Stars: Nature's nuclear plants

It is said that a man in the street once asked the scientist Descartes the question: ‘Tell me, wise man, how many stars are there in heaven?’ Descartes apparently replied, ‘Idiot! no one can comprehend the incomprehensible’. Well, Descartes was wrong. We today have a fairly reasonable idea about not only the total number of stars but also many of their properties.

To begin with, it is not really all that difficult to count the number of stars visible to the naked eye. It only takes patience, persistence (and a certain kind of madness!) to do this, and many ancient astronomers have done this counting. There are only about 6000 stars which are visible to the naked eye – a number which is quite small by astronomical standards. The Greek astronomer Hipparchus not only counted but also classified the visible stars based on their brightness. The brightest set (about 20 or so) was called the stars of ‘first magnitude’, the next brightest ones were called ‘second magnitude’, etc. The stars which were barely visible to the naked eye, in this scheme, were the 6th magnitude stars. Typically, stars of second magnitude are about 2½ times fainter than those of first magnitude, stars of third magnitude are 2½ times fainter than those of second magnitude, and so on. This way, the sixth magnitude stars are about 100 times fainter than the brightest stars. With powerful telescopes, we can now see stars which are about 2000 million times fainter than the first magnitude stars, and – of course – count them.

Cosmic inventory

Think of a large ship sailing through the ocean carrying a sack of potatoes in its cargo hold. There is a potato bug, inside one of the potatoes, which is trying to understand the nature of the ocean through which the ship is moving. Sir Arthur Eddington, famous British astronomer, once compared man's search for the mysteries of the universe to the activities of the potato bug in the above example. He might have been right as far as the comparison of dimensions went; but he was completely wrong in spirit. The ‘potato bugs’ – called more respectably astronomers and cosmologists – have definitely learnt a lot about the contents and nature of the Cosmos.

If you glance at the sky on a clear night, you will see a vast collection of glittering stars and – possibly – the Moon and a few planets. Maybe you could also identify some familiar constellations like the Big Bear. This might give you the impression that the universe is made of a collection of stars, spiced with the planets and the Moon. No, far from it; there is a lot more to the universe than meets the naked eye!

Each of the stars you see in the sky is like our Sun, and the collection of all these stars is called the ‘Milky Way’ galaxy. Telescopes reveal that the universe contains millions of such galaxies – each made of a vast number of stars – separated by enormous distances. Other galaxies are so far away that we cannot see them with the naked eye.

Expansion of the universe

The cosmic tour which we undertook in the last chapter familiarized us with the various constituents of the universe from the stars to clusters of galaxies. We saw that the largest clusters have sizes of a few megaparsec and are separated typically by a few tens of megaparsec. When viewed at still larger scales, the universe appears to be quite uniform. For example, if we divide the universe into cubical regions, with a side of 100 Mpc, then each of these cubical boxes will contain roughly the same number of galaxies, clusters, etc. distributed in a similar manner. We can say that the universe is homogeneous when viewed at scales of 100 Mpc or larger. The situation is similar to one's perception of the coastline of a country: when seen at close quarters, the coastline is quite ragged, but if we view it from an airplane, it appears to be smooth. The universe has an inhomogeneous distribution of matter at small scales, but when averaged over large scales, it appears to be quite smooth. By taking into account all the galaxies, clusters, etc. which are inside a sufficiently large cubical box, one can arrive at a mean density of matter in the universe. This density turns out to be about 10−30 gm cm−3.

The matter inside any one of our cubical boxes is affected by various forces. From our discussion in chapter 2 we know that the only two forces which can exert influence over a large range are electromagnetism and gravity. Of these two, electromagnetism can affect only electrically charged particles.

A microscopic tour

The physical conditions which exist in the centre of a star, or in the space between galaxies, could be quite different from the conditions which we come across in our everyday life. To understand the properties of, say, a star or a galaxy, we need to understand the nature and behaviour of matter under different conditions. That is, we need to know the basic constituents of matter and the laws which govern their behaviour.

Consider a solid piece of ice, with which you are quite familiar in everyday life. Ice, like most other solids, has a certain rigidity of shape. This is because a solid is made of atoms – which are the fundamental units of matter – arranged in a regular manner. Such a regular arrangement of atoms is called a ‘crystal lattice’, and one may say that most solids have ‘crystalline’ structure (see figure 2.1). Atoms, of course, are extremely tiny, and they are packed fairly closely in a crystal lattice. Along one centimeter of a solid, there will be about one hundred million atoms in a row. Using the notation introduced in the last chapter, we may say that there are 108 atoms along one centimeter of ice. This means that the typical spacing between atoms in a crystal lattice will be about one part in hundred millionth of a centimeter, i.e., about 1/100 000 000 centimeter. This number is usually written 10−8 cm. The symbol 10−8, with a minus sign before the 8, stands for one part in 108; i.e., one part in 100 000 000.

