Advances in observational astronomy during the 1990s have finally allowed direct study of the population of normal galaxies at high redshifts, as discussed in chapter 13. For more than two decades prior to this, the only objects that could be studied out to cosmologically important distances were ‘active’ galaxies such as quasars, where the dominant energy output is not due to stars. This chapter attempts to separate out those aspects of active galaxies that are of especial cosmological interest, although any such division is inevitably blurred. Many of the interesting details of the subject will be omitted: good references for digging deeper into this area are Weedman (1986), Blandford, Netzer & Woltjer (1990), Hughes (1991) and Robinson & Terlevich (1994).

The population of active galaxies

classification Active galaxies come in a variety of species, many of which overlap. The definition of an active galaxy is one where a significant fraction of the energy output in at least some waveband is not contributed by normal stellar populations or interstellar gas; however, all galaxies emit non-thermal radiation at some level, and so classification as active is only a matter of degree. Things are a little more clear cut with AGN (active galactic nuclei), where the non-thermal emission comes mainly from the central few pc of the galaxy.

Elementary particles and fields

The apparatus of quantum field theory is an effective tool for calculating the rates of physical processes. All that is needed is a Lagrangian, and then there is a relatively standard procedure to follow. The trouble with this generality is that there is no way of understanding why certain Lagrangians are found in nature while others are not. The present chapter is concerned with the progress that has been made in solving this problem. The last four decades have seen tremendous developments in understanding: a few simple principles end up specifying much of the way in which elementary particles interact, and point the way to a potential unification of the fundamental interactions. These developments have led to the standard model of particle physics, which in principle allows any observable quantity related to the interactions of particles to be calculated in a consistent way.

The standard model asserts that the building blocks of physics are a certain set of fundamental particles from which the composite particles seen in experiments are constructed; their properties are listed in table 8.1 (see the references to the Particle Data Group in the bibliography). This set is much larger than the electron, proton and photon, which were all that was needed in 1920, but it is believed to be complete.

The idea of this chapter is to go into more detail on a few selected topics in relativity, concentrating on those that are of the most direct interest to the astrophysicist: fluid mechanics, weak fields and orbits therein, gravitational radiation and black holes. A word of warning: so far, all equations have been explicitly dimensional, and contain the correct powers of c; from now on, this will not always be the case. It is common in the literature on relativity to simplify formulae by choosing units where c = 1. Since this can be confusing for the beginner, c will be retained where it does not make the algebra too cumbersome. However, sometimes it will disappear from a derivation temporarily. This should encourage the good habit of always being aware of the dimensional balance of any given equation.

Relativistic fluid mechanics

One of the attractive features of relativity is the economical form that many of its fundamental equations can take. The price paid for this is that the quantities of interest are not always immediately available; the process of ‘unpacking’ some of these expressions can become rather painful and reveal considerable buried complexity. It is worth illustrating this with the example of fluid mechanics, not just for its own sake, but because we will end up with some results that are rather useful in astrophysics and cosmology.

Magnetic fields in the Cosmos

Around 1600 William Gilbert, physician to Queen Elizabeth I of England, proposed a bold hypothesis to explain why a suspended compass needle points in the north–south direction. He suggested that the whole Earth is a huge magnet and attracts the compass needle. This is probably the first time that somebody proposed an astronomical object—the planet Earth—to have a large-scale magnetic field. Initially it was thought that the Earth's magnetism was of ferromagnetic origin. By the end of the nineteenth century, it became clear that a ferromagnetic substance does not retain the magnetism when heated beyond a certain temperature (the Curie point). Since the interior of the Earth is believed to be hotter than the Curie temperature of any known ferromagnetic substance, it was apparent that one has to look for alternative explanations for the Earth's magnetic field.

Until the beginning of the twentieth century, it was not known whether other astronomical objects have magnetic fields as well. When Hale (1908) made the momentous discovery of magnetic fields in sunspots on the basis of the Zeeman splittings of sunspot spectra, the existence of magnetic fields outside the Earth's environment was conclusively established for the first time. Large sunspots can have magnetic fields of the order of 3000 G, which is much stronger than the Earth's field (the maximum value on the Earth's surface is about 0.6 G). One of the major achievements of twentieth century astronomy is to establish that magnetic fields are ubiquitous in the Universe.

We have come to the end of a long journey. Before saying a final goodbye to the reader, we wish to present an assortment of mixed fares in this final chapter. The main purpose of the book has been to develop the fundamentals fully. We now give a glimpse of what lies beyond the horizon.

Often it happens that one does not know the details of the physical conditions inside an astrophysical system, but can make rough estimates of different kinds of energies contained in the system (kinetic, potential, magnetic, etc.). To handle such situations, one can suitably integrate the basic equations to obtain an equation connecting different types of total energies of the system. This equation is known as the virial equation. Since this approach is very general, we present a discussion of it in this final chapter, when the reader should be in a position to possess a broad overview of the whole field. While applying hydrodynamics and magnetohydrodynamics to astrophysical systems, often it becomes necessary to incorporate relativistic corrections or to include the effects of radiation pressure. The subjects of relativistic hydrodynamics and radiation hydrodynamics respectively deal with these problems. These are vast fields of study, and we cannot provide proper treatments of these two fields in this elementary book. Just to give an idea of how one proceeds, we discuss the basic equations of these two fields in §17.2 and §17.3. Compared to the usual style of presentation in this book, these two sections would appear like skeletons without flesh and blood.

Hydrodynamics, magnetohydrodynamics, kinetic theory and plasma physics are becoming increasingly important tools for astrophysics research. Many graduate schools in astrophysics around the world nowadays offer courses to train graduate students in these areas. This was not the case even a few years ago—say around 1980—when it was rare for an astrophysics graduate school to teach these subjects, and the students who needed the knowledge of these subjects for their research were supposed to pick up the tricks of the trade on their own. With increasing applications of these subjects to astrophysics—especially to understand many phenomena discovered in the radio, X-ray or infrared wavelengths—the need is felt to impart a systematic training in these areas to all graduate students in astrophysics.

When I joined the faculty of the Astronomy Programme in Bangalore in 1987, I argued that a course covering these subjects should be introduced. My colleague and friend, Rajaram Nityananda, shared my enthusiasm for it, and we together managed to convince the syllabus committee of the need for it. From then onwards, this course has been taught regularly in our graduate programme, the responsibility of teaching it falling on my shoulders on several occasions. When I taught this course for the first time in 1988, I had to work very hard preparing lectures from different sources. I was lucky to have taken such a course myself as a graduate student in Chicago in 1981—taught by E. N. Parker—although it was somewhat unusual at that time for astronomy departments in the U.S.A. to offer such courses.