Introduction

Astronomy in the early part of this century demonstrated that galaxies were systems made of tremendous numbers of stars. Spectroscopy of galaxies revealed the absorption lines that would be expected in the composite light from stars of different spectral classes. Galaxies showing dominant emission lines in their spectra were recognized as highly unusual. The first of these to be studied, NGC 1068, was commented upon even before the real size and nature of galaxies were understood (Slipher 1918). For several decades, because of their rarity, such galaxies were sufficiently outside mainstream research as to be given little attention. The subject of emission line spectroscopy for extragalactic objects suddenly became extremely important with the discovery of quasars, whose visible spectra are characterized by strong emission lines. Emission lines can provide diagnostics of velocities, temperatures and densities unavailable from any other technique. The lines which can be seen represent a wide range of ionization, so line fluxes also provide indirect measurements of unobserved portions of the continuum. Not least is the fact that emission lines are spectroscopically conspicuous, calling attention to locations where unusual events are occurring. The general similarities among the emission line spectra of quasars, and the scaling of these lines with the continuum source, means that the emission line spectrum is a characteristic quasar feature. To understand the origin of these lines, it is necessary to review the general physical concepts of spectroscopy.

Basic test for evolution

Determining whether the properties of the universe have changed as a function of its age is a major concern of observational cosmology. Not without logic, a universe maintaining the same characteristics through all of time has a satisfying nature. If we could understand it now, we would by definition understand it always. Even those who do not adhere to such a steady state universe have been loath to invoke changing characteristics to the observable galaxies in the universe. Another one of the ironies of the history of astronomy is that the cosmological tests utilized to prove that we inhabit an evolving Friedmann universe, tests applied using the bright elliptical galaxies as distance probes for cosmological purposes, could not allow evolution of those same galaxies (Sandage 1961). Constancy of the galaxy properties was a necessary prerequisite to using them for cosmological purposes. It is presumed now that such galaxies do change, even over observable time scales, and our ignorance about the proper evolutionary corrections to apply has removed much of the stimulus for drawing cosmological conclusions (Tinsley 1977).

Yet, astronomers who two decades ago accepted little evolution for galaxies were never hesitant to accept a lot of evolution for quasars. Even now, it is necessary to invoke far more evolution in quasars than in galaxies to explain the data seen. Few are troubled by this inconsistency, but it is not too surprising that some are.

Optical surveys for quasars

Quasars cannot be studied until they are found. The purpose of any quasar survey is simply to provide an efficient method of discovering quasars. This efficiency is greatly enhanced if many quasars can be found with a single observation by the detecting instrument, so it is preferable if the observation has a wide enough field of view to include many detectable quasars. Furthermore, it is desirable but usually not feasible to identify a quasar with the survey observation alone, without the necessity of a subsequent observation with another instrument. Because of their characteristic signatures in many different parts of the spectrum, quasars can be surveyed for using various techniques. Much of the subsequent research effort goes into comparison of results from various techniques, to determine whether the same quasars are being found in different ways, or whether there are categories of quasars conspicuous to one form of observation but invisible to another.

Color based surveys

Quasars are easy to find with optical telescopes; a summary compilation by Smith (1984) lists over 40 surveys. The reason is because their spectral characteristics are so different from most stars and galaxies that broad band optical surveys using only three effective wavelengths can differentiate most quasars from other objects. Despite many other techniques for quasar surveys, including X-ray and radio surveys, the great majority of quasars have been discovered optically, and it is very probable that this will continue to be so.

Galactic envelopes of quasars

The discovery of quasars heralded the present era of astrophysics, characterized by wide ranging investigations of every part of the spectrum, whether easily accessible or not. Observers were stimulated to open new spectral windows, primarily in the hope of finding something as extraordinary and unexpected as the quasars. None succeeded. Even when observations were pushed to X-ray wavelengths, quasars stood out. When discovered, quasars came as a stunning surprise to the small community of theoreticians who dabbled in extragalactic astrophysics. The quasars seemed so unlike galaxies that it was not clear whether their redshifts should be interpreted with the same cosmological relations that applied to galaxies. Doing so gave unbelievable answers; the quasars were just too luminous to explain. Furthermore, surprise piled upon surprise, these luminosities arose in volumes so small that luminosity variations could be seen in times of less than a year. It was fair, even necessary, to question any assumptions made for quasars, including assumptions about cosmological redshifts. I have argued at some length (Weedman 1976), so will not repeat much of it here, that this bewilderment arose as a consequence of the sequence of discovery for quasars. Had quasars been discovered initially as events in the nuclei of galaxies, the nature of their redshifts would have never been questioned. As it happened, it was only realized after the fact that identical phenomena can be observed in galactic nuclei.

