Yogi Berra once said that ‘you can observe a lot by just watching’. The truth of this aphorism struck me when the first prints of the Palomar Sky Survey started to arrive at the Universitäts Sternwarte in Göttingen, where I was a graduate student in 1955. Just looking at this marvellous atlas immediately showed a number of interesting things that had not been so obvious on the smaller, and less homogeneous, databases that had previously been available: (1) The most luminous galaxies in clusters are ‘pretty’ because they have long well-defined spiral arms, whereas ‘ugly’ spirals of lower luminosity tend to exhibit short patchy arms. (2) Intrinsically faint galaxies generally have lower surface brightnesses than do luminous ones. (3) Galaxies in rich clusters sometimes exhibit peculiarities, like fuzzy spiral arms, that are rare among isolated field galaxies.

In the present volume, which is based on a series of lectures given at the University of Victoria in early 1997, I have tried to provide an up-to-date summary of current ideas on the morphology [morphe = shape] and classification of galaxies. I am indebted to Roberto Abraham for suggesting that I write this review. I also thank Ralf Bender, Scott Tremaine and Stephen Zepf for discussions on the interpretation of the classification of elliptical galaxies, and Guy Worthey and Masafumi Noguchi for discussion of the abundance ratio of elements to iron in normal and barred spirals.

Introduction

Dwarf spheroidals are the most common type of galaxy in the Universe. The fact that they were not discovered until 1938 is entirely due to their feeble luminosity and low surface brightness. Of the 29 galaxies that are known to be located within 1.0 Mpc, approximately half are dwarf spheroidals (dSph). A listing of these Local Group dSph galaxies is given in Table 14. For the sake of completeness the dSph/dE galaxies NGC 147 and NGC 185, which are both brighter than Mv= −15.0, have been included in the table. Since most of the faintest known Local Group members are dwarf spheroidals it is almost certain that additional very faint dSph galaxies remain to be discovered in the Local Group. In particular it seems probable that more dSph companions to M31 will eventually be found. Only three such objects (And I, And II and And III) are presently known (van den Bergh 1972), whereas seven dSph companions (Sgr, UMi, Dra, Scl, Sex, Car, For) are known to be located within 150 kpc of the Galaxy – even though the Milky Way system is less luminous than the Andromeda nebula. It is, of course, possible that the small number of M31 dSph satellites is due to the fact that some dwarf companions to M31 were destroyed by tidal interactions with M32 and NGC 205. For reviews on dwarf spheroidal galaxies the reader is referred to Da Costa (1992), Gallagher & Wyse (1994) and Ferguson & Binggeli (1994).

A short history of stellar astrophysics

Since the Sun is a star it is probably correct to say that stellar astrophysics began with Newton's well-known explanation for the Keplerian laws of planetary motion. Although J. Goodricke observed the eclipsing binary variable Algol (β Persei) in 1782, it was not until 1803 that Sir William Herschel's observations of Castor proved that two stars revolve around each other owing to their mutual gravitational attraction.

The first measurements of stellar parallax were made by F. W. Bessel and F. G. W. Struve in 1838. F. Schlesinger revolutionized stellar distance determinations in 1903 when he introduced photographic parallaxes and thereby enabled astronomers to measure parallaxes to an accuracy of about 0.01 arc seconds. K. Schwarzschild initiated photographic photometry during the years 1904–8. Photoelectric photometry of stars began shortly after the photocell was invented in 1911.

J. Fraunhofer discovered Fraunhofer absorption lines in the solar spectrum in 1814 and subsequently observed similar lines in other stars. In 1860 Kirchhoff formulated the relationship between radiative absorption and emission of radiation which is known as Kirchhoff's law. The Doppler effect and Kirchhoff's law formed the conceptual basis of early studies of stellar atmospheres. The quantum theory of blackbody radiation was introduced by M. Planck in 1900. To a first approximation most stars radiate as blackbodies with superimposed absorption and emission lines. The modern theory of radiative transfer in stellar atmospheres was initiated in 1906 by K. Schwarzschild.

Remarkable progress in understanding stellar phenomena has occurred in recent decades. This textbook discusses in some detail those equations and physical processes that are of greatest relevance to stellar interiors and atmospheres and closely related astrophysics. Motivation for writing this book came from my own research interests and also from teaching graduate astrophysics courses, especially a course on stellar interiors at the University of Maryland. Although the text emphasizes physical principles, astronomical results and unresolved issues are also described.

