Introduction

The interpretation of the diverse forms of observed radio source structure has always been problematical since this normally involves the use of some form of classification scheme. With the benefit of hindsight, it is clear that this exercise has not always proved to be a total success. Every astronomical object is the product of a unique set of physical circumstances which must, at some level, ultimately preclude the imposition of a generalised classification scheme covering many objects. It remains, however, a necessary basic stage in the process of scientific investigation. Any classification scheme is based upon gross structural features derived from observation. Such observations are of an inhomogeneous set of objects and are limited by sensitivity and imaging techniques. Schemes are therefore subject to strong selection effects and their subdivisions are arbitrary. A scheme can, however, prove useful provided the subdivisions broadly map out differing segments in the parameter space of the physical conditions of radio sources. The problem is, of course, that it is those very same physical conditions that are as yet unknown and that one is attempting to investigate. Thus, any current classification scheme is dominated by the characteristics of the telescopes available to observers at the time, and incorporates the ‘conventional wisdom’ derived from the interpretation of previous work. Such circumstances are profoundly inelegant but probably unavoidable.

Introduction

Flat spectrum nuclei are found at the centre of many types of extragalactic radio source, including the powerful classical doubles, and the ‘isolated’ compact sources (that have comparatively weak extended structure). They turn out (when examined with sufficient resolution) to be the self-absorbed bases of jets that feed the extended structure, whose continuations are often seen on much larger scales. The systematic properties of VLBI jets have been reviewed frequently and can be summarised thus:

1. The jets are nearly always seen on only one side of the nucleus. ‘Counterjets’ have only been seen in a few sources (for example 3C 236, Schilizzi et al. 1988).

2. The jets contain bright ‘knots’ of emission that are often seen to move outwards, away from the base at speeds commonly in the region of 5 to 10 times the speed of light (Ho = 100 km s−1 Mpc−1). Although some apparently stationary knots have been observed, for example the outer component in 4C 39.25 (Shaffer & Marscher 1988), none has ever been observed to move inwards (Marcaide et al. 1985).

3. The speeds and trajectories of the individual knots do not in general vary greatly as the knots move out; it is difficult to place very severe limits on acceleration because of the limited accuracy of positional measurements and the relatively short distances over which the knots are observed to move. Significant changes in speed and direction have been detected in 3C 345 (Biretta et al 1986).

4. […]

Cartesian tensors: an invitation to indices

LOCAL DIFFERENTIAL GEOMETRY consists in the first instance of an amplification and refinement of tensorial methods. In particular, the use of an index notation is the key to a great conceptual and geometrical simplification. We begin therefore with a transcription of elementary vector algebra in three dimensions. The ideas will be familiar but the notation new. It will be seen how the index notation gives one insight into the character of relations that otherwise might seem obscure, and at the same time provides a powerful computational tool.

The standard Cartesian coordinates of 3-dimensional space with respect to a fixed origin will be denoted xi (i = 1,2,3) and we shall write A = Ai to indicate that the components of a vector A with respect to this coordinate system are Ai . The magnitude of A is given by A · A = AiAi . Here we use the Einstein summation convention, whereby in a given term of an expression if an index appears twice an automatic summation is performed: no index may appear more than twice in a given term, and any ‘free’ (i.e. non-repeated) index is understood to run over the whole range.

Gross morphology

A crucial morphological feature of extended extragalactic radio sources is that (see Chapter 2) there are actually two fundamentally distinct classes of object, in which the weaker, Fanaroff & Riley (FR) class I, sources are characterized by quasi-continuous luminous jets which often become distorted as they interact with the inter-galactic medium (Fig. 2.3), whereas the more powerful, FR II, sources have a simple, linear, double-lobed structure, with the brightest emission occurring in compact hotspots at the edge of each lobe (Fig. 2.8). A central challenge for any theoretical model of extragalactic radio source structure is therefore to reproduce this observed dichotomy, and to identify the factor, or factors, that determine which type of extended structure develops. Furthermore, we might hope that an improved theoretical understanding of the Fanar off & Riley classification would enable us to make improved, dynamical, estimates for the, observationally badly determined, physical parameters of jets in radio sources.

Although a complete model for radio source structure would probably have to involve variations in both the strength and direction of the central engine, and a non-uniform external medium, considerable insight into their gross morphology can be gained from axisymmetric simulations of steady jets in a constant ambient medium. This model, which we shall refer to as the basic model, has the additional virtue of being less computationally expensive than fully three-dimensional simulations, permitting a wider range of jet parameters to be investigated.

Introduction

What are extragalactic radio sources?

We believe that extragalactic radio sources are interactions between large-scale jets and the hot, diffuse gas that surrounds elliptical galaxies. The interactions not only cause the hotspots, bridges, tails etc., but also the radio emission from the jets themselves. Radio sources should be thought of as processes rather than objects: the overall radio structure must change substantially on the shortest possible dynamical time scale, the sound-crossing time. Another way to put this is that, at least in the FR II sources, there is no steady-state description. This is the main reason why radio sources are much harder to understand than, say, main-sequence stars. On the other hand, the lack of equilibrium means that the structure of radio sources reflects their past history, so that in principle it should be much easier to deduce the life-cycle of radio sources than that of stars. At present, the most successful theoretical models concentrate on regions for which a local steady-state description is likely to be appropriate, notably the bases of jets, far from any end-effects, and in the co-moving frame of the hotspots, where the jets terminate.

