The saga of pre-stellar evolution begins with the Big Bang and the evolution of large scale structure, continues with the formation of galaxies and giant molecular clouds, and extends finally to the formation of protostellar condensations that collapse into objects recognized as stars which, evolving on a quasistatic time scale, form the main subject of this book.

Nucleosynthesis, beginning with protons and neutrons in the early phases of the expanding Universe, prior to the formation of structure, is responsible for the fact that hydrogen and helium are the most abundant elements in the Universe. The presence in the current Universe of elements such as carbon, nitrogen, oxygen, and iron, coupled with the fact that these elements are not produced in models of the early Universe, is evidence that stars make these elements and inject them into the interstellar medium. Thus, the initial composition and therefore the detailed evolutionary history of stars of a given generation differs from the composition and history of stars of earlier and later generations.

Whatever the physics is that is responsible for their existence, giant molecular clouds are the birthplaces of smaller condensations, or protostellar clouds, which are thought to develop into protostars consisting initially of small, quasistatic cores that accrete from dynamically collapsing envelopes. In Section 9.1, some considerations involved in understanding the properties of giant molecular clouds and early protostar evolution are presented. After almost a century of thought, where a real star appears in the HR diagram as an isolated, quasistatically evolving object has not been determined from first principles.

Polytropes are simple but pedagogically very useful models of self gravitating spheres. They were invented and explored in the last quarter of the nineteenth century, long before the development of theories for describing energy generation and energy flow in the stellar interior. The models follow when an exact balance between an outward pressure gradient force and the inward gravitational force is assumed and a parameterized power-law relationship between pressure and density is adopted. Solutions require no explicit use of a temperature-dependent equation of state, a law of energy transport, or a law of energy generation. The only equations to be solved are Poisson's equation for the gravitational field and the pressure balance equation. By varying the parameters in the power law, one can obtain plausible zeroth order models of various classes of real stars. A discussion of the contributions to the subject by Lane, Ritter, Emden, Kelvin, and others is given at the end of Chapter IV of Subrahmanyan Chandrasekhar's book Stellar Structure (1939). It is revealing that the construction of complete polytropes did not begin until 1878, five years after Cornu & Baile in 1873 determined explicitly for the first time the value of the gravitational constant G from results of Cavendish's 1798 tortional balance experiments. Arthur S. Eddington, who pioneered the development of the theory of radiative energy transport in stellar interiors, made imaginative use of polytropes and argued that one particular polytrope, that of index N = 3, provides an approximate description of the observed properties of main sequence stars.

Stars spend most of their nuclear burning lives on the main sequence converting hydrogen into helium in central regions. After leaving the main sequence, single stars and stars in wide binaries continue to burn hydrogen in a shell as helium is converted into carbon and oxygen in the hydrogen-exhausted core. The lifetime of a star in the core helium-burning phase, which in intermediate mass stars is typically 10–30% of the main sequence lifetime, is determined by the rate of helium burning, but hydrogen-burning reactions contribute most of the light emitted by the star. The time spent in more advanced stages of nuclear burning is quite small compared with that spent during the main hydrogen- and helium-burning phases. Thus, over most of a star's nuclear burning lifetime, hydrogen-burning reactions are the major contributors to the stellar luminosity.

In population I stars of mass smaller than ˜2 M☉, the reactions which dominate energy production during the main sequence phase are those in the so-called pp chains, which are initiated by the transformation of two protons into a deuterium nucleus. The reactions which follow this initial pp-chain reaction terminate with the formation of 3He (at low temperatures) or with the formation of 4He (at higher temperatures). These subsequent reactions release considerably more energy than is released in the pp reaction itself, but the overall rate of energy release is nevertheless controlled by the pp reaction since it is, by far, the slowest reaction in the chains.

An understanding of the manner in which matter and radiation interact is crucial for understanding how the structure of a star is influenced by the flow of energy. In this chapter, the physics of three processes whereby photons are absorbed by electrons interacting through the Coulomb potential with heavy ions is examined. The three processes are photo-ionization, inverse bremsstrahlung on free electrons, and transitions between bound atomic levels. Approximations to the cross sections for these processes are derived and the manner in which calculated cross sections are weighted to obtain the opacity under conditions of thermodynamic equilibrium is described and utilized in sample calculations of the opacity. Of primary interest here is not a presentation of definitive results, but rather a conceptual understanding of the basic ingredients of a quantitative calculation of absorption cross sections and of the related opacity.

An excellent monograph which describes the processes rigorously is The Quantum Theory of Radiation by Walter Heitler (1954), a pedagogically excellent text of relevance is Quantum Mechanics by Leonard I. Schiff (1949), and a delightfully intuitive approach to the calculation of transition probabilities is presented in Quantum Electrodynamics, based on lectures by Richard P. Feynman (1962). It would be remiss not to acknowledge the debt which the theory of quantum electrodynamics owes to Michael Faraday (1791–1867) and James Clerk Maxwell (1831–1879), the principle inventors of classical electrodynamics, as described in Maxwell's two volume Treatise on Electricity and Magnetism (1873).

