Introduction

Baade and Zwicky (1934) were the first to envision the formation of neutron stars as the end product of a supernova explosion. Their forward thinking was not vindicated for another three decades, with the discovery of the first radio pulsars by Bell and Hewish (Hewish et al. 1968). What Baade and Zwiscky could not have anticipated, however, was the menagerie of astrophysical objects that are now associated with neutron stars. Today, we observe them as magnetically braking pulsars, accreting pulsars in binary systems, isolated cooling blackbodies, sources of astrophysical jets, and emitters of high-luminosity bursts of X-rays. Here, we focus on two of the most extraordinary evolutionary paths of a neutron star, namely soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs).

Soft gamma repeaters were discovered as high-energy transient burst sources; some were later found also to be persistent X-ray pulsars, with periods of several seconds, that are spinning down rapidly. Anomalous X-ray pulsars are identified through their persistent pulsations and rapid spin down; some have also been found to emit SGR-like bursts. In spite of the differing methods of discovery, this convergence in the observed properties of the SGRs and AXPs has made it clear that they are, fundamentally, the same type of object. What distinguishes them from other neutron stars is the likely source of energy for their radiative emissions, magnetism.

Introduction

Section 2.6.4 established the fundamental concept underlying ideal MHD, namely that magnetic flux is frozen into the plasma. This concept means that the magnetic topology of an ideal MHD plasma cannot change because a change in magnetic topology would require a change of magnetic flux within the frame of the plasma. Chapter 10 showed that ideal MHD plasmas are susceptible to two distinct types of instabilities, pressure-driven and current-driven. Pressure-driven modes draw on free energy associated with heavy fluids stacked on top of light fluids in an effective gravitational field whereas current-driven instabilities draw on free magnetic energy and involve the plasma attempting to increase its inductance in a flux-conserving manner. Both of these instabilities occur on the Alfvén time scale defined as some characteristic distance divided by vA.

It is possible for an MHD equilibrium to be stable to all ideal MHD modes and yet not be in a lowest energy state. Because ideal MHD does not allow the topology to change, a plasma that is not initially in the lowest energy state will not be able to access this lowest energy state if the lowest energy state is topologically different from the initial state. However, the lowest energy state could be accessed by non-ideal modes, i.e., modes that violate the frozen-in flux condition, and so the available free energy could drive an instability involving these non-ideal modes.

This text is based on a course I have taught for many years to first-year graduate and senior-level undergraduate students at Caltech. One outcome of this experience has been the realization that although students typically decide to study plasma physics as a means towards some specific goal, they often conclude that the study of this subject has an attraction and charm of its own; in a sense the journey becomes as enjoyable as the destination. This conclusion is shared by me and I feel that a delightful aspect of plasma physics is the frequent transferability of ideas between extremely different applications so, for example, a concept developed in the context of astrophysics might suddenly become relevant to fusion or vice versa.

Applications of plasma physics are many and varied. Examples include controlled thermonuclear fusion, ionospheric physics, magnetospheric physics, solar physics, astrophysics, plasma propulsion, semiconductor processing, antimatter confinement, and metals processing. Furthermore, because plasma physics is extremely rich in both concepts and regimes, it has often served as an incubator for new ideas in applied mathematics. Concepts first developed in one of the areas listed above frequently migrate rather quickly to one or more of the other areas so it is very worthwhile to keep abreast of developments in areas of plasma physics outside of one's immediate field of interest.

Introduction

The last decade has witnessed amazing progress in our empirical and theoretical understanding of galaxy formation and evolution.

Overview

We begin this chapter by developing the concept of conservation of particles in phase-space and then use this concept as the basis for establishing the three main models of plasma dynamics, namely Vlasov theory, two-fluid theory, and magnetohydrodynamics (MHD). The Vlasov model is the most detailed and characterizes plasma dynamics by following the temporal evolution of electron and ion velocity distribution functions. The two-fluid model is intermediate in complexity and approximates plasma as a system of mutually interacting, finite-pressure electron and ion fluids. The MHD model is the least detailed and approximates plasma as a single, finite-pressure, electrically conducting fluid. The question of which of these models to use when analyzing a given situation is essentially a matter of selecting the best tool for the task and furthermore, just as a mechanic might alternate between using a screwdriver and a pair of pliers for a specific task, it is often advantageous to alternate between these models when analyzing a specific problem. As we develop these three models, we will also take the opportunity to explore some immediate and important fundamental consequences of these models, most notably the strong dependence of a collisionless plasma on its past history (Vlasov model) and the freezing of magnetic flux into the arbitrarily moving frame of a perfectly conducting plasma (MHD).

Introduction

In the 1995 X-ray Binaries book edited by Lewin, van Paradijs and van den Heuvel, the chapter on Normal galaxies and their X-ray binary populations (Fabbiano 1995) began with the claim that “X-ray binaries are an important component of the X-ray emission of galaxies. Therefore the knowledge gathered from the study of Galactic X-ray sources can be used to interpret X-ray observations of external galaxies. Conversely, observations of external galaxies can provide us with uniform samples of X-ray binaries, in a variety of different environments.” This statement was based mostly on the Einstein Observatory survey of normal galaxies (e.g., Fabbiano 1989; Fabbiano, Kim & Trinchieri 1992). Those results have been borne out by later work, yet at the time the claim took a certain leap of faith. Now, nearly a decade later, the sensitive sub-arcsecond spectrally resolved images of galaxies from Chandra (Weisskopf et al. 2000), complemented by the XMM-Newton (Jansen et al. 2001) data for the nearest galaxies (angular resolution of XMM-Newton is ∼15″), have made strikingly true what was then largely just wishful anticipation.

