Distances in astronomy

The unit of distance used in astronomy is the parallax-second, or parsec. It is defined to be the distance at which the mean radius of the Earth's orbit about the Sun subtends an angle of one second of arc. In metres, the parsec, abbreviated to pc, is 3.0856 × 1016 m. For many purposes, it is sufficiently accurate to adopt 1 pc = 3 × 1016 m. The parsec is a recognised SI unit and it is often convenient to work in kiloparsecs (1 kpc = 1000 pc = 3 × 1019 m), megaparsecs (1 Mpc = 106 pc = 3 × 1022 m) or even gigaparsecs (where 1 Gpc = 109 pc = 3 × 1025 m).

Sometimes, it is convenient to measure distances in light-years, which is the distance light travels in one year: 1 light-year = 9.4605 × 1015 m. Thus, 1 pc = 3.26 light-years.

Another commonly used distance unit in astronomy is the astronomical unit, abbreviated to AU, which is the mean radius of the Earth's orbit about the Sun: 1 AU = 1.49578 × 1011 m. The very nearest stars to the Earth are at a distance of about 1 pc, and so they are about 2 × 105 times as far away as the Earth is from the Sun.

Accurate distances are among the most difficult measurements to make in astronomy, and there must, therefore, exist corresponding uncertainties in all the derived physical properties of astronomical objects.

At last, after the 12 chapters which comprise the whole of Volume 1, we leave the Solar System behind and enter the astronomical domain, where we can no longer detect high energy particles directly but can only infer their presence from the radiations they emit. High energy processes are now known to be important in essentially all classes of astronomical object, and so we begin our study with a survey of the contents of the Universe – this will provide the astrophysical context for our study. This will be a very broad-brush description, and should be supplemented by the more specialised texts listed in the Further reading and references section.

The large-scale distribution of matter and radiation in the Universe

The modern picture of how matter and radiation are distributed in the Universe on a large scale is derived from a wide variety of different types of observation.

The isotropy of the Universe as a whole

On the very largest scale, the best evidence for the overall isotropy of the Universe comes from measurements of the cosmic microwave background radiation. This is the intense diffuse radiation observed in the centimetre and millimetre wavebands discovered by Penzias and Wilson in 1965. It is wholly convincing that this radiation is the cooled remnant of the very hot early phases of the Big Bang. The radiation decoupled from the matter when the Universe was only about 1/1000 of its present size, and provides direct evidence for the isotropy of the matter and radiation content of the Universe.

There is little to add to the remarks which I made in the preface to Volume 1 of High energy astrophysics. The process of revising and updating the first edition has resulted in a very major expansion in the length of the text, so that it could not be contained within a single volume. I had hoped to complete the work in two volumes, but, as the work progressed, it became apparent that the second volume would have become unwieldy, and so this book is Volume 2 of what will be a three-volume work. In this volume, I concentrate upon the high energy astrophysics of our own Galaxy, and Volume 3 will be devoted to extragalactic high energy astrophysics.

It is worthwhile explaining the point of view which I have adopted in introducing the various topics contained in Volumes 2 and 3. As in the first edition, my aim has been to produce self-contained texts which include most of the essential astronomy and astrophysics needed to understand the context as well as the content of high energy astrophysics. For this reason, the present volume begins with descriptions of the current picture of the large-scale distribution of matter and radiation in the Universe, as well as a broad survey of relevant astrophysics, before getting down to studying the high energy astrophysics in detail. In my view, it is no longer possible, if it ever was, to consider the high energy processes independently of the astrophysical environments within which they take place.

The problem

We have left to the last chapter of this volume one of the most intriguing problems in high energy astrophysics – the mechanisms by which high energy particles are accelerated to ultrarelativistic energies. In these first two volumes, sites where particles are accelerated include solar flares, the boundary of the Earth's magnetosphere, pulsar magnetospheres, supernovae and supernova remnants. In volume 3, we will find evidence for particle acceleration in active galactic nuclei and in extended radio sources. It is appropriate to consider the problem of the acceleration of charged particles at this point because a number of important features of the cosmic rays are common to the energy spectra of particles in other astrophysical environments.

The specific features of particle acceleration which we have to account for are as follows.

1. 1 A power-law energy spectrum for particles of all types. The energy spectrum of cosmic rays and the electron energy spectrum of many non-thermal sources have the form

2. where the exponent x lies in the range roughly 2.2–3. For the cosmic rays, x = 2.5–2.7 at energies ∼ 1–103 GeV (Section 9.1), with slightly flatter spectra for primary nuclei such as iron. The typical spectra of radio sources correspond to electron spectra with x ≈ 2.6 with a scatter of about 0.4 about this mean value. The continuum spectra of quasars in the optical and X-ray wavebands correspond to x ∼ 3.

3. 2 The acceleration of cosmic rays to energies E ∼ 1020 eV.