It is worth emphasizing that in the standard model of FR II sources, and to a lesser extent FR Is, we only see half the story in the radio. As we shall see, it is usually assumed that synchrotron radiation is only emitted by plasma which has entered the system via the jet.

NO SINGLE theoretical development in the last three decades has had more influence on gravitational theory than the discovery of the Kerr solution in 1963. The Kerr metric is a solution of the vacuum field equations. It is a generalization of the Schwarzschild solution, and represents the gravitational field of a special configuration of rotating mass, much as the external Schwarzschild solution represents the gravitational field of a spherical distribution of matter.

However, unlike the Schwarzschild case, no simple non-singular fluid ‘interior’ solution is known to match onto the Kerr solution. There is, nevertheless, no reason a priori why such a solution shouldn't exist.

Fortunately such speculations are in some respects beside the point, since the real interest in the Kerr solution for many purposes is its characterization of the final state of a black hole, after the hole has had the opportunity to ‘settle down’ and shed away (via gravitational radiation and other processes) eccentricities arising from the structure of the original body that formed the black hole.

To put the matter another way, suppose someone succeeded in exhibiting a good fluid interior for the Kerr metric. Well, that would be in principle very interesting; but there is no reason to believe that naturally occurring bodies (e.g. stars, galaxies, etc.) would tend to fall in line with that particular configuration.

Introduction

Whilst the luminous jets of radio galaxies and quasars are the most powerful examples of collimated outflow in the cosmos, there are many examples of jets and outflows to be found much closer to home, within our own Galaxy. These span a great range of luminosities and collimation factors, from the optically visible jets and “lobes” associated with low-mass young stellar objects, which are morphologically very similar to the classical radio galaxies, to the poorly collimated and much less clearly denned “jets” associated with the Galactic Centre and with various supernova remnants. Galactic jet sources also include the singular object SS 433, which is known to be emitting a two-sided jet at a quarter of the speed of light. This jet is known to be associated with a binary star system, and there is some evidence that other mass-transfer binaries may also have jets.

In many cases the jet material itself is insufficiently excited to dissociate it completely, giving us a variety of spectral lines at optical, infrared and radio frequencies with which to probe the underlying kinematics, while the mere fact that these objects are close gives us greatly enhanced linear resolution. If there is a lesson to be learnt from the wide variety of systems which exhibit collimated mass-loss it is that jets are very easily formed once symmetry is broken through rotation.

IT IS INEVITABLE that with the passage of time Einstein's general relativity theory, his theory of gravitation, will be taught more frequently at an undergraduate level. It is a difficult theory—but just as some athletic records fifty years ago might have been deemed nearly impossible to achieve, and today will be surpassed regularly by well-trained university sportsmen, likewise Einstein's theory, now over seventy-five years since creation, is after a lengthy gestation making its way into the world of undergraduate mathematics and physics courses, and finding a more or less permanent place in the syllabus of such courses. The theory can now be considered both an accessible and a worthy, serious object of study by mathematics and physics students alike who may be rather above average in their aptitude for these subjects, but who are not necessarily proposing, say, to embark on an academic career in the mathematical sciences. This is an excellent state of affairs, and can be regarded, perhaps, as yet another aspect of the overall success of the theory.

A fresh look at anti-symmetric tensors

WE have introduced local differential geometry in a notation that makes great use of indices. This is the classical route and it does have a great deal of merit. There is a parallel development in an index free notation that is more generally used by pure mathematicians. The different approaches have their separate advantages and drawbacks: a calculation with indices may be cumbersome and sprawling; conversely an index-free notation may labour what is easily written with indices.

Introduction

In Chapters 1 through 4, we saw that the outer radio lobes associated with active galaxies receive their energy from a bulk hydrodynamic flow which emanates from the galactic nucleus. Bisymmetric outflow occurs on a wide range of scales in less energetic objects as well, as will be shown in Chapter 10.

Perhaps the most astonishing feature of cosmic jets is their ability to stay together over a very large range of distance scales. On their way from the black hole in the galactic nucleus to a radio lobe, cosmic jets cover a stupendous factor 109 in length scale. That is as if, exhaling forcefully at my desk in Leiden, I could blow about the papers on the desk of a colleague in Minneapolis. This should be a caution against off-the-cuff comparison between jets in radio galaxies and such comparatively easily understood items as laboratory jets, rocket exhausts, and numerical simulations.

The most natural explanation of the coherence of jets is that they are not jets at all, but gaseous cannonballs with a density that is much higher than that of their surroundings. What we perceive as jets would be a mixture of gas ablated from these “tracer bullets” and surrounding gas set aglow by their passage.