While a substantial body of ROSAT and ASCA observations exists, which was not included in the 1995 chapter, the revolutionary quality of the Chandra (and to a more limited degree of XMM-Newton) data is such that the present review will be based on these most recent results.

Introduction

Non-neutral plasmas had one less species than a conventional plasma (one species instead of two); dusty plasmas have one more species (three species instead of two). Not surprisingly, the addition of another species provides new freedoms, which give rise to new behaviors.

The third species in a dusty plasma, electrically charged dust grains, typically have a charge to mass ratio quite different from that of electrons or ions. Several methods for charging dust grains are possible. Electron bombardment is the usual means for charging laboratory dusty plasmas, but photoionization or radioactive decay could also be operative mechanisms and may be important for certain space and astrophysical situations. Photoionization would make dust grains positive because photoionization causes electrons to leave dust grains. Radioactive decay of dust grains would make the dust grains develop a polarity opposite to that of the particle emitted in the decay process, e.g., alpha particle emission by dust grains would make the dust grains negative.

We shall consider here only the typical laboratory dusty plasma situation where the plasma is weakly ionized and dust grain charging is due to electron bombardment. Negative charging occurs because the electrons, being much lighter than the ions and usually much hotter, have a much larger thermal velocity than the ions. As a result, when a dust grain is inserted into the plasma it is initially subject to a greater flux of impacting electrons than impacting ions, thereby causing the dust grain to become negatively charged.

Introduction

In the 35 years since the first X-ray binary was optically identified (Sco X-1) the basic division of X-ray binaries into the high-mass (HMXBs) and low-mass (LMXBs) systems has become firmly established. The nomenclature refers to the nature of the mass donor, with HMXBs normally taken to be ≥10 M⊙, and LMXBs ≤1 M⊙. However, the past decade has seen the identification and measurement of a significant number of X-ray binaries whose masses are intermediate between these limits. Nevertheless, the nature of the mass-transfer process (stellar wind dominated in HMXBs, Roche lobe overflow in LMXBs) produces quite different properties in the two groups and so this chapter will be divided into two main sections on HMXBs and LMXBs. A more complete introduction can be found in Chapter 1.

While the nature of the compact object and its properties are largely determined from X-ray studies, longer-wavelength observations allow detailed studies of the properties of the mass donor. This is most straightforward for the intrinsically luminous early-type companions of HMXBs, which provide the potential for a full solution of the binary parameters for those systems containing X-ray pulsars. This is particularly important for HMXB evolution in that it allows a comparison of the derived masses with those obtained for neutron stars in the much older binary radio pulsar systems (Thorsett & Chakrabarty 1999).

However, when HMXBs are suspected of harboring black holes (e.g., Cyg X-1), the mass measurement process runs into difficulties.

Introduction and brief historical review

In this chapter we present an overview of the formation and evolution of compact stellar X-ray sources. For earlier reviews on the subject we refer to Bhattacharya & van den Heuvel (1991), van den Heuvel (1994) and Verbunt & van den Heuvel (1995). The observations and populations of high-mass X-ray binaries (HMXBs) and low-mass X-ray binaries (LMXBs) were covered earlier in Chapter 1 by Psaltis.

In our Galaxy there are about 100 bright X-ray sources with fluxes well above 10−10 erg cm−2 s−1 in the energy range 1–10 keV (above the Earth's atmosphere). The distribution of these sources shows a clear concentration towards the Galactic center and also towards the Galactic plane, indicating that the majority do indeed belong to our Galaxy. Furthermore, a dozen strong sources are found in Galactic globular clusters (Section 8.2) and in the Magellanic Clouds. Shortly after the discovery of the first source (Sco X-1, Giacconi et al. 1962) Zel'Dovitch and Guseinov (1966), Novikov and Zel'Dovitch (1966) and Shklovskii (1967) suggested that the strong Galactic X-ray sources are accreting neutron stars or black holes in binary systems. (The process of mass accretion onto a supermassive black hole had already been suggested as the energy source for quasars and active galactic nuclei by Salpeter (1964), Zel'Dovitch (1964) and Zel'Dovitch and Novikov (1964).)

The X-ray fluxes measured correspond to typical source luminosities of 1034 – 1038 erg s−1 (which is more than 25 000 times the total energy output of our Sun).

Introduction

Wave nonlinearity is a vast subject and is not specific to plasma physics because nonlinear wave behavior occurs in virtually any physical medium where waves can propagate. However, because of the enormous variety of plasma waves, there is usually at least one plasma context where any given type of wave nonlinearity is an important issue. Three general types of nonlinear wave behavior will be discussed in this chapter: mode–mode coupling instabilities, self-modulation, and solitons. Before discussing these phenomena in detail, we first present a qualitative overview showing how certain basic wave nonlinearities are manifested.

Mode–mode coupling instabilities

Suppose a linear wave is excited in a plasma by an antenna driven by an appropriately tuned sine wave generator. In particular, suppose the plasma frequency is ωpe/2π = 100 MHz and the sine wave generator is tuned to a frequency well above the plasma frequency, say ω/2π = 500 MHz, so as to cause the antenna to radiate an electromagnetic plasma wave with dispersion relation. This wave propagates through the plasma and is picked up by a distant receiving probe connected to a spectrum analyzer, a device that provides a graphic display of signal amplitude versus frequency. The received signal shows up on the spectrum analyzer display as a sharp peak at 500 MHz, as shown in Fig. 15.1(a).