Introduction

In a compact binary a black hole, neutron star, or white dwarf accretes from a companion star. These systems have long been a paradigm for accretion theory. Much of our present view of how accretion occurs comes directly from the comparison of theory with observations of these sources. Since theory differs little for other objects such as active galaxies, increasing efforts have recently gone into searching for correspondences in observed behavior. This chapter aims at giving a concise summary of the field, with particular emphasis on new developments since the previous edition of this book.

These developments have been significant. Much of the earlier literature implicitly assumed that accreting binaries were fairly steady sources accreting most of the mass entering their vicinity, often with main-sequence companions, and radiating the resulting accretion luminosity in rough isotropy. We shall see that in reality these assumptions fail for the majority of systems. Most are transient; mass ejection in winds and jets is extremely common; a large (sometimes dominant) fraction of even short-period systems have evolved companions whose structure deviates significantly from the zero-age main sequence; and the radiation pattern of many objects is significantly anisotropic. It is now possible to give a complete characterization of the observed incidence of transient and persistent sources in terms of the disc instability model and formation constraints. X-ray populations in external galaxies, particularly the ultraluminous sources, are revealing important new insights into accretion processes and compact binary evolution.

Introduction

A census of baryons in the local universe indicates that the majority of this normal matter is undetected, or “missing.” At high redshifts (z ∼ 3), big-bang nucleosynthesis models and QSO absorption line observations indicate a baryon mass fraction of Ωb ∼ 0.04 (e.g., Fukugita, Hogan & Peebles 1998). The stars and gas detected in local galaxies account for only 20% of this (Ωb ∼ 0.008). The absence of a local Lyα forest indicates that these baryons are likely in a hot (T > 105 K), diffuse medium which has heretofore remained undetectable (e.g., Fukugita, Hogan & Peebles 1998; Cen & Ostriker 1999a; Davé et al. 2001).

Wave propagation in inhomogeneous plasmas

Thus far in our discussion of wave propagation it has been assumed that the plasma is spatially uniform. While this assumption simplifies analysis, the real world is usually not so accommodating and it is plausible that spatial non-uniformity might modify wave propagation. The modification could be just a minor adjustment or it could be profound. Spatial non-uniformity might even produce entirely new kinds of waves. As will be seen, all these possibilities can occur.

To determine the effects of spatial non-uniformity, it is necessary to re-examine the original system of partial differential equations from which the wave dispersion relation was obtained. This is because the technique of substituting ik for ∇ is, in essence, a shortcut for spatial Fourier analysis, and so is mathematically valid only if the equilibrium is spatially uniform. The criteria for whether or not ∇ can be replaced by ik can be understood by considering the simple example of a high-frequency electromagnetic plasma wave propagating in an unmagnetized three-dimensional plasma having a gentle density gradient. The plasma frequency will be a function of position for this situation. To keep matters simple, the density non-uniformity is assumed to be in one direction only, which will be labeled the x direction. The plasma is thus uniform in the y and z directions, but non-uniform in the x direction.

Introduction

The X-ray sky is extremely variable. Transient sources occur on probably all timescales. Historically, the easiest timescales to study are seconds to minutes, and days to months. Most of these transients are Galactic in origin and have been shown to be powered by gravitational energy release during accretion of matter onto a compact object or by thermonuclear runaway processes on neutron stars (see Chapter 3 by Strohmayer and Bildsten). Less well understood are the transients with timescales between a minute and a day, the so-called “fast X-ray transients” (FXTs). These often occur off the Galactic plane and are, therefore, sometimes also referred to as “high latitude transients” (see Fig. 6.1). In general an FXT is loosely defined as a new temporary X-ray source that disappears on a timescale of less than a day and is not related to a known persistent X-ray source. The term, however, has been used as a repository for all sorts of ill-understood flares, bursts, flashes and related phenomena.