The broad picture

In the previous chapters, we have explored the conventional thinking of cosmologists and astrophysicists in their attempt to understand the structures in the universe. Some of these attempts have been very successful, while others must be still thought of as theoretical speculations. Since different aspects of structure formation were touched upon in different chapters of this book, it is worthwhile to summarize the conventional picture in a coherent manner.

The key idea behind the models for structure formation lies in treating the formation of small-scale structures like galaxies, clusters, etc. differently from the overall dynamics of the smooth background universe. This is linked to the assumption that, in the past, the universe was very homogeneous with small density fluctuations.

The evolution of the smooth universe is well described by the standard big bang model. Starting from the time when the universe was about one second old, one can follow its evolution till the time when matter and radiation decoupled – which occured when the universe was nearly 400 000 years old. During this epoch, the energies involved in the physical processes ranged from a few million electron volts to a few electron volts. This band of energies has been explored very thoroughly in the laboratory experiments dealing with nuclear physics, atomic physics and condensed matter physics. We understand the physical processes operating at these energy ranges quite well, and it is very unlikely that theoretical models based on this understanding could go wrong. In other words, we can have a reasonable amount of confidence in our description of the universe when it evolved from an age of one second to an age of 400 000 years.

The cosmic rainbow

In chapter 1, we did a rapid survey of the universe, listing its contents, and in chapter 4, we plan to discuss these objects in more detail. You may wonder how such a detailed picture about the universe has been put together. This has been possible because we can now observe the universe in a wide variety of wavebands of the electromagnetic spectrum, and virtually every cosmic object emits radiation in one band or another. In this brief chapter, we shall have a rapid overview of how these observations are made. While describing the observational techniques, we will also mention briefly the astronomical objects which are relevant to these observations. These objects are described in detail in the next chapter, and you could refer back to this cha46 pter after reading chapter 4.

It is rather difficult to ascertain when the first astronomical observation was made. Right from the days of pre-history, human beings have been wondering about the heavens and making note of the phenomena in the skies. The earliest observations, needless to say, were made with the naked eye. With the advent of the optical telescope, one could probe the sky much better and detect objects which were too faint to be seen with the naked eye. As the telescopes improved, the quality of these observations increased.

There is, however, an inherent limitation in these early observations. All these observations were based on visible light. We now know that visible light is an electromagnetic wave whose wavelength is in a particular range.

The subject of cosmology – and our understanding of how structures like galaxies, etc., have formed – have developed considerably in the last two decades or so. Along with this development came an increase in awareness about astronomy and cosmology among the general public, no doubt partly due to the popular press. Given this background, it is certainly desirable to have a book which presents current thinking in the subject of cosmology in a manner understandable to the common reader. This book is intended to provide such a nonmathematical description of this subject to the general reader, at the level of articles in New Scientist or Scientific American. An average reader of these magazines should have no difficulty with this book.

The book is structured as follows: chapter 1 is a gentle introduction to the panorama in our universe, various structures and length scales. Chapter 2 is a rapid overview of the basic physical concepts needed to understand the rest of the book. I have tried to design this chapter in such a manner as to provide the reader with a solid foundation in various concepts, which (s)he will find useful even while reading any other popular article in physical sciences. Chapter 3, I must confess, is a bit of a digression.

Probing the past

The discussion in the last chapter shows that most of the prominent structures in the universe have formed rather recently. In terms of redshifts we may say that galaxy formation probably took place at z < 10. Our understanding of galaxy formation could be vastly improved if we could directly observe structures during their formative phases. Remember that in the case of stars we can directly probe every feature of a stellar life cycle from birth to death; this has helped us to understand stellar evolution quite well. Can we do the same as regards galaxies?

Unfortunately, this task turns out to be very difficult. The life span of a typical star — though large by human standards — is small compared to the age of the universe. This allows one to catch the stars at different stages of their evolution. For galaxies, the timescale is much longer and so we cannot hope to find clear signals for galaxies of different ages. Secondly, the distance scales involved in extragalactic astronomy are enormously large compared to stellar physics. This introduces several observational uncertainties into the study.

In spite of all these difficulties, astronomers have made significant progress in probing the universe during its earlier phases. We saw in chapter 5 that the farther an object is the higher its redshift will be. But since light takes a finite time to travel the distance between a given object and us, what we see today in a distant object is a fossilized record of the past. Consider, for example, a galaxy which is at a distance of one billion light years.

