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.

In Chapter 3 we discussed principally the interaction of electromagnetic radiation with the surface and bulk of the material being sensed. However, the radiation also has to make at least one journey through at least part of the Earth's atmosphere, and two such journeys in the case of systems that detect reflected radiation, whether artificial or naturally occurring. Each time radiation passes through the atmosphere it is attenuated to some extent. In addition, as we have already seen in Section 3.1.2 and Figure 3.5, the atmosphere has a refractive index that differs from unity so that radiation travels through it at a speed different from the free-space speed of 299 792 458 m s−1. These phenomena must be considered if the results of a remotely sensed measurement are to be corrected for the effects of atmospheric propagation, or if they are to be used to infer the properties of the atmosphere itself. We have already considered them in general terms in discussing the radiative transfer equation (Section 3.4). In this chapter we shall relate them more directly to the constituents of the atmosphere.

Composition and structure of the gaseous atmosphere

At sea level, the principal constituents of the dry atmosphere are molecules of nitrogen (about 78% by volume), oxygen (21%) and the inert gas argon (1%). There is also a significant but variable (typically 0.1% to 3%) amount of water vapour, often specified by the relative humidity H.

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.

Preface

There are many books that explain the subject of remote sensing to those whose backgrounds are primarily in the environmental sciences. This is an entirely reasonable fact, since they continue to be the main users of remotely sensed data. However, as the subject grows in importance, the need for a significant number of people to understand not only what remote sensing systems do, but how they work, will grow with it. This was already happening in 1990, when the first edition of Physical Principles of Remote Sensing appeared, and since then increasing numbers of physical scientists, engineers and mathematicians have moved into the field of environmental remote sensing. It is mainly for such readers that this book, like its previous editions, has been written. That is to say, the reader for whom I have imagined myself to be writing is educated to a reasonable standard (although not necessarily to first degree level) in physics, with a commensurate mathematical background. I have however found it impossible to be strictly consistent about this, because of the wide range of disciplines within and beyond physics from which the material has been drawn, and I trust that readers will be understanding when they find the treatment either too simple or over their heads.

In Chapter 1 we noted that electromagnetic radiation is fundamental to remote sensing as we have defined it: the information about the sensed object is carried by this radiation. We therefore need to develop an understanding of the essential characteristics of this radiation and of how it interacts with its surroundings. This is a large topic and it is covered in this chapter and the next two. In this chapter we consider electromagnetic radiation in its simplest form, when it is propagating in (travelling through) a vacuum, usually termed ‘free space’. This is practically useful, because for much of its journey towards the sensor the radiation is propagating in a medium that approximates to free space, and it also allows us to develop some of the essential ideas that describe electromagnetic radiation without too much confusing detail.

A particularly important part of this chapter deals with thermal radiation. As we noted in Chapter 1, most passive remote sensing systems detect thermal radiation (in the infrared or microwave regions) or they detect reflected solar radiation. Solar radiation is itself, as explained in this chapter, essentially just another form of thermal radiation, so by developing an understanding of thermal radiation we are able to describe many of the characteristics of the radiation detected by passive systems.

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).