The early detections of fast X-ray transients

The very first X-ray satellite, Uhuru, detected fast transient X-ray sources (Forman et al. 1978), but it was through studies with Ariel-V (Pye & McHardy 1983) and the High Energy Astronomy Observatory-1 (HEAO-1) (Ambruster & Wood 1986; Connors et al. 1986) that FXTs came to be recognized as a separate class of transients.

General method for analyzing small-amplitude waves

All plasma phenomena can be described by combining Maxwell's equations with the Lorentz force equation where the latter is represented by the Vlasov, the two-fluid, or the MHD approximation. The subject of linear plasma waves provides a good introduction to the study of plasma phenomena because linear waves are relatively simple to analyze and yet demonstrate many essential features of plasma behavior.

Linear analysis, a straightforward method applicable to any set of partial differential equations describing a physical system, reveals the physical system's simplest non-trivial, self-consistent dynamical behavior. In the context of plasma dynamics, the method is as follows:

1. By making appropriate physical assumptions, the general Maxwell–Lorentz system of equations is reduced to the simplest set of equations characterizing the phenomena under consideration.

2. An equilibrium solution is determined for this set of equations. The equilibrium might be trivial such that densities are uniform, the plasma is neutral, and all velocities are zero. However, less trivial equilibria could also be invoked where there are density gradients or flow velocities. Equilibrium quantities are designated by the subscript 0, indicating “zero-order” in smallness.

3. […]

Introduction

Starbursts are not simply scaled-up versions of the disks of normal spiral and irregular galaxies. The composite HST WFPC2 image of the classic starburst galaxy M82 in Figure 1 illustrates some of the differences. Star formation is localized in a well-defined central zone, where it is concentrated in clumps, beyond which there is virtually no star-forming activity (O'Connell & Mangano 1978). The well-known superwind extends above and below the plane out to kiloparsecs beyond the main starburst zone (Shopbell & Bland-Hawthorn 1998 and references therein). In M82 we can observe the combined effects of stellar feedback and a weak interaction with M81 in sufficient detail to test our models of galactic star formation. This is critical for understanding how the cycling of baryonic matter through stars relates to the overall structure of a galaxy, including its dark matter halo; e.g., through its influence in varying the luminosity part of the Tully–Fisher relationship (van Driel, van den Broek & Baan 1995).

Introduction

Logically, this chapter ought to be located at the beginning of Chapter 2, just after the discussion of phase-space concepts. This chapter is not located there because the theory in this chapter is too advanced to be so close to the beginning of the book and its location near the beginning would have delayed the introduction of other important topics that do not need the detail of this chapter.

The discussion of collisions in Chapter 1 was very approximate. Collisions were shown to scale as an inverse power of temperature, but this was based on a “one size fits all” analysis since it was assumed that collision frequencies of slow and fast particles were nominally the same as that of a particle moving at the thermal velocity. Because the collision frequency scales as v−3, it is quite dubious to assume that the collision rates of both super-thermal and sub-thermal particles can be well represented by a single collision frequency and a more careful averaging over velocities is clearly warranted. This careful averaging is provided by a Fokker–Planck analysis due to Rosenbluth, Macdonald, and Judd (1957). If this much more detailed analysis simply provided more accuracy, it would not be worth the considerable effort it requires except for occasional situations where high accuracy is important. However, the Fokker–Planck theory not only provides more accuracy, but also reveals new and important phenomena and, in particular, indicates when resistive MHD fails.

Introduction

The previous chapter introduced the concept of magnetic helicity via the energy principle and showed that total helicity K = ∫ d3rA · B is a conserved quantity in an ideal plasma. This chapter shows that helicity can be interpreted in a topological sense as a count of the linkages of magnetic flux tubes with each other. Furthermore, it will be shown that when the plasma is not ideal so energy is not conserved, helicity conservation remains a rather good approximation.

