Even casual users of CCDs have run across the terms read noise, signal-to-noise ratio, linearity, and many other possibly mysterious sounding bits of CCD jargon. This chapter will discuss the meanings of the terms used to characterize the properties of CCD detectors. Techniques and methods by which the reader can determine some of these properties on their own and why certain CCDs are better or worse for a particular application are discussed in the following chapters. Within the discussions, mention will be made of older types of CCDs. While these are generally not available or used anymore, there is a certain historical perspective to such a presentation and it will likely provide some amusement for the reader along the way.

One item to keep in mind throughout this chapter and in the rest of the book is that all electrons look alike. When a specific amount of charge is collected within a pixel during an integration, one can no longer know the exact source of each electron (e.g., was it due to a stellar photon or is it an electron generated by thermal motions within the CCD itself?). We have to be clever to separate the signal from the noise. There are two notable quotes to cogitate on while reading this text. The first is from an early review article on CCDs by Craig Mackay (1986), who states: “The only uniform CCD is a dead CCD.”

Classical orbit calculation in Newtonian mechanics has experienced a renaissance in recent decades. With the beginning of space flights there was suddenly a great practical need to calculate orbits with high accuracy. At the same time, advances in computer technology have improved the speed of orbit calculations enormously.

These advances have also made it possible to study the gravitational three-body problem with new rigour. The solutions of this problem go beyond the practicalities of space flight into the area of modern astrophysics. They include problems in the Solar System, in the stellar systems of our Galaxy as well as in other galaxies. The present book has been written with the astrophysical applications in mind.

The book is based on two courses which have been taught by us: Celestial Mechanics and Astrodynamics. The former course includes approximately Chapters 2–5 of the book, with some material from later chapters. It is a rather standard introduction to the subject which forms the necessary background to modern topics. The celestial mechanics course has been developed in the University of Helsinki by one of us (H. K.) over about two decades. The remainder of the book is based on the astrodynamics course which arose subsequently in the University of Turku. Much of the material in the course is new in the sense that it has not been presented at a textbook level previously.

The formalism of the previous chapters used a rather arbitrary coordinate system. In the Hamiltonian formalism the coordinates are chosen in quite a different way to reflect more deeply the dynamical properties of the system. In this chapter we derive the Hamiltonian equations of motion. The results of this chapter are later needed mainly to derive some standard results that are the starting point for further studies. The same results can also be obtained in a more traditionalway, but the Hamiltonian approach makes the calculations considerably shorter and more straightforward.

Hamiltonian mechanics and its applications to mechanics in general are explained more extensively in many books on theoretical mechanics. This chapter is based mainly on Goldstein (1950).

Generalised coordinates

We have this far used ordinary Euclidean rectangular coordinates to describe positions and velocities of the objects. They are purely geometric quantities that describe the system in a very simple and understandable way. However, they do not tell us anything about the dynamic properties of the system nor do they utilise any specific features of the system.We now want to find a different kind of description in terms of quantities which do not have these problems.

Motions of bodies may be constrained in various ways. For example, two points of a solid body must always be at the same distance from each other.

Three-body scattering

Three-body scattering is a process where a third body comes from a large distance in a hyperbolic orbit and interacts with a binary. The interaction may result in a capture of the third body into the vicinity of the binary. Then we say that a resonance (a long lasting state, as in atomic physics) has formed. We expect that the resonance will finally end with an escape of one of the bodies. The other alternatives are an exchange where the interaction leads to an immediate expulsion of one of the binary members, or a flyby when the third body immediately leaves the scene of the close interaction with the binary. These processes will be discussed in turn, in the following sections. Here the basic theoretical groundwork is formulated, using the results from Section 7.1. At very high energies the three bodies may fly apart separately; then the process is called ionisation.

Sometimes a different definition of exchange is used: whenever one of the original binary members is ejected, the process is called exchange. It may happen immediately (prompt exchange) or after an intermediate resonance (resonance exchange). We do not follow this wider definition but define exchange as prompt exchange.

The calculation of the scattering process is performed in two steps: (1) the probability that the third body meets the binary is calculated, and (2) the probability that the binary gains or loses a given amount of energy in the interaction with the third body is estimated.

Binary black holes in centres of galaxies

Galactic nuclei are regions of high star densities as well as sites of very massive black holes, at least in many galaxies. For example, the central black hole in our own Galaxy is thought to be about 2 × 106M⊙ while the giant elliptical galaxy M87 possesses a dark central body of 3 × 109M⊙. The observed masses of these central objects are typically 1.2 × 10–3 times the mass of the spheroidal stellar component of their host galaxies (Merritt and Ferrarese 2001).

It is quite likely that there are also supermassive binary black holes in the centres of some galaxies, based both on theoretical (Saslaw et al. 1974, Begelman et al. 1980) and observational grounds (Komberg 1967, Sillanpää et al. 1988, Lehto and Valtonen 1996). They result most likely from mergers of galaxies. While the stars and gas of the two merged galaxies intermingle and form a new single galaxy, the central black holes remain separate for a long time, perhaps as long as the Hubble time (Milosavljevic and Merritt 2001). In the currently popular cold dark matter (CDM) model of cosmology it is believed that merging of galaxies is a common process (e.g. Frenk et al. 1988). Therefore binary black holes must also be common. How common they are depends on the interaction of the binary with the surrounding stars and gas clouds.

Complete analytical solutions are not available for systems with more than two bodies. However, it is possible to describe three-body orbits by approximate methods when the system is hierarchical, i.e. if there is a clearly defined binary and a third body which stays separate from the binary. These methods may be validated by comparison with numerical orbit integrations. Then we may take exact two-body orbits as a first approximation, and the effects of other bodies and other disturbances are taken into account as small forces which make the true trajectory deviate from this reference orbit.

