This book is intended for those people, perhaps final-year undergraduates and research students, who are already familiar with the terminology of stellar astrophysics (spectral types, magnitudes, etc.) and would like to explore the fascinating world of binary stars. I hope it will also be useful to those whose main astrophysical interests are in planets, galaxies or cosmology, but who wish to inform themselves about some of the basic blocks on which much astronomical knowledge is built. I have endeavoured to put into one book a number of concepts and derivations that are to be found scattered widely in the literature; I have also included a chapter on the internal evolution of single stars.

In the interest of keeping this volume short, I have been brief, some might say cursory, in surveying the enormous literature on observed binary stars. It is almost a truism that theoretical ideas stand or fall by comparison with observation. My intention is to produce a second volume, with my colleagues Dr Ludmila Kiseleva-Eggleton and Dr Zhanwen Han, in which individual binary and triple stars that rate less than a line in this volume will be discussed in the paragraph or two each, at least, which they deserve. In addition, the synthesis of large theoretical populations of binary stars will be discussed. Some individual binaries can be seen as flying entirely in the face of the theoretical ideas outlined here – see OW Gem, Section 2.3.5.

Background

Because gravity is a long-range force, it is difficult to define precisely the concept of an ‘isolated star’ – and consequently also the concept of a binary or triple star. Nevertheless, many stars are found whose closest neighbouring star is a hundred, a thousand or even a million times closer than the average separation among stars in the general neighbourhood. Such pairings of stars are expected to be very long lived. There also exist occasional local clusterings of perhaps a thousand to a million stars, occupying a volume of space which would much more typically contain only a handful of stars. These clusters can also be expected to be long lived – although not as long lived as an ‘isolated’ binary, since the combined motion of stars in a large cluster causes a slow evaporation of the less massive members of the cluster, which gain kinetic energy on average from close gravitational encounters with the more massive members. Intermediate between binaries and clusters are to be found small multiple systems containing three to six members, and loose associations containing somewhat larger numbers. Starting from the other end, some clusters may contain sub-clusters, and perhaps sub-sub-clusters, down to the scale of binaries and triples.

Even with the naked eye, a handful of the 5000 stars visible can be seen to be double; and in the northern hemisphere two clusters of stars, the Hyades and the Pleiades, are quite recognisable.

Matter that leaves the surface of one component of a binary can be partly or wholly accreted by the companion. We have seen that the loser could be losing mass either by RLOF or by stellar wind, perhaps binary-enhanced; the accretion process has even more options, and these are modelelled with even less confidence. A major reason why the accretion process can be more complex than the mass-loss process is that gainers can have a very wide range of radii, from black holes and neutron stars (at ∼3–30 km) to white dwarfs (∼104 km) to normal dwarfs (∼0.1–10 Gm), and even occasionally to sub-giants (∼3–30 Gm) or giants (≳10–30 Gm); whereas the loser is usually only in the last three of these categories. Not only does the available energy of the accreted material vary (inversely) over the same range, but also different physical forces (magnetic, viscous, rotational, gravitational) may dominate at different radii from the gainer.

The study of accretion is one of the most active areas in stellar astrophysics. Phenomena, often dramatic, are observed to happen on timescales ranging upwards from milliseconds. This book will not attempt to cover the ground in detail – partly for lack of space, but also because this book is intended to concentrate on the long-term evolution of binaries rather than on their short-term behaviour. For a fuller treatment the reader is referred to some standard works: Lewin and van den Heuvel (1983), Frank et al. (2002).

Background

The evolution of single stars, and of those stars which are in binaries sufficiently wide that the effect of a companion can be ignored, has been much studied, especially with the aid of increasingly powerful computers over the last 50 years. This is not to say, however, that every problem has been solved: in the final section of this chapter I emphasise some of the outstanding problems.

Figure 2.1 shows a comparison between recently computed models, and data obtained by observation. They are shown in a Hertzsprung–Russell diagram (HRD) where luminosity, i.e. the total energy output of the star, is plotted against surface temperature; the latter is plotted backwards, for traditional reasons. Our theoretical understanding of the internal structure and evolution of single stars is based on the concepts of hydrostatic equilibrium, thermodynamic equilibrium and the consumption of nuclear fuel, mainly hydrogen. In hydrostatic equilibrium, the inward force of gravity is balanced by the outward push of a pressure gradient. In thermodynamic equilibrium, the heating or cooling of a spherical layer of material is determined by the balance of heat production in nuclear reactions, at temperatures of about 10MK(megakelvin) and upwards in the deep interior, against heat loss as heat flows down the considerable temperature gradient until it can be radiated into space from the photosphere at temperatures observed to be about 2–100 kK. The heat flux is carried either wholly by radiation, or by a combination of convection and radiation, depending on whether the temperature gradient that would be required to carry the heat entirely by radiation is less than or greater than the critical (i.e. adiabatic) temperature gradient at which convective instability sets in. Most stars contain some region or regions that are predominantly convective and some that are wholly radiative.

The importance of the Sun as the most observable of all stars cannot be overstated. As shown in Figure 15.1, no other star can be studied with the degree of detail that we achieve in even the simplest observations of this source of all of our light and energy. As a result, what we have learned from the Sun we have applied in our study and analysis of the stars. Our knowledge of the sizes and distances of the stars is based upon our knowledge of the Sun. Also, we calibrate the luminosities of the stars in terms of our measurements of the output of energy from the Sun. In this chapter we shall first describe methods of observing the Sun in simple ways that can be used by anyone with a telescope. Then, we shall move on to more specialized methods and instruments that are used at observatories dedicated mainly to solar research.

Observing the Sun with a small telescope

The Sun is so bright that one should never try to make direct, naked-eye or telescopic observations of it. This is an absolute rule, for the observer can be blinded by even a brief attempt. There are, however, safe ways to view the Sun, and some of these require no complex equipment.

The most readily available method of seeing the Sun's apparent surface or photosphere is by means of eyepiece projection.