Introduction

Coronal loops are a phenomenon of active regions (Chapter 1) and there is growing evidence that they are in fact the dominant structures in the higher levels (inner corona) of the Sun's atmosphere. Our knowledge of loops has greatly expanded in recent years as a result of space observations in the far ultraviolet and X-ray regions of the spectrum. However, the success of the space work should not be allowed to obscure the fact that a considerable amount of quantitative information on the morphological, dynamical, and physical properties of coronal loops has been derived from ground-based observations in the visible and near-visible regions. In fact, observations at these wavelengths have achieved significantly higher spatial resolution (better than 1″ of arc) than almost all of the space observations so far obtained. Our aim in this and the following chapter is to bring together all the available data and thus present an integrated and consistent picture of the properties of non-flare coronal loops.

Observations show that coronal loops, depending on their temperature, can be divided into two distinct categories. The properties of the two types differ radically. Loops formed at temperatures in excess of ∼ 1 × 106 K are conventionally referred to as ‘hot’ loops, while those formed at lower temperatures are termed ‘cool’ loops. It is convenient to deal with the two types separately, cool loops in the present chapter and hot loops in Chapter 3.

Space, time, and gravitation

GENERAL RELATIVITY is Einstein's theory of gravitation. It is not only a theory of gravity: it is a theory of the structure of space and time, and hence a theory of the dynamics of the universe in its entirety. The theory is a vast edifice of pure geometry, indisputably elegant, and of great mathematical interest.

When general relativity emerged in its definitive form in November 1915, and became more widely known the following year with the publication of Einstein's famous exposé Die Grundlage der allgemeinen Relativitätstheorie in Annalen der Physik, the notions it propounded constituted a unique, revolutionary contribution to the progress of science. The story of its rapid, dramatic confirmation by the bending-of-light measurements associated with the eclipse of 1919 is thrilling part of the scientific history. The theory was quickly accepted as physically correct—but at the same time acquired a reputation for formidable mathematical complexity. So much so that it is said that when an American newspaper reporter asked Sir Arthur Eddington (the celebrated astronomer who had led the successful solar eclipse expedition) whether it was true that only three people in the world really understood general relativity, Eddington swiftly replied, “Ah, yes—but who's the third?”

Introduction

The actual initiation of jets is a subject that remains extremely difficult to discuss in a detailed and convincing manner despite the obvious importance of this fundamental topic. There are two main reasons for this. The first is a lack of unequivocal observations. Although VLBI measurements have provided structural information on scales corresponding to ≲ 0.1 pc in extragalactic sources, the phenomena that govern the beginnings of jets almost certainly occur on scales at least two to three orders of magnitude smaller. Other observations, especially of X-ray and optical variability, are indubitably important and provide useful constraints on models; however, they do not yield information that is clearly interpretable in a model-independent fashion.

The second generic difficulty has to do with the certainty that the physical processes involved in producing jets are extraordinarily complex. The core of the picture, that accretion onto a super-massive black hole (SMBH) of somewhere between 106 and 1010M≲ is at the heart of beam generation as well as the other properties of active galactic nuclei (AGN), has been commonly accepted for about a decade. However, in attempting to add details to this picture, astrophysicists find that general relativity, hydrodynamics, plasma physics and radiation transport all form thick blobs on their palettes, and the portraits which emerge from combining them in different proportions are, not surprisingly, rather different.

Introduction

The attractive features of the ‘beam’ model for galactic and extragalactic radio sources are predicated on the contention that astrophysical processes permit the formation of high-power collimated flows, and that such flows survive their passage from the generating engine to the outer parts of the source without losing most of their energy. In other words, astrophysical plasma beams must be capable of exceptional stability, although there are sources for which less stability is necessary. This may be seen in the ‘P-D’ diagram of Baldwin (1982) (cf. Chapter 2) – for a given radio power (say 1027 W Hz −1 sr −1), radio sources spanning a wide range of linear sizes (about 1 to 1000 kpc) are found, and hence the beams driving these sources must be stable over distances exceeding 1 Mpc in the largest objects, but need be stable for only 1 kpc in the smallest. The purpose of this chapter is to discuss the physical mechanisms that are effective in stabilising and destabilising beam flows, and to calculate the stability properties of some beams that might be components of extragalactic radio sources. Much of the physics discussed here can be applied to Galactic jets (Chapter 10), with some modification for the difference in physical parameters.

THE AIM OVER the next two chapters is to construct a solution of Einstein's equations with sources that will provide a model for the large scale features of the universe. First, we must find a reasonable form for the metric and energy-moment urn tensor consistent with the observed symmetries of the universe. Then we shall be led to specific cosmological models by the imposition of the Einstein equations.

We are thinking of the average features of the universe on the scale of tens of millions of light years and we may regard the basic building blocks as clusters of galaxies. The first observational fact about the universe that we must use is that the observed distribution of the clusters of galaxies is isotropic to a high degree. If we assume that our position is in no particular way privileged, we must assume the universe is isotropic about every point, which leads to an assumption of homogeneity.

We must distinguish a preferred class of observers, namely those that actually see the universe as isotropic. Thus our cosmological model admits a preferred time-like vector field ua , tangent to the world lines of the preferred or ‘fundamental’ observers.

Introduction

Our interferometric images of radio sources reflect the synchrotron emissivity arising from their relativistic electrons and magnetic fields. These trace the underlying plasma flow, albeit imperfectly. The local dynamical evolution of the particles and fields is determined by their transport from the nuclear source, and by their in situ dynamics. This chapter presents the physics necessary for an understanding of current theories of particle acceleration and magnetic field evolution. It describes these theories and attempts to assess whether or not they provide an adequate account of the inferred particle spectra, energetics and magnetic field geometry of extragalactic jets.

It was shown in Chapter 3 that some sources have severe lifetime problems, in that the time for the electrons to be carried out to the lobes (even with a jet speed ~ c) is longer than their radiation lifetime (the upper limit of which is the lifetime to Compton losses on the 3 K background) and that the surface brightness and spectral index distributions do not decay as fast as would be expected in a constant velocity, expanding flow. These problems may be overcome by the local reacceleration of the radiating particles. Further, simple estimates of convection of flux-frozen magnetic field out from the core predict that the convected field decays significantly; however, this is probably offset by in situ amplification of the magnetic field by some dynamo process.

WE PROCEED to solve the geodesic equations in the Schwarzschild solution and use the solution to describe the classical tests of general relativity. These are the precession of the perihelion of planetary orbits and the bending of light by the sun, effects that arise from the small differences between orbits in Newtonian gravitation and orbits, i.e. geodesies, in general relativity.