Introduction

We have seen in the foregoing chapters that a huge variety of accretion flows are at least theoretically possible. The equations describing axially symmetric flows with gravity, pressure and rotation allow a wide array of solutions of astrophysical interest. If one includes Ω = 0 (no rotation) as a special case, then even ordinary stars and spherically symmetrical Bondi accretion are solutions. More realistically, accretion flows with low angular momentum may produce supersonic flows which shock at smaller radii if they lack pressure support, or produce settling, cooling solutions if partially supported by pressure. We have already studied in detail spherically symmetrical accretion, the standard thin disc, and thick discs, and we will study other solutions which have acquired recognition in the astrophysical literature, such as slim discs and advection dominated accretion flows (ADAFs). In this chapter we shall attempt to organize all the different solutions into a coherent picture in order to clarify their relation to each other.

The fact that black holes possess an event horizon instead of a hard surface makes the inner boundary condition for black hole accretion flows qualitatively different from that for a normal star, and allows the existence of a family of solutions in which a significant fraction of the dissipated energy is advected through the horizon. Hence, for an external distant observer, ADAFs on to black holes are characterized by a low radiative efficiency η. (In ADAFs on to objects with a hard surface the advected energy must be ultimately reprocessed and released near the surface – see Section 11.8.3.)

Introduction

All accreting matter, like most of the material in the Universe, is in a gaseous form. This means that the constituent particles, usually free electrons and various species of ions, in teract directly only by collisions, rather than by more complicated short-range forces. In fact, these collisions involve the electrostatic interaction of the particles and will be considered in more detail in Chapter 3. On average, a gas particle will travel a certain distance, the mean free path, λ, before changing its state of motion by colliding with another particle. If the gas is approximately uniform over lengthscales exceeding a few mean free paths, the effect of all these collisions is to randomize the particle velocities about some mean velocity, the velocity of the gas, v. Viewed in a reference frame moving with velocity v, the particles have a Maxwell–Boltzmann distribution of velocities, and can be described by a temperature T. Provided we are interested only in lengthscales L ≫ λ we can regard the gas as a continuous fluid, having velocity v, temp erature T and density ρ defined at each point. We then study the behaviour of these and other fluid variables as functions of position and time by imposing the laws of conservation of mass, momentum and energy. This is the subject of gas dynamics. If we wish to look more closely at the gas, we have to consider the particle interactions in more detail; this is the domain of plasma physics, or, more strictly, plasma kinetic theory, about which we shall have something to say in Chapter 3.

In the years since the first edition of this book appeared the study of astrophysical accretion has developed rapidly. Perhaps the most fundamental change has been the shift in attitude over active galaxies and quasars: the view that accretion is the energy source is now effectively standard, and the emphasis is much more on close comparison of observation and theory. This change, and the less spectacular but still profound one which has occurred in the study of close binary accretion, have been largely brought about by the wealth of new data accumulated in the interval. In X-rays, the ability of EXOSAT to observe continuously for as much as 3 to 4 days was a dramatic advance. In the optical, new instrumentation has produced far tighter observational constraints on theory. Despite these challenges, the basic outlines of the theory are still recognizably the same.

Of course our understanding is very incomplete. As the most glaring example, we still have essentially no idea what drives disc accretion; and there are new problems such as the dynamical stability of thick discs, or the nature of fieldline threading in magnetic binaries. But it is now difficult to deny that some close binaries possess discs approximately conforming to theoretical ideas; or that some kind of anisotropic accretion occurs in active galactic nuclei. Encouragingly, accretion theory is increasingly integrated into wider pictures of the relevant systems. The process is well advanced for close binaries, particularly for the secular evolution of cataclysmic variables, and is in its early stages for active galaxies.

Introduction

In these final three chapters we come to the mechanism by which the gravitational potential energy of material accreting on to a superrnassive black hole is extracted as radiation. We start with the radio emission on kpc–Mpc scales which, where it occurs, is probably the best understood feature. To power the extended radio lobes the central engine in sources with such large-scale radio structure must turn accretion energy into directed bulk relativistic outflow. It is universally accepted that the power law radio spectrum from the lobes is synchrotron radiation from relativistic electrons. At the other extreme the X-ray emission appears to be produced on scales down to tens of Schwarzschild radii, providing the deepest possible probe of conditions near the black hole. However, the X-ray power law spectrum seems to admit any number of explanations. There is a problem here in distinguishing the primary radiation from any reprocessed components.