The greater robustness of magnetic helicity compared to magnetic energy in the presence of dissipation leads to the Woltjer–Taylor relaxation theory, which shows that a dissipative plasma will spontaneously relax from an arbitrary initial state to a specific final state. Relaxation theory has two remarkable features, namely (i) it sidesteps describing the actual MHD dynamics and simply predicts the end state after all dynamics is over, and (ii) it thrives on complexity so the more complicated the dynamics, the more applicable is the theory. The second feature results because increased complication simply provides more channels whereby the plasma can relax to the specific final state. Relaxation theory has been very successful at predicting the approximate behavior of many laboratory, space, and astrophysical plasmas.

This chapter concludes by showing that magnetic helicity can be manifested in different forms. In particular, the kink instability will be shown to be a mechanism that converts helicity from one of these forms (twist) to another (writhe).

Introduction: The inner structure of AGNs

There is now general consensus that the long-standing paradigm for active galactic nuclei (AGNs) is basically correct, i.e., that AGNs are fundamentally powered by gravitational accretion onto supermassive collapsed objects. Details of the inner structure of AGNs, however, remain sketchy, although both emission lines and absorption lines reveal the presence of large-scale gas flows on scales of hundreds to thousands of gravitational radii. The accretion disk produces a time-variable high-energy continuum that ionizes and heats this nuclear gas, and the broad emission-line fluxes respond to the changes in the illuminating flux from the continuum source. The geometry and kinematics of the broad-line region (BLR), and fundamentally, its role in the accretion process, are not understood. Immediate prospects for understanding this key element of AGN structure do not seem especially promising with the realization that the angular size of the nuclear regions projects to only microarcsecond scales even in the case of the nearest AGNs.

Introduction

Abundance studies of the oldest stars provide critical clues to—and constraints upon—the characteristics of the earliest stellar populations in our Galaxy. Such constraints include those upon: light element production and BBN; the early star-formation and nucleosynthesis history of the Galaxy; the characteristics of heavy-element nucleosynthesis mechanisms; and the ages of early stellar populations from nuclear chronometers. Discussions of many of these issues are to be found in a number of review papers (Wheeler et al. 1989; McWilliam 1997; Truran et al. 2002; Gratton, Sneden, & Caretta 2004).

While much of the available data has been obtained with ground-based telescopes, there is much to learn with HST. Studies in the wavelength region accessible with HST can, in fact, address issues ranging from the origin of the light elements Li, Be, and B to the production mechanisms responsible for the synthesis of the heaviest elements through thorium and uranium. In the following two sections, we will review specifically first boron abundance studies at low Z and then abundances of the heavy elements Ge, Zr, Os, Pt, Au, and Pb, at low Z.

Boron abundances in halo stars

Knowledge of lithium, beryllium, and boron abundances in stars play a major role in our understanding of Big Bang nucleosynthesis, cosmic-ray physics, and stellar interiors.

In the standard model for the origin and evolution of the light elements, only 7Li is produced in significant amounts from Big Bang (primordial) nucleosynthesis.

Introduction

Since their discovery in 1962 (Giacconi et al. 1962), accreting compact objects in the Galaxy have offered unique insights into the astrophysics of the end stages of stellar evolution and the physics of matter at extreme physical conditions. During the first three decades of exploration, new phenomena were discovered and understood, such as the periodic pulsations in the X-ray lightcurve of spinning neutron stars (Giacconi et al. 1971) and the thermonuclear flashes on neutron-star surfaces that are detected as powerful X-ray bursts (see, e.g., Grindlay et al. 1976; Chapter 3). Moreover, the masses of the compact objects were measured in a number of systems, providing the strongest evidence for the existence of black holes in the Universe (McClintock & Remillard 1986; Chapter 4).

