 4 size, 2 velocity, 9

Supergiants, 8 Supernova, 4

Telescopes, 8 TengMu, 7 Trapezium system, 28 Tunguska meteorite, 71 Tunnelling theory, 3 Turbulence, 15

Universe age, 10, 13, 45

Index 79

expansion, 6, 9, 11, 24, 31, 38,41,47,48, 52,68

formation, 11 hot big bang model, 11, 12,

16, 17,32, 38,46,52 irregularities in, 13, 23, 46,

52 steady-state, 12, 13, 31, 68

von Weizsacker theory, 15

Waves, 1 White dwarf, 5 White holes, 62, 69 Wolfe theory, 61 Wright theory, 8

X-rays, 60

Zel'dovich theory, 27