Although locally conspicuous, stars are but one of many forms in which matter and energy in the Universe can manifest themselves; and there is a continuous interaction between these other forms and the stars. Stars are made out of diffuse interstellar matter that gathers itself into the condensations seen as giant molecular clouds; the stars lose mass as they evolve, returning to the interstellar medium material which they have enriched in heavy elements, thus causing a gradual change in the composition and cooling characteristics of the interstellar medium. Radiation from the stars interacts with interstellar matter in the immediate environment, changing the thermodynamic characteristics of this matter. Ejection at high velocity of stellar envelope material, such as occurs in supernova explosions, makes another important contribution to the energetic of the interstellar medium. The change in the composition, thermodynamic, and dynamical characteristics of the interstellar medium then alters the character and dynamics of the star formation process. Thus, although one may concentrate on the evolutionary behavior of stars as if they were isolated entities, stars are actually in a state of interaction with their environment, both feeding and feeding upon the matter in this environment. There is, however, a degree of asymmetry in the interaction. Although one cannot understand the evolution of the interstellar medium without taking into account the influence of stars, one can understand the evolution of a star without worrying about how it was made. Thus, in this book, stars are viewed as more or less isolated entities, their existence being accepted as a given and the circumstances that lead to their formation being examined only to the extent that they offer insight as to an appropriate initial configuration with which to begin evolutionary model calculations.

One might think that the most appropriate division of topics in a two volume book on stellar evolution physics would be the placement of all chapters describing the input physics required for the construction of stellar models in the first volume and the placement of all chapters describing stellar evolutionary models in the second volume. However, such a division disguises the fact that it is the operation of the input physics in stars that explains why they shine and evolve and that, therefore, both the input physics and the response of stars to the operation of this physics comprise the science of stellar evolution physics.

In preparing this book, after describing much of the input physics required for the construction of stellar models during early evolutionary stages, I constructed models in these early stages of evolution. Then, after describing some of the more complicated physical processes that play important roles during more advanced stages of evolution, I constructed models in these more advanced stages. The ordering of topics in the two volumes of this book reflects this chronological development.

After providing a general introduction to the observed properties of real stars and to the results of stellar evolution calculations, the first volume focusses on equations of state, energy generation by hydrogen-burning reactions, energy transport by radiation and convection, and on the elementary equations of stellar evolution and methods of solution.

In constructing models of evolving stars in volume 1 of this monograph, it has been assumed that particle diffusion can be neglected. However, the current abundance of Li at the solar surface is much smaller than predicted by models neglecting diffusion and this suggests that, during the gravitationally contracting phase which preceeds the main sequence, diffusion carries Li from the convective envelope into higher temperature regions below the base of the envelope where it can be destroyed. The abundance of Fe observed at the solar surface is smaller than the interior Fe abundance indicated by comparison between neutrino fluxes observed from the Sun and fluxes predicted by solar models, suggesting that Fe has diffused out of the convective envelope during the main sequence phase into regions below the base of the convective envelope. The fact that many low luminosity white dwarfs exhibit monoelemental surface abundances is a dramatic demonstration that, in regions where the gravitational acceleration is orders of magnitude larger than near the surface of the Sun, gravitationally induced diffusion is a first order effect. Thus, there is ample motivation for studying the physics of diffusion.

A description of the physics of particle diffusion can be given on many levels of sophistication. The description adopted in this chapter is based on an analysis of Boltzmann transport equations constructed on the assumptions that there exists an equilibrium distribution function for every species of particle and that, when a system is not in equilibrium, the time rate of change of each distribution function can be determined as the consequence of binary interactions between all particles.

History of s-process nucleosynthesis and outline

In the middle of the twentieth century, Paul W. Merrill (1952) detected the beta-unstable element technetium in the spectra of red supergiants known as S stars, which have long been recognized as being AGB stars. 99Tc is the longest lived isotope of technetium, and its half life of 211 000 yr is several orders of magnitude shorter than the lifetime of a core helium-burning precursor of an AGB star. When observed mass-loss rates are taken into account, the lifetime of a star in the AGB phase is roughly an order of magnitude larger than the half life of 99Tc. It is therefore incontrovertible that the 99Tc observed has been formed in AGB stars. On the other hand, given the temperatures and densities in AGB models, it is clear that an element of atomic charge as large as that of Tc cannot be a consequence of reactions between charged particles and it has become accepted that neutron capture must be involved.

The earliest theoretical studies of neutron-capture nucleosynthesis were carried out by A. G.W. Cameron (1955) and by E. Margaret Burbidge, Geoffrey R. Burbidge, William A. Fowler, and Fred Hoyle (1957) and, over the years, numerous studies have been devoted to examining how the distribution of abundances in an initial set of heavy elements is altered when this set is placed in a bath of neutrons at various assumed number densities for various exposure times.