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).

The bump-in-tail instability

Many microinstabilities have both reactive and kinetic forms. From a mathematical viewpoint one treats the reactive form by ignoring the imaginary part of the dielectric tensor and solving a real dispersion equation to find complex solutions, and one treats the kinetic form by assuming real frequencies to a first approximation and then including weak (negative) damping. To be more specific, in the weak-beam instability (§3.3) thermal motions are neglected and the correction to the real part of the dielectric tensor due to the presence of trie beam leads to a cubic equation (3.11) for the frequency shift of the Langmuif waves; this cubic equation has a real solution and a pair of complex conjugate solutions in the regime of interest. The kinetic version of this instability is known as the bump-in-tail instability. It is treated by first finding the imaginary contribution of the beam to the dielectric tensor and using this to evaluate the imaginary part of the frequency shift.

It is apparent from the foregoing discussion that the reactive and kinetic versions should be limiting cases of a single instability. This may be shown by finding both the real and imaginary parts of the frequency shift simultaneously. The real and imaginary parts of the frequency can be found as a complex solution for ω as a function of real k to the complex dispersion equation KL(ω, k) = 0, where both real and imaginary parts of KL are retained.

Resonant scattering

The scattering rate due to Coulomb interactions between a fast particle (speed v) and thermal particles decreases with increasing v as v−3. Thus one might expect that fast particles are scattered very ineffectively. The reverse is the case in the low density (low β) plasmas in the magnetosphere, and in space and astrophysical plasmas generally. Fast particles are scattered very efficiently due to resonant interaction with low frequency waves, called resonant scattering.

The evidence which led to the initial development of the theory of resonant scattering came from the properties of the trapped particles in the magnetosphere. By the early 1960's it was clear that for the stability of the distributions of trapped magnetospheric particles (in the terrestrial ‘radiation’ or ‘van Allen’ belts) to be consistent with the observations of precipitation of these particles, both the fast electrons and the fast ions must be scattered very efficiently. The development of the theory of resonant scattering led to a satisfactory qualitative and semi-quantitative explanation for these magnetospheric observations. Resonant scattering also offered ways of resolving serious difficulties connected with the scattering and acceleration of fast particles in astrophysical plasmas. The most obvious of these concerns the confinement of galactic cosmic rays (§13.4). Another serious difficulty was with the acceleration of fast particles: early theories for the acceleration required (either implicitly or explicitly) very efficient scattering.

Introduction

In the chapters that follow, nearly a quarter century of intensive research and substantial progress in understanding the quasars will be summarized. From the perspective of an astronomer, it would be satisfying to report that this progress was primarily attributable to the cleverness and diligence of astronomers in attacking the problem. To be honest, however, most of the progress should be credited to the engineers and physicists who have developed the tools that allow our wide ranging probes into the mysteries of quasars. Trying to understand quasars forced astronomers into realizing that observations must extend over the broadest possible spectral coverage, that we must learn how to use X-ray, ultraviolet, optical, infrared and radio astronomy. It is now possible for an individual astronomer to have access to telescopes that access all of these spectral regions, and I am convinced that the definition of a ‘good’ observer in the next few decades will weigh heavily on the ability to be comfortable with all of these techniques. To realize how much this has changed the science of astronomy, one need only recall that the analogously important talents in 1960 were the ability to work efficiently at night, to withstand cold temperatures, and to develop photographic emulsions without accidently turning on the lights. At that time, the technically sophisticated astronomer was one who could use a photomultiplier tube.