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.

Galaxies and clusters of galaxies are complex systems, but the aim of the cosmologist is not to explain all their detailed features. Rather, it is to explain howlarge-scale structures formed in the expanding Universe in the sense that, if δρ is the enhancement in density of some region over the average background density ρ, the density contrast δρ/ρ reached amplitude 1 from initial conditions which must have been remarkably isotropic and homogeneous. Once the initial perturbations have grown in amplitude to δρ/ρ ~ 1, their growth becomes non-linear and they rapidly evolve towards bound structures in which star formation and other astrophysical process lead to the formation of galaxies and clusters of galaxies as we know them. The cosmologist's objectives are therefore twofold – to understand how density perturbations evolve in the expanding Universe and to derive the initial conditions necessary for the formation of structure in the Universe.

Galaxies, clusters of galaxies and other large-scale structures of our local Universe must have formed relatively late in the history of the Universe. The average density of matter in the Universe today corresponds to a density parameter Ω 0 ~ 0. 3. The average densities of gravitationally bound systems, such as galaxies and clusters of galaxies, are much greater than this value, typically their densities being about 106 and 1000 times greater than the mean background density, respectively. Superclusters have mean densities a few times the background density.

Somewhat surprisingly, Fraunhofer's great discoveries in astronomical spectroscopy were not followed up in any detail until 1863, almost 40 years later,when a number of independent investigators, Giovanni Donati (1826–1873) in Florence, Rutherfurd in New York, George Airy (1801–1892) at the Royal Greenwich Observatory, Huggins in London and Secchi in Rome, began the systematic study of the spectra of the stars and nebulae.

William Huggins – the founder of stellar astrophysics

William Huggins (1824–1910) was inspired to take up astronomical spectroscopy on reading Kirchhoff 's great papers of 1861 to 1863 on the chemical composition of the solar atmosphere. In his words,

This news came to me like the coming upon a spring of water in a dry and thirsty land. Here, at last presented itself the very order of work for which in an indefinite way I was looking for – namely, to extend his novel methods of research upon the Sun to the other heavenly bodies.

Huggins was an inspired amateur astronomer who had no formal university training in the sciences, but from 1856 until his death in 1910 he supported himself by his private income and dedicated his efforts to the advance of astrophysics. Much of his early work was carried out in collaboration with William Miller (1817–1870), who was professor of chemistry at King's College London and an expert on spectral analysis, as well as being his friend and neighbour at Tulse Hill in London.

Radio astronomy and high-energy astrophysics

The early history of radio astronomy was recounted in Section 7.3; that story ended in the mid 1950s, by which time the Galactic and extragalactic nature of the discrete radio sources was established. From the point of view of astrophysics, the key realisation was that, in most cases, the radio emission was the synchrotron radiation of ultra-high-energy electrons gyrating in magnetic fields within the source regions. The synchrotron radiation process began to be applied to other astronomical objects in which there was evidence for high-energy astrophysical activity.

In 1942, Rudolph Minkowski showed that the emission of the supernova remnant known as the Crab Nebula consists of two components, the filaments, which form a network defining the outer boundary of the remnant, and diffuse continuum emission originating within the nebula, which contributes most of its optical luminosity (Minkowski, 1942). The continuum emission had a featureless spectrum and could not be accounted for by any form of thermal spectrum. In 1949, John Bolton and Gordon Stanley found that the flux density of the Crab Nebula at radio wavelengths was about 1000 times greater than in the optical waveband (Bolton and Stanley, 1949). To account for the continuum emission, Iosif Shklovsky (1916–1985) proposed in 1952 that both the radio and optical continuum was synchrotron radiation, the energies of the electrons radiating in the optical waveband being very much greater than those radiating in the radio waveband (Shklovsky, 1953).

Introduction

By 1945, many of the physical processes involved in the evolution of stars on the main sequence were beginning to be understood, but there remained an enormous amount of detailed work to be undertaken before a precise comparison between theory and observation could be made. To build detailed models of the stars, three types of data are required. The first is the equation of state of the material of the star; the second are accurate nuclear reaction rates; and the third is the opacity of stellar material for the transfer of radiation. These quantities need to be known for the wide ranges of temperature and density encountered inside the stars. Then, the problems of radiation transfer through the body of the star and its surface layers have to be solved so that meaningful comparisons can be made between the theory and observations. As a result, the astrophysicists had to have access to a very wide range of data from nuclear, atomic and molecular physics, which began to become available with the great expansion in the funding for the physical sciences after the Second World War.

Then, there was the need to develop models for the evolution of stars from one region of the Hertzsprung–Russell diagram to another. It was a daunting task, but there was light at the end of the tunnel with the development of high-speed digital computers in the 1950s and 1960s, which was to convert the study of the structure and evolution of the stars into a precise astrophysical science. The new wavebands brought important new insights into many of the key phases of stellar evolution using techniques which could not have been imagined by the pioneers of the first half of the twentieth century.

Evidence for strong evolutionary changes in the properties of extragalactic objects with cosmic epoch was first found in the 1950s and 1960s as a result of surveys of radio sources and quasars. An excess of faint sources was found in radio source and quasar surveys, as compared with the expectations of uniform world models. The inference was that there were many more of these classes of object at early cosmic epochs as compared with their number at the present epoch. During the 1980s, as the first deep counts of galaxies became available, a large excess of blue galaxies at faint apparent magnitudes was discovered. These studies culminated in the remarkable observations of the Hubble Deep Field in 1998 and the Hubble Ultra-Deep Field in 2004 by the Hubble Space Telescope.

In the 1990s, the first deep surveys of the X-ray sky were carried out by the ROSAT X-ray observatory, and evidence for an excess of faint X-ray sources was found, similar in many ways to the evolution inferred from studies of extragalactic radio sources and quasars. In the thermal infrared wavebands, the IRAS survey, although not extending to as large redshifts as the surveys mentioned above, also provided evidence for an excess of faint sources, which appear to be evolving in a manner similar to the active galaxies. Then, in the last few years of the century, evidence was found for a large population of submillimetre or far-infrared galaxies at large redshifts.

Early theories of stellar structure and evolution

The origin of the theory of stellar structure and evolution can be traced to the understanding of the first law of thermodynamics. As a result of the experimental ingenuity of Julius Mayer (1814–1878) and, particularly, of James Prescott Joule (1818–1889), and the deep theoretical insights of Rudolph Clausius (1822–1888) and William Thomson, later Lord Kelvin (1824–1907), the two laws of thermodynamics were established in the early 1850s. In popular terms, they can be stated as follows.

1. Energy is conserved when heat is taken into account.

2. The entropy of any isolated system can only increase.

Applying the first lawto the stars, the source of energy could be attributed to the heat liberated when matter is accreted onto their surfaces. The kinetic energy of infall from infinity, which is equal to the gravitational binding energy of the material at the surface, is converted into heat when the matter hits the surface. A popular version of the theory involved meteoritic bombardment of stars as the means of providing the necessary energy release. This proposal contained, however, the serious flaw that the necessary flux of meteoroids would perturb the orbits of the inner planets and would also have resulted in a quite unacceptably high rate of meteoroid bombardment of the Earth.