Since, therefore, we are not certain of either the geometry of the central source or the emission mechanism responsible for any part of the spectrum from this region, a discussion of accretion power in active nuclei contrasts sharply with our previous consideration of binary star systems. We shall present a range of partial theories each focussed on a different aspect of the problem. The thick discs expected at super- Eddington accretion rates to be considered in Chapter 10, and the electrodynamic disc theories discussed here in Sections 9.6–9.8 are primarily concerned with the production of power in the form of bulk relativistic outflows.

Introduction

In previous chapters we have discussed extensively the theory and applications of thin (H ≪ R) accretion discs. We hope the reader will by now be convinced that this theory is reasonably well understood, and that it rests on a fairly firm observational basis. The case for thick (H ∼ R) accretion discs however is less compelling as the theory is still under development and the relevant observations are few, difficult and indirect. Furthermore, since the publication of the first papers on equilibrium thick discs or tori much work has been done on extending these solutions allowing some form of poloidal flow and studying extensively their dynamical stability. The wealth of these investigations is a testimony to the interest generated by these structures. The results obtained so far virtually rule out the reality of thick discs as non-accreting toroidal equilibria but leave open the more exciting possibility of the existence of closely related accreting flows which could be of astrophysical interest. We begin here by discussing the toroidal equilibria without accretion and summarize the stability results at the end of this chapter. More recent and more general solutions with radial and other poloidal flows are discussed in Chapter 11.

The current interest in the theory of the structure, evolution and stability of thick accretion discs is due to the possibility that thick discs may be relevant to the understanding of the central power sources in radio galaxies and quasars (see Chapters 7–9).

Observations

Accretion on to stellar mass objects occurs in a wide variety of systems and yields a wide variety of observational behaviour. While there may be many arguments over detailed models, the broad basis of these differences is largely understood. Active galactic nuclei also come in many observed forms. From an observational viewpoint, they can be defined as apparently stellar sources but with non-thermal spectra, and, in cases where they can be determined, significant redshifts. Beyond this, we find a wide variety of properties, which we shall classify in more detail below. But in these cases it is not at all clear how these differences arise, or, indeed, whether one is even dealing with variants of a single basic model. We shall argue that the sources are all manifestations of accretion on to supermassive black holes (of order 108M⊙), although even this is still not universally accepted. Furthermore, for stellar-mass objects, at least in some cases, we have a complete picture of the system even if some of the details are missing. In no case do we have anything comparable for active galactic nuclei. That is not to say that there are no aspects of active galactic nuclei that are thought to be fairly well understood, but those that are do not include the mechanism of the basic energy source. Thus we have to try to extract from the available data what clues we can to the nature of the central engine.

In the decade since the second edition of this book, accretion has become a still more central theme of modern astrophysics. We now know for example that a γ-ray burst briefly emits a gravitationally powered luminosity rivalling the output of the rest of the Universe. This and other startling discoveries are a result of observational progress, driven as ever by technological advances. But these advances are also having a powerful effect on theory; modern supercomputers allow one to perform as a matter of routine calculations which were unthinkable a decade ago. This increasing capability will significantly alter the way theory is done, and indeed thought about.

The impact on accretion theory has already been profound. Most obviously, supercomputer simulations have been central in verifying that angular momentum transport in accretion discs is probably mediated by the magnetorotational instability. This opens the prospect of at last understanding how accretion is driven in the discs we see.

These changes and others make a new edition of this book timely. We are grateful for the opportunity of revising and extending the treatments of the earlier editions. As always, we have been obliged to be selective, but have tried to convey the essence of recent developments. In addition to discussing the new work on disc viscosity referred to above, we give a more thorough treatment of the thermal–viscous disc instability model now generally thought to be the basic cause of the outbursts of dwarf novae and soft X-ray transients.

Introduction

The importance of accretion as a power source was first widely recognized in the study of binary systems, especially X-ray binaries. This is still the area where the greatest progress in the understanding of accretion has been made. The reason for this is simply that, by their very nature, binaries reveal more about themselves, notably their masses and dimensions, than do other astronomical objects. This is particularly true in the case of eclipsing binaries, where we get direct information about spatial relations within the source. The importance of accretion is further manifested by the realization that probably a majority of all stars are members of binary systems which, at some stage of their evolution, undergo mass transfer.

The detailed study of interacting binary systems has revealed the importance of angular momentum in accretion. In many cases, the transferred material cannot land on the accreting star until it has rid itself of most of its angular momentum. This leads to the formation of accretion discs, which turn out to be efficient machines for extracting gravitational potential energy and converting it into radiation. This property has made accretion discs attractive candidates for the role of the central engine in quasars and active galactic nuclei; the question of whether or not this assignment is correct will be a theme of later chapters. In the context of binaries, however, their existence and importance is well attested through observation; we shall discuss the evidence for this in Chapter 5.