During the past ten years, the launch of X-ray telescopes with unprecedented capabilities, such as RXTE, BeppoSAX, the Chandra X-ray Observatory, and XMM-Newton opened new windows onto the properties of accreting compact objects. Examples include the rapid variability phenomena that occur at the dynamical timescales just outside the neutron-star surfaces and the black-hole horizons (van der Klis et al. 1996; Strohmayer et al. 1996; Chapters 2 and 4) as well as atomic lines that have been red- and blue-shifted by general relativistic effects in the vicinities of compact objects (Cottam et al. 2001; Miller et al. 2002b).

History of the term “plasma”

In the mid nineteenth century the Czech physiologist Jan Evangelista Purkinje introduced use of the Greek word plasma (meaning “formed” or “molded”) to denote the clear fluid that remains after removal of all the corpuscular material in blood. About half a century later, the American scientist Irving Langmuir proposed in 1922 that the electrons, ions, and neutrals in an ionized gas could similarly be considered as corpuscular material entrained in some kind of fluid medium and called this entraining medium plasma. However it turned out that, unlike blood where there really is a fluid medium carrying the corpuscular material, there actually is no “fluid medium” entraining the electrons, ions, and neutrals in an ionized gas. Ever since, plasma scientists have had to explain to friends and acquaintances that they were not studying blood!

Brief history of plasma physics

In the 1920s and 1930s a few isolated researchers, each motivated by a specific practical problem, began the study of what is now called plasma physics. This work was mainly directed towards understanding (i) the effect of ionospheric plasma on long-distance short-wave radio propagation and (ii) gaseous electron tubes used for rectification, switching, and voltage regulation in the pre-semiconductor era of electronics. In the 1940s Hannes Alfvén developed a theory of hydromagnetic waves (now called Alfvén waves) and proposed that these waves would be important in astrophysical plasmas.

Introduction

Solutions to Eq. (9.50), the Grad–Shafranov equation, (or to some more complicated counterpart in the case of non-axisymmetric geometry) provide a static MHD equilibrium. The question now arises whether the equilibrium is stable. This issue was forced upon early magnetic fusion researchers who found that plasma that was expected to be well confined in a static MHD equilibrium configuration would instead became violently unstable and crash destructively into the wall in a few microseconds.

The difference between stable and unstable equilibria is shown schematically in Fig. 10.1. Here a ball, representing the plasma, is located at either the bottom of a valley or the top of a hill. If the ball is at the bottom of a valley, i.e., a minimum in the potential energy, then a slight lateral displacement results in a restoring force, which pushes the ball back. The ball then overshoots and oscillates about the minimum with a constant amplitude because energy is conserved. On the other hand, if the ball is initially located at the top of a hill, then a slight lateral displacement results in a force that pushes the ball further to the side so that there is an increase in the velocity. The perturbed force is not restoring, but rather the opposite. The velocity is always in the direction of the original displacement; i.e., there is no oscillation in velocity.

Motivation

Single particle motion in neutral gases is trivial – particles move in straight lines until they hit other particles or the wall. Because of this simplicity, there is no point in keeping track of the details of single particle motion in a neutral gas and instead a statistical averaging of this motion suffices; this averaging shows that neutral gases have Maxwellian velocity distributions and are in a local thermodynamic equilibrium. In contrast, plasma particles are nearly collisionless and typically have complex trajectories that are strongly affected by both electric and magnetic fields.

As discussed in the previous chapter, the velocity distribution in a plasma will become Maxwellian when enough collisions have occurred to maximize the entropy. However, since collisions occur infrequently in hot plasmas, many important phenomena have time scales shorter than the time required for the plasma velocity distribution to become Maxwellian. A collisionless model is thus required to characterize these fast phenomena. In these situations randomization does not occur, entropy is conserved, the distribution function need not be Maxwellian, and the plasma is not in thermodynamic equilibrium. Thermodynamic concepts therefore do not apply, and the plasma is instead characterized by concepts from classical mechanics such as momentum or energy conservation of individual particles. In these collisionless situations the complex details of single particle dynamics are not washed out by collisions but instead persist and influence the macroscopic scale.