The beginnings

The term ‘science fiction’ was first used by one of the founders of the modern genre, Hugo Gernsback. Gernsback, after whom the annual science fiction 'Hugo’ awards are named, was the founder of the Amazing Stories magazine in April, 1gz6.The slogan on the title page proclaimed its mission: 'Extravagant Fiction Today … Cold Fact Tomorrow'. Of course, few of the stories published in Amazing Stories lived up to this claim, but science fiction does have some notable successes to its credit over its relatively brief history. Two of the founding fathers of science fiction – H. G. Wells and Isaac Asimov – have already been mentioned in earlier chapters. In this final chapter, we shall examine the interplay between relativity and science fiction. We begin with Johannes Kepler, arguably the first writer of the genre.

Kepler was born in south-west Germany in a small town called Weil-der-Stadt. Kepler's first great work, A New Astronomy, was published in I 609, and it remains a landmark in the history of science. In it, Kepler formulated the first ‘natural laws’ – precise, verifiable statements about natural phenomena expressed in terms of mathematical equations. Arthur Koestler, in his marvellous book The Sleepwalkers, claims that it was Kepler's laws that 'divorced astronomy from theology and married astronomy to physics'. Unlike Copernicus, Galileo or Newton, Kepler did not attempt to disguise the way in which he arrived at his conclusions -all his errors and sidetracks are faithfully recorded along with his final revelation.

Geometry and gravity

The discovery of ‘non-Euclidean’ geometry in the nineteenth century came as a great surprise and was greeted by disbelief. One of the pioneers of this new geometry, Janos Bolyai, a Hungarian army officer, expressed his joy with the words:

'Euclidean’ geometry is the geometry we learn in school, with its familiar apparatus of points, straight lines, circles, ellipses and triangles. In particular, we are all brought up to believe that the three angles of a triangle add up to 180 degrees and that parallel lines never meet. Such Euclidean geometry is the geometry of the plane – technically called a ‘flat’ space. By contrast, non- Euclidean geometry describes a ‘curved’ space. What do we mean by these terms?

Some idea of a curved space can be gained by considering geometry on the surface of the Earth. The Earth is approximately spherical, and on its surface it is easy to construct triangles whose angles add up to more than I 80 degrees (Figure 9. I). Similarly, lines of longitude start out parallel at the equator but converge and cross at the poles. The surface as a whole does not obey Euclid's rules. Since such a familiar example of a surface is non- Euclidean, why are such geometries so unfamiliar to most of us?

The momentous day in May

In May of 1905, Einstein was twenty-six years old, and his ten-year struggle with the problems of relativity was about to come to a triumphant climax. About a year before this, he had begun to feel that the velocity of light must be universal – independent of the motion of the source. If this were true, then there was no need to worry about motion relative to any mythical aether, and the null result of Michelson and Morley became obvious: the speed of light is the same in both arms of the apparatus, whatever direction they are pointing relative to the Earth's motion. But the Earth does move round the Sun – so something was wrong with the ‘relativity’ of Galileo and Newton and their familiar addition of velocities, at least where light is concerned. As we asserted in chapter 2, and as we shall show in the next chapter, in Einstein's relativity speeds do not add up in the expected way. We are also forced to re-think our notions of space and time. This new vision of space and time is what we shall look at in this chapter. Let us start by recalling what Galileo and Newton believed, before looking at Einstein's version of the relativity principle.

In the sixteenth century, it seemed natural to believe that, if the Earth was moving, neither an arrow shot straight up nor a stone dropped from a tower would follow the same straight-line path.

Einstein's revolution

The famous Russian scientist Lev Landau used to keep a list of names, in wich he graded, physicists into ‘leagues’. The first division contained the names of physicists such as Niels Bohr, Werner Heisenberg and Erwin Schroedinger, the founding fathers of modern quantum physics, as well as historical ‘giants’ such as Isaac Newton. He was rather modest about his own classification, grading himself 2½, although he later promoted himself to a 2. Most working physicists would be happy even to make it into Landau's fourth division: David Mermin, a well-known and perceptive American physicist, once wrote an article entitled ‘My life with Landau: homage of a 4½ to a 2’. What is the point of this story? The point is that any book about relativity is inevitably also about Albert Einstein, and Einstein was a remarkable physicist by any standard. Landau, in fact, created a special ‘superleague’ containing only one physicist, Einstein, whom he classified uniquely as a½. Thus, the popular opinion that Einstein was the greatest physicist since Newton is widely shared among professional physicists.

When Einstein wrote about ‘The wonderful events which the great Newton experienced in his younger days…’, and commented that, to Newton, Nature was ‘an open book’, he could well have been writing about himself.