Ideal MHD instabilities

Macroturbulence in plasma is generated by MHD instabilities. These instabilities can be classfied as ‘ideal’ and ‘resistive’: dissipative processes play no role in ideal MHD and play an essential role in resistive MHD. Ideal MHD instabilities can be further divided according to the source of free energy and to the geometric structure of the plasma. In this Section we summarize the ideal MHD instabilities which depend solely on the geometric structure of the plasma. This topic is of central importance for laboratory devices, such as tokamaks, which need to be designed to maximize the confinement time. It is also of interest in astrophysical applications, e.g. to the stability of magnetic loop structures in the solar atmosphere. Our primary interest in this Chapter is in the generation and dissipation of MHD turbulence; the ideal MHD instabilities discussed in this Section are not particularly effective in generating turbulence because the supply of free energy is limited to that made available from changing the geometric configuration of the plasma. The discussion of these instabilities here involves little more than an introduction to the terminology used to describe the various instabilities and brief summaries of their properties.

A plasma confined by a magnetic field is intrinsically unstable. This follows from the fact that the only stable solution of the Vlasov equation is a uniform Maxwellian distribution, and this is independent of the presence or absence of a magnetic field.

Fundamentals of a luminosity function

Understanding the true distribution of objects in space has always been a basic objective of astronomy. Highly sophisticated statistical techniques were developed for determining the distribution of stars in our Galaxy (Trumpler & Weaver 1953). Many of these techniques have recently resurfaced for application to quasars. In many respects, there are great similarities between quasar counting, as done today, and the star counting in the early part of this century that led to an understanding of the structure of our Galaxy. Let us hope that similarly significant results may eventually arise from current quasar surveys. It would be convenient to apply the older techniques directly to quasars, just plugging in a few new numbers. This cannot be done, however. Determining the distributions of interest requires dealing with three dimensions, and the cosmological equations that relate distance for quasars to the observable redshift are much more complex than the euclidean geometry usable by galactic astronomers. Furthermore, quasars are not distributed uniformly in the universe, so statistical techniques based upon homogeneous distributions will not work. Finally, all of the equations of statistical stellar astronomy use magnitude units. This is still the case for most optical astronomy of quasars, but not so for quasar counts based on radio or X-ray observations. So we must deal with the additional complication of discussing both magnitude and flux units. It is necessary, therefore, to build a discussion of ‘statistical astronomy’ for quasars from first principles.

Preliminary remarks

One of the most obvious features of the plasma state is the rich variety of wave motions which plasmas can support. Waves of a particular kind are said to be in a particular wave mode. The idea of a wave mode is familiar from other contexts. For example in a compressible gas there are sound waves and, if there is a gravitational field present, there are also internal gravity waves. These waves have specific dispersion relations, which relate the frequency ω to the wave vector k. For sound waves and internal gravity waves the dispersion relations are ω = kcs and ω = (gk)½ respectively, where cs is the sound speed and g is the gravitational acceleration. One could cite numerous examples of wave modes in other media, e.g. spin waves in ferromagnetic media and seismic waves in the solid Earth, each of these is characterized by its dispersion relation and other properties which determine the nature of the wave motion. The wave modes of a plasma depend on the plasma properties and these are described in terms of various plasma parameters. Of particular importance are the natural frequencies of the plasma: the electron plasma frequency ωp, the electron cyclotron frequency Ωe, the corresponding ion frequencies ωpi and Ωi, and various collision frequencies (vei, vee, vii) between electrons (e) and ions (i).