4. 3 […]

Introduction

In the last chapter I have derived the equations of stellar structure. In these equations there are three quantities, the pressure, P, the energy release per kilogram per second, ε, and the opacity coefficient, K, which depend on the density, temperature and chemical composition of the stellar material. In Chapter 3 I did not discuss how P, ε and K depend on these quantities, and the present chapter is concerned with discussing how P, ε and K are to be calculated if the density, temperature and chemical composition are known. To calculate ε a considerable knowledge of nuclear physics is required and a similar knowledge of atomic physics is required for the determination of K. All three quantities depend on the thermodynamic state of the stellar material. Once ρ, T and the chemical composition are known, the calculation of P, ε and k is pure physics and no further astronomical concepts are required and it is for this reason that this chapter is called The physics of stellar interiors.

Because of the great complexity of the problems involved I am only able to describe the basic processes determining P, ε and k and am not able to give detailed calculations. In the first place, I consider the law of energy release.

Energy release from nuclear reactions

As mentioned in the last chapter, it is now believed that most of the energy radiated by stars has been released by nuclear reactions in the stellar interior.

Introduction

In Chapter 2 we have seen that the majority of stars are main sequence stars and I have already suggested that this could mean either that most stars are main sequence stars for all of their lives or that all stars spend a considerable fraction of their life in the main sequence state. It is now believed that the latter is true and that the main sequence phase is one in which stars are obtaining their energy from the conversion of hydrogen into helium which, as we have seen in the last chapter, releases 83% of the maximum energy which can be obtained from nuclear fusion reactions. It is also believed that main sequence stars are chemically homogeneous, which means that there are no significant variations of chemical composition from place to place within the stars. As hydrogen burning is the first important nuclear reaction to occur as the central temperature of a star rises, stars should be chemically homogeneous when they reach the main sequence, provided the same was true of the interstellar cloud out of which they were formed. In this chapter I consider the structure of such stars. In the last two chapters I have discussed all of the relevant equations and have concluded that in general their solution can only be obtained with the use of a large computer.

Introduction

The subject matter of this book is stars and in particular the properties of individual stars but, before I start discussing these properties, I give a general description of the Universe in which the stars are situated and of which they may be the most important component. The may in this sentence be very important. At one time there would have been little doubt that stars are the most important constituent in the Universe. More recently it has become clear that there may be a considerable amount of material in the Universe which is not in the form of stars and it is possible that most of the mass in the Universe is in the form of weakly interacting elementary particles. In giving a brief description of the Universe, no attempt will be made to explain how the results are obtained, but subsequently a detailed discussion will be given of how the properties of stars are deduced from observation.

With the naked eye on a clear night one can observe a few thousand stars and it can be seen that there is a region in the sky, known as the Milky Way, in which there is a particularly large density of faint stars. With even a small telescope, the number of stars which can be seen is greatly increased and it is now known that the solar system belongs to a large flattened system of stars known as the Galaxy, which probably contains about 100000 million stars. Schematic views of the Galaxy as it would look from outside are shown in figs. 3 and 4.

This book is in effect a second edition of a book first published by Wykeham Publications in 1970. The Wykeham series was designed to bridge the gap between school and university science and the mathematical level of the book was designed to be suitable for sixth formers. In fact the main use of the book has been as a university textbook and some of the mathematics which was then taught in schools is now taught at university. In rewriting the book, I have not changed its general level, but I have introduced two appendices containing more mathematical detail relating to topics discussed in the main text.

Many branches of physics such as gravitation, thermodyamics, atomic physics and nuclear physics are combined in determining the structure of stars. As a result the subject provides an ideal example of the application of fundamental physics. Physical conditions in stars are more extreme than on Earth and a successful understanding of their structure should show how valid it is to extrapolate established physical laws to these conditions. Although it is profitable to study stars as isolated objects, an understanding of star formation and stellar evolution is central to the whole study of astronomy.

Significant progress has been made in explaining the observed properties of stars but there is still room for considerable improvement in the relation between theory and observation. In particular the process of star formation is not well understood theoretically or observationally. In fundamental physics there is still need for a reliable theory of fully developed convection.

Introduction

Throughout the book so far I have only discussed the structure of isolated stars, although I have stressed the importance of binary stars in providing information about stellar masses and radii. Although most stars may be partners in binary or multiple systems, for most of them at least for most of their life history the stars are sufficiently far apart that the internal structure of the stars is not affected by the presence of a companion. The mutual gravitational attraction of the two stars causes them to orbit about their common mass centre but otherwise their binary nature can be ignored. This ceases to be the case if binary stars are initially very close or if they become close during their evolution, possibly because one star expands substantially to become a red giant and as a result its surface gets very close to its companion.

When stars are close there are two distinct types of interaction between them. The properties of the surface layers of one star may be affected as a result of irradiation by the other star. This will be particularly true when one component is much more luminous than the other, when the effect on the less luminous star will be very great. In addition both the gravitational attraction of the companion star and the rapid rotation, which must occur because the stars orbit around one another, will cause a star to deviate substantially from spherical symmetry.