Introductory material on the history of stellar astrophysics, astronomical observations, star formation and stellar evolution are given in Chapter 1, which also contains a discussion of spectroscopic binaries. Differences between single and binary star evolution have explained a number of interesting observations that are described further in later chapters.

Stellar interiors is one of the most fundamental subjects in astrophysics. Although complicated physical processes are decisive in explaining some predictions of stellar model calculations, the basic principles of stellar interiors do not require a comprehensive knowledge of them. Chapter 2 gives an introductory discussion of the physics and equations of stellar interiors. It also includes a short description of numerical methods.

Statistical physics provides the theoretical basis for much of stellar astrophysics. In Chapter 3 those aspects of statistical physics that are of greatest relevance are developed in some detail. Stellar opacities play a vital role in interpreting observations. Absorption processes are described in Chapter 4.

Morgan (1958) has said that ‘The value of a system of classification depends on its usefulness.’ Using this criterion the Hubble classification system has proved to be of outstanding value because it has provided deep insights into the relationships between galaxy morphology, galactic evolution and stellar populations. However, some classification parameters, such as the r and s varieties in the de Vaucouleurs system, have not yet been tied as firmly to physically significant differences between galaxies (cf. Kormendy (1982)). Furthermore, it is not yet clear if the dichotomy between ordinary and barred spirals allows one to draw any useful conclusions about the past evolutionary history of a particular galaxy.

The Hubble system was designed to provide a framework for the classification of galaxies in nearby regions of the Universe. It is therefore not surprising that it does not provide a useful reference frame for the classification of very distant galaxies (which are viewed at large look-back times), or for galaxies in unusual environments such as the cores of rich clusters. Furthermore, the existence of some classes of objects, such as (1) amorphous/Ir II galaxies, (2) anemic galaxies and (3) cD galaxies, which cannot be ‘shoehorned’ into the Hubble system, suggests that such galaxies have had an unusual evolutionary history. It has also become clear that the Hubble system, which is defined in terms of supergiant prototypes, does not provide a very useful framework for the classification of low-luminosity galaxies.

Pulsational instability

In Chapter 1 we discussed some of the observational properties of periodic variable stars. The instability that drives pulsations in RR Lyrae variables, Cepheids and long-period variables is associated with hydrogen and helium ionization zones. The large heat capacity of these ionization zones causes the phase of maximum luminosity to be delayed by approximately 90° as compared to the phase of minimum radius. Thermonuclear reactions can also cause stars to become pulsationally unstable. Very massive stars and white dwarfs in which thermonuclear runaways are caused by mass accretion from a binary companion become pulsationally unstable as the result of their hydrogen-burning sources. To determine whether a particular star is pulsationally unstable one first determines the structure of the star (i.e. r = r(Mr), P = P(Mr), ρ = ρ(Mr), Lr = Lr(Mr)) and then solves the linearized equation of motion for the oscillatory modes. It is usually adequate to assume that stellar oscillations are adiabatic. If the oscillatory modes of a star have been determined we can evaluate a stability integral which will be derived below. The sign of this stability integral determines whether a particular stellar model is unstable to self-excited oscillations at a particular frequency (eigenmode). We are usually interested only in radial modes of oscillation and in most circumstances only the longest period mode is pulsationally unstable. In β Canis Majoris stars (also known as β Cepheid variables) nonradial oscillatory modes can also become excited.

Gravitational instability

We saw in chapter 4 that our universe contains a hierarchy of structures from planetary systems to super clusters of galaxies. Between these two extremes we have stars, galaxies and groups and clusters of galaxies. Any enquiring mind will be faced with the question: how did these structures come into being?

Is it possible that structures like our galaxy have always existed? The answer is ‘no’ for several reasons. To begin with, stars are shining due to nuclear power which runs out after some time. So it is clearly impossible for any single star to have existed for infinite amount of time. One can, of course, recycle the material for a few generations but eventually even this process will come to an end when all the light elements have been exhausted. So clearly, no galaxy can last for ever. Secondly, we saw in chapter 5 that – at the largest scales – the universe is expanding, with the distance between any two galaxies continuously increasing. This led us to a picture of the early universe with matter existing in a form very different from that which we see today. It follows that the structures like galaxies which we see today could not have existed in the early universe, which was much hotter and denser. They must have formed at some finite time in the past.

How early in the evolution of the universe could these structures have formed? As we shall see, we do not have a definite answer to this question. However, we saw in the last chapter that neutral gaseous systems formed when the universe was about 1000 times smaller.

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.