The formation of dead stars

The types of stars described in Chapters 13 and 14 are held up by the thermal pressure of hot gas, the source of energy to provide the pressure being nuclear energy generation in their cores. As evolution proceeds off the main sequence, up the giant branch and towards the final phases when the outer layers of the star are ejected, the nuclear processing continues further and further along the route to using up the available nuclear energy resources of the star. The more massive the star, the more rapidly it evolves and the further it can proceed along the path to the formation of iron, the most stable of the chemical elements. An intriguing question is whether or not the star is disrupted by the various ‘flashes’ which are expected to take place as new regimes of nucleosynthesis are switched on, for example, at the points E and G in Fig. 13.19. In the most massive stars, M ≥ 10M⊙, it is likely that the nuclear burning can proceed all the way through to iron, whereas, in less massive stars, the oxygen flash, which occurs when core burning of oxygen begins, may be sufficient to disrupt the star. In any case, at the end of these phases of stellar evolution, the core of the star runs out of nuclear fuel, and it collapses until some other form of pressure support enables a new equilibrium configuration to be attained.

The possible equilibrium configurations which can exist when the star collapses are white dwarfs, neutron stars and black holes.

Synchrotron radiation

The synchrotron radiation of relativistic and ultrarelativistic electrons is the process which dominates high energy astrophysics. It is the radiation emitted by very high energy electrons gyrating in a magnetic field. It was originally observed in early betatron experiments, in which electrons were first accelerated to ultrarelativistic energies. This same mechanism is responsible for the radio emission from the Galaxy, from supernova remnants and extragalactic radio sources. It is also responsible for the non-thermal optical emission observed in the Crab Nebula and possibly for the optical and X-ray continuum emission of quasars. The reasons for these assertions will become apparent in the course of this chapter.

The word non-thermal is used frequently in high energy astrophysics to describe the emission of high energy particles. I find this an unfortunate terminology, since all emission mechanisms are ‘thermal’ in some sense. The word is conventionally taken to mean ‘continuum radiation from particles, the energy spectrum of which is not Maxwellian’. In practice, continuum emission is often referred to as ‘nonthermal’ if it cannot be accounted for by the spectrum of thermal bremsstrahlung or black-body radiation.

It is a very major undertaking to work out properly all the properties of synchrotron radiation, and that is beyond the scope of this book. For details, I refer the enthusiast to the books by Bekefi (1966), Pacholczyk (1970) and Rybicki and Lightman (1979) and the three review articles by Ginzburg and his colleagues (see the References section for this chapter).

Introduction

In this chapter, we look in a little more detail into some aspects of stellar evolution which will be important for studies of high energy astrophysical processes in our Galaxy and in extragalactic systems. For example, we need to know how far we can trust the theory of stellar structure and evolution; we need to know more details of the processes of nucleosynthesis in stars in order to understand the origin of the chemical composition of the interstellar gas and of the cosmic rays; we need to study what is known about the processes of mass loss from stars and the processes which can lead to the formation of dead stars; we need to investigate binary star systems in order to contrast their properties with those of X-ray binary systems containing neutron stars and black holes, and to discuss how such close binary stars can be formed. This survey is in no sense complete, and reference should be made to the texts recommended at the end of the book for more details.

The Sun as a star

Granted the outline of stellar evolution presented in Section 13.3, how well can the theory account for the properties of our own Sun? As by far the brightest star from our location in the Universe, it can be studied in much more detail than any other star, and is a benchmark for the theory of stellar structure and evolution. Until the last 20 years, the study of the Sun and the stars was largely confined to the interpretation of their surface properties.

Introduction – a global view of the interstellar medium

Hendrik van de Hulst, the theorist who predicted the 21-cm line of neutral hydrogen, once remarked that, if you set out to detect an emission or absorption line from an atom, ion or molecule in astronomy, you are bound to discover it somewhere in the Universe. This statement is particularly true of the interstellar medium because it is now understood that it is far from equilibrium and that a very wide range of densities and temperatures are present – those found largely reflect the characteristics of the observing tools used by the astronomer. It is no surprise, therefore, that there is a great deal of physics to be studied. Astrophysically, the understanding of the nature and properties of the interstellar gas is of the first importance, since it is out of this medium that new stars are formed. It is continually replenished because of mass loss from stars, and so the medium plays a key role in the birth-to-death cycle of stars. The same astrophysics is applicable to the study of diffuse gas anywhere in the Universe, be it galaxies, the intergalactic gas or the gas clouds in the vicinity of active galactic nuclei. These diagnostic tools are essential for determining the physical conditions in which high energy astrophysical processes take place. Furthermore, interstellar gas will prove to be an essential ingredient of the fuelling mechanisms for active galactic nuclei.

The interstellar medium amounts to about 5% of the visible mass of our Galaxy.

γ-ray observations of the Galaxy

Just as the Galactic radio emission outlines the distribution of high energy electrons and magnetic fields in the Galaxy, so the distribution of γ-radiation can provide information about high energy protons and the overall distribution of interstellar gas. As described in Section 5.4, in collisions between high energy particles and protons and nuclei of atoms and molecules of the interstellar gas, pions of all charges, π+, π0 and π-, are produced. The positive and negative pions decay into positive and negative muons, which, in turn, decay into positrons and electrons with relativistic energies (see Fig. 5.11). The latter may make a contribution to the low energy electron spectrum, and the predicted presence of positrons provides a direct test of the importance of the pion production mechanism in interstellar space. The neutral pions decay almost instantly into two γ-rays. In proton-proton collisions, the cross-section for the production of a pair of high energy γ-rays is roughly the geometric size of the proton, σγ ≈ 10-30 m2. The spectrum of γ-rays produced in such collisions is shown in Fig. 20.1. The characteristic signature of this process is that the spectrum of γ-rays has a broad maximum at about 70 MeV. Knowing the physical conditions in the interstellar gas, the γ-ray production rates by various mechanisms can be worked out. Stecker (1977) has carried out these calculations assuming an interstellar gas density of 106 particles m-3 and a local energy density of starlight of 4.4 × 105 eV m-3.

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.