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).

Why use MHD?

Of the three levels of plasma description – Vlasov, two-fluid, and MHD – Vlasov is the most accurate and MHD is the least accurate. So, why use MHD? The answer is that, because MHD is a more macroscopic point of view, it is more efficient to use MHD in situations where the greater detail and accuracy of the Vlasov or two-fluid models are unnecessary. MHD is particularly suitable for situations having complex geometry because it is very difficult to model such situations using the microscopically oriented Vlasov or two-fluid approaches and because geometrical complexities are often most important at the MHD level of description. The equilibrium and gross stability of three-dimensional, finite-extent plasma configurations are typically analyzed using MHD. Issues requiring a two-fluid or a Vlasov point of view can exist and be important, but these more subtle questions can be addressed after an approximate understanding has first been achieved using MHD. The MHD point of view is especially relevant to situations where magnetic forces are used to confine or accelerate plasmas or liquid conductors such as molten metals. Examples of such situations include magnetic fusion confinement plasmas, solar and astrophysical plasmas, planetary and stellar dynamos, arcs, and magnetoplasmadynamic thrusters. Although molten metals are not plasmas, they are described by MHD and, in fact, the MHD description is actually more appropriate and more accurate for molten metals than it is for plasmas.

Introduction

One of the principal motivations for studying X-ray binaries is that accretion onto neutron stars and black holes provides a unique window on the physics of strong gravity and dense matter. Our best theory of gravity, general relativity, while tested, and confirmed, with exquisite precision in weak fields (GM/R ≪ c2; e.g., Taylor et al. 1992) has not yet been tested by direct observation of the motion of particles in the strong gravitational field near compact objects, where the gravitational binding energy is of order the rest mass. Among the extreme predictions relativity makes for these regions are the existence of event horizons, i.e., black holes (Section 2.4.1), the existence of an inner radius within which no stable orbits exist, strong dragging of inertial frames, and general-relativistic precession at rates similar to the orbital motion itself, ∼1016 times as fast as that of Mercury.

In a neutron star the density exceeds that in an atomic nucleus. Which elementary particles occur there, and what their collective properties are, is not known well enough to predict the equation of state (EOS), or compressibility, of the matter there, and hence the mass–radius (M–R) relation of neutron stars is uncertain. Consequently, by measuring this relation, the EOS of supra-nuclear density matter is constrained. As orbital motion around a neutron star constrains both M and R (Section 2.8.1), measurements of such motion bear on the fundamental properties of matter.

Introduction

In this contribution I have selected three main issues in contemporary star-formation studies. I have chosen these themes because 1) they represent important areas of uncertainty in our current understanding, 2) they involve a synergy between theory and observation, and 3) they span the range of length scales—from planetary to galactic scales—that are involved in different aspects of the star-formation process.

History

Relativistic outflows, or “jets”, represent one of the most obvious, important and yet poorly explained phenomena associated with accreting relativistic objects, including X-ray binaries. Originally recognized in images as long, thin structures apparently connected at one end to the nuclei of galaxies, it was soon established that they represent powerful flows of energy and matter away from accreting black holes and back to the Universe at large. From their earliest association with the most luminous sources in the Universe, the active galactic nuclei (AGN), the conclusion could have been drawn that jets were a common consequence of the process of accretion onto relativistic objects. Nevertheless, their association with the analogous accretion processes involving stellar-mass black holes and neutron stars was not systematically explored until the past decade or so.

Although it is now clear that the electromagnetic radiation from X-ray binary jets may extend to at least the X-ray band, historically the key observational aspect of jets is their radio emission. High brightness temperatures (see Section 9.2), “non-thermal” spectra and polarization measurements indicate an origin as synchrotron emission from relativistic electrons. Following the discovery of luminous binary X-ray sources in the 1960s and 1970s, radio counterparts were associated with the brightest of these, e.g., Sco X-1 (Hjellming & Wade 1971a), Cyg X-1 (Hjellming & Wade 1971b) and the outbursting source Cyg X-3 (Gregory et al. 1972).

Rather than starting from abstract mathematical definitions related to dynamical systems and the concepts used to analyse them, I prefer to start from the outset with a few familiar examples. The systems described below are related to the paradigms of deterministic chaos, some of which have indeed been the ones leading to the discovery, definition and understanding of chaotic behaviour. Instead of repeating here the so often quoted examples such as biological population growth, nonlinearly driven electrical oscillations, weather unpredictability, three-body Hamiltonian dynamics and chemical reaction oscillations and patterns, I shall attempt to motivate the reader by trying to find such examples among simplistic models of astrophysical systems. Obviously, the underlying mathematical structure of these will be very similar to the above mentioned paradigms. This only strengthens one of the primary lessons of nonlinear dynamics, namely that this is a generic, universal approach to natural phenomena.

Examples and analogies may sometimes be misleading and decide nothing, but they can make one feel more at home. This was, at least, the view of Sigmund Freud, the father of psychology, whose advice on matters didactic should not be dismissed. Indeed, as stressed before, these examples are the readers' old acquaintances from their astrophysics educational ‘home’. In the next chapter, where the basic notions characterising chaotic behaviour will be dealt with in detail, these examples will sometimes be used again for demonstrating abstract concepts.

Developments in the theory of nonlinear conservative dynamical systems and Hamiltonian chaos have often been motivated, as we have seen, by problems in celestial mechanics. Fluid dynamics has, likewise, motivated much of the dissipative dynamical systems and pattern theory. However, while celestial mechanics is certainly a part of astronomy (a discussion of chaotic dynamics in planetary, stellar and galactic n-body systems can be found in Chapter 9 of this book), fluid dynamics can be regarded as an essentially separate discipline of the physical sciences and applied mathematics. Its uses and applications are widespread, ranging from practical engineering problems to abstract mathematical investigations, and its importance to astrophysics stems from the fact that most of the observable cosmos is made up of hot plasma, whose physical conditions are very often such that a fluid (or sometimes magneto-fluid) dynamical description is appropriate.

As is well known, and we shall shortly discuss explicitly, fluid dynamics has as its basis the description of matter as a continuum. Various assumptions then give rise to appropriate sets of the basic equations and these are usually nonlinear PDEs. The nonlinear PDEs of fluid (or magneto-fluid) dynamics are complicated dynamical systems and they have so far defied (except for the simplest cases) a rigorous and complete mathematical understanding.