Overview

In previous chapters, we have discussed noble gas characteristics in major geological divisions in the Earth, such as ocean, crust, and mantle. Differences in noble gas isotopic ratios and in relative elemental abundances among these divisions are primarily due to the addition of radio- and nucleogenic isotopes and to elemental fractionation in the course of evolution of the respective regions. An implicit assumption underlying these discussions is that the Earth was endowed with a primordial noble gas common to all the regions. Although we still do not have direct evidence to prove (or disprove) this, discussions in previous chapters and also in this chapter seem to support this assumption. A question then arises: what would be the primordial noble gas in the Earth? In this regard, we emphasize that the primordial noble gas in the Earth, especially its isotopic compositions, is a key constraint as a reference in any Earth evolution model including noble gases. Through various discussions of noble gas characteristics given in previous chapters, we have learned that the primordial noble gas in the Earth was likely to be derived from solar noble gas by some massdependent fractionation. In this chapter, especially in Sections 7.3 and 7.7, we will discuss these questions in more detail.

As already mentioned, current noble gases in the Earth have been modified by addition of radio- and nucleogenic isotopes and by elemental fractionation due to various geological processes.

Introduction

As a good first-order generalization, the noble gases found in natural waters are acquired from air and are present in concentrations approximately consistent with air equilibration. Solubility data (Tables 4.1–4.4 and Fig. 4.1) are thus of central importance in evaluating noble gas observations in water. A comprehensive review and data evaluation for the general phenomenon of gas solution in water is given by Wilhelm et al. (1977).

On the whole, noble gases exhibit about the same order of magnitude of solubility in water as do other gases that do not react chemically with the water. Ar, in particular, is approximately as soluble as the major atmospheric gases: its solubility (pure water at 0°C) is 2.26 times that of N2 and 1.09 times that of O2. As a group, however, the noble gases exhibit a fairly wide spread in solubilities, with the characteristic features of strongly increasing solubility and temperature dependence of solubility with increasing atomic weight. This signature, combined with the useful feature that (with exceptions discussed later) they are conservative – no sources or sinks in organisms or other material in sea water and unlikely to participate in complex chemical reactions – makes the noble gases useful in a variety of geochemical studies.

A noteworthy feature of such studies is that they frequently make the most stringent demands encountered in noble gas geochemistry for high-precision absolute elemental abundances.

For noble gases much more than for other elements, it is impossible to have a coherent appreciation of circumstances on the Earth without a background appreciation of circumstances in the solar system as a whole, or more generally the cosmos at large. This generalization reflects the situation that the original complement of noble gases in the Earth is likely at least partially different from noble gases in other objects in the solar system, and that one cannot adequately understand the unique modifications arising in the Earth's own evolution without understanding the nature of the starting materials. The “cosmochemistry” of the noble gases, based largely but not entirely on the study of meteorites, is a discipline very rich both in data and in competing theories seeking to explain the data. It may also be noted that this is one of the disciplines that has changed dramatically since publication of the first edition of this book. It is not our intention to provide a comprehensive review of noble gas cosmochemistry, which would go considerably beyond our scope; instead, the intention is to focus on aspects most relevant as background to the study of terrestrial noble gases. A number of specific issues and questions in which cosmochemistry is important are raised in Chapter 7.

Cosmic Abundances

The atoms, specifically their nuclei, that comprise the solar system were made in a variety of environments (cf. Woolum, 1988).

Introduction

Except for radiogenic components, the amount of noble gases in the solid crust is safely assumed to be insignificant in terrestrial noble gas inventory. In general, except for in situ derived radiogenic and nucleogenic noble gases, trapped noble gases in crustal rocks are of an atmospheric origin. Because of the higher concentration of U, Th in the crust than in the mantle, however, nucleogenic Ne isotopes are often discernible in crustal materials. Near the Earth's surface, down to a few meters in depth, cosmic ray-induced cosmogenic Ne and He isotopes can also be observed. In deepocean bottom where sedimentation rate is extremely slow, extraterrestrial noble gases carried by cosmic dusts become conspicuous. In this chapter, we will discuss these unique features of noble gases in the crust.

Sediments

Noble gases in sediments once attracted much interest of noble gas geochemists for the following reasons. First, sediments could be a major reservoir for Xe and may account for the “missing Xe”, a long-standing puzzle in noble gas geochemistry (cf. Section 7.5). Because of the fine particle size, sedimenting particles would very effectively adsorb noble gases, especially the heaviest noble gas Xe, during sedimentation. Adsorption of atmospheric noble gases would also be substantial after emplacing sediments on the surface. It is also conceivable that they may have trapped a considerable amount of noble gases dissolved in water in the rock fabrics.