Introduction

In the previous discussion of stellar evolution it has frequently been remarked that, so long as the stellar material remains in the form of an ideal classical gas, its central temperature can only increase as it evolves. This result was originally deduced from the Virial Theorem (3.24) on page 55. As I have mentioned on page 201 in Chapter 9, there is at present no completely clear solution to the problem of what happens to a star whose central temperature is still rising at the time that nuclear fusion reactions have converted the central regions to iron, although the association with supernovae of type II seems highly probable; in fact, as I shall explain in the last section of this chapter, the problem can arise even earlier than that. However, if the centre of the star ceases to be an ideal classical gas and becomes a degenerate gas, it is possible that the central temperature may pass through a maximum and that the star may cool down and die. This possibility has already been illustrated for low mass stars in figs. 76 and 86 Such a dying star is likely to have a low luminosity. It is also likely to have a high density. It can only begin to cool down after its central regions have become degenerate and, if the central temperature has previously risen sufficiently for one or more sets of energy-releasing nuclear reactions to occur, a very high density is necessary before degeneracy can occur, as has been seen in Chapter 4 (fig. 45)

Such under-luminous dense stars have been oberved.

Historical introduction

After the main sequence the most prominent group of stars in the HR diagram (fig. 56) is the red giants and supergiants. These stars have larger luminosities and radii than main sequence stars of the same colour. From the discussion in Chapter 5, it appears that red giants are not stars of homogeneous chemical composition and I must now discover how red giants differ from main sequence stars in their internal structure as well as in their surface properties. I have already indicated at the end of Chapter 2 (fig. 30) that stars become red giants when nuclear reactions in their interiors lead to a non-uniformity of chemical composition. Before I discuss this further, I will give a brief historical introduction to the problem of the red giants. Although in this book I mainly discuss the present state of knowledge, it is perhaps instructive in one case to trace the steps by which the present knowledge has been obtained.

When the first theoretical calculations of stellar structure were made, it was very difficult to explain the occurrence of red giants, since at the time it was believed that stars remained chemically homogeneous as they evolved. As will now be described, it was believed that the rotation of stars caused them to be well mixed. Most stars are observed to rotate, even if the rotation of many of them is not sufficiently rapid to distort their structure substantially. Rotation is detected by the Doppler effect.

In this book I have described the methods used in the theoretical study of stellar structure and evolution and I have discussed many of the results obtained. I have tried to discuss the present state of a developing subject and to mention the main uncertainties. As I have stressed, particularly at the end of Chapter 9, some of the detailed theoretical ideas may prove to be wrong, but it is confidently expected that the broad outline of the subject as presented in Chapters 3–5 is correct. In this chapter I discuss further some of the points where important uncertainties remain.

In the first place it is important to realise that, although this book has been written by a theoretical astrophysicist, who has a particular interest in obtaining a theoretical understanding of the subject, ultimately all of the theoretical work must be related to observations. This has a twofold implication. The theoretical worker must keep the observational results in mind and there is a continuing need for new observations. The subject depends considerably on some of the less glamorous parts of observational astronomy. In these days of quasars, pulsars and the cosmic microwave radiation, the work of measuring parallaxes and proper motions and studying the orbits of binary star systems is often regarded as being very humdrum. However, it is vitally important in supplementing the information possessed about such things as masses, radii and absolute magnitudes.

Introduction

In this chapter I consider what are the main physical processes which determine the structure of stars and what equations must be solved in order to find the details of this structure. At the outset it must be stressed that the theoretical astrophysicist does not usually attempt to calculate the properties of a particular star which has been observed. As we have learnt in the last chapter, the number of stars for which there is sufficiently detailed observational knowledge to make this procedure worthwhile is very small. Instead the theoretician tries to isolate the factors which mainly determine the properties of stars and then tries to calculate the structure of a wide range of possible stars. We shall see that the most important factors are the mass and initial chemical composition of the star and the time that has passed since it was formed. In what follows I shall often refer to the birth of a star, its age and its chemical composition at birth. Once calculations have been made for a range of values of mass, chemical composition and age, the results can be compared with the general properties of stars rather than with the properties of individual stars. I shall consider this comparison in Chapters 5 to 10. For one star, the Sun, we possess extremely detailed observational information and there has been a considerable effort to try to obtain a theoretical understanding of its properties.

Introduction

In most of my previous discussion I have assumed that stars spend their entire life with a constant mass, whose chemical composition changes as a result of nuclear reactions. I have also mentioned that, in fact, mass loss from stars is important and I shall now say more about this subject. Observationally mass loss is apparent in the explosions of supernovae and, to a lesser extent, novae and it is also clear that planetary nebulae are formed of mass ejected by stars. Evidence of mass loss from ordinary stars has only been well-established since the development of space astronomy as will become clear in what follows. In this chapter I shall restrict myself to a discussion of mass loss from single stars or from binary stars whose separation is so great that the two components evolve independently. In the next chapter I shall discuss mass exchange between components in close binary systems, which may also involve mass loss from the entire system.

The solar wind

It has been known since about 1960 that the Sun is losing mass at a rate of between one part in 1014 and one part in 1013 a year. This loss is known as the solar wind because it flows through interplanetary space and past the Earth with a velocity of several hundred kilometres a second.