Whenanalysing perturbations we have to make some approximations that depend on the form of the perturbing force. Thus perturbation theory is a collection of various methods applicable in different situations rather than a single theory. In this chapter we will study a classical method that applies to the usual orbital elements. Another method will be discussed in the next chapter.

The problem which we consider by using this method is the long term evolution of a binary orbit when it is perturbed by a distant companion. This applies especially to triple stars and to the stability of planetary orbits around binary members.

Osculating elements

Consider the motion of a planet in a heliocentric xyz-frame. At the moment t = t0 the planet is at (x0, y0, z0).

About the three-body problem

The three-body problem arises in many different contexts in nature. This book deals with the classical three-body problem, the problem of motion of three celestial bodies under their mutual gravitational attraction. It is an old problem and logically follows from the two-body problem which was solved by Newton in his Principia in 1687. Newton also considered the three-body problem in connection with the motion of the Moon under the influences of the Sun and the Earth, the consequences of which included a headache.

There are good reasons to study the three-body gravitational problem. The motion of the Earth and other planets around the Sun is not strictly a two-body problem. The gravitational pull by another planet constitutes an extra force which tries to steer the planet off its elliptical path. One may even worry, as scientists did in the eighteenth century, whether the extra force might change the orbital course of the Earth entirely and make it fall into the Sun or escape to cold outer space. This was a legitimate worry at the time when the Earth was thought to be only a few thousand years old, and all possible combinations of planetary influences on the orbit of the Earth had not yet had time to occur.

Another serious question was the influence of the Moon on the motion of the Earth.

This appendix provides a reading list covering the aspects of CCD development, research, and astronomical usage. There are so many articles, books, and journal papers covering the innumerable aspects of information on CCDs that the material presented in a book this size or any size can only cover a small fraction of the details of such work. Even the list presented here does not cover all aspects of interest concerning the use of CCDs in astronomy, but it does provide a very good starting point. The growth of information on CCDs has risen sharply over the past ten years and will, no doubt, continue to do so. Thus the student of CCD science must constantly try to keep up with the latest developments both in astronomy and within the field of opto-electronics, both areas where progess is being made. The internet is a powerful tool to help in this pursuit. Using a good search engine (e.g. Google) type in items such as “deep depletion,” or “L3CCD,” or “MIT/LL” and you'll get back many items of interest.

Much of the information on CCDs is contained in books devoted to the subject. Numerous SPIE, IEEE, and other conferences publish their proceedings in books as well. Detailed information is available in the scientific literature some of which we reference in this volume. Many refereed articles of interest are not listed here as they are easily searched for via web-based interfaces such as the Astrophysics Data System (ADS).

Seven years ago, Cambridge University Press began a new series of books called Handbooks. I was fortunate enough to be asked to author the one on CCDs. Little did I realize how wonderful of an undertaking that writing this book would be. I have learned and relearned a number of details about CCDs and had cause to read many scientific and popular papers and articles I otherwise would have overlooked. The greatest benefit, however, has been the many gracious colleagues and students who have provided comments, revisions, suggestions, support, and simply said thanks. The first edition of the Handbook of CCD Astronomy was written for you and you have truly made it your own through this volume.

When I was first asked to write a second edition, I have to admit I was skeptical that enough had changed to warrant it. I am happy to say I was completely wrong. Upon going back and reading the original volume, I had no problem seeing its many pages of outdated material. There are, however, some fundamental discussions and properties of CCDs that are timeless, and remain in the present volume. New areas of CCD development abound and to highlight a few this second edition is a bit longer and has a few more illustrations. The areas of faster and higher performance electronics to control and read out a CCD, better analog-to-digital circuitry, and better manufactured CCDs are some of the additions discussed within.

Silicon. This semiconductor material certainly has large implications on our life. Its uses are many, including silicon oil lubricants, implants to change our bodies' outward appearance, electric circuitry of all kinds, nonstick frying pans, and, of course, charge-coupled devices.

Charge-coupled devices (CCDs) and their use in astronomy will be the topic of this book. We will only briefly discuss the use of CCDs in commercial digital cameras and video cameras but not their many other industrial and scientific applications. As we will see, there are four main methods of employing CCD imagers in astronomical work: imaging, astrometry, photometry, and spectroscopy. Each of these topics will be discussed in turn. Since the intrinsic physical properties of silicon, and thus CCDs, are most useful at optical wavelengths (about 3000 to 11 000 Å), the majority of our discussion will be concerned with visible light applications. Additional specialty or lesser-used techniques and CCD applications outside the optical bandwidth will be mentioned only briefly. The newest advances in CCD systems in the past five years lies in the areas of (1) manufacturing standards that provide higher tolerances in the CCD process leading directly to a reduction in their noise output, (2) increased quantum efficiency, especially in the far red spectral regions, (3) new generation control electronics with the ability for faster readout, low noise performance, and more complex control functions, and (4) new types of scientific grade CCDs with some special properties.

We are all aware of the amazing astronomical images produced with telescopes these days, particularly those displayed as color representations and shown off on websites and in magazines. For those of us who are observers, we deal with our own amazing images produced during each observing run. Just as spectacular are photometric, astrometric, and spectroscopic results generally receiving less fanfare but often of more astrophysical interest. What all of these results have in common is the fact that behind every good optical image lies a good charge-coupled device.

Charge-coupled devices, or CCDs as we know them, are involved in many aspects of everyday life. Examples include video cameras for home use and those set up to automatically trap speeders on British highways, hospital X-ray imagers and high-speed oscilloscopes, and digital cameras used as quality control monitors. This book discusses these remarkable semiconductor devices and their many applications in modern day astronomy.

Written as an introduction to CCDs for observers using professional or off-the-shelf CCD cameras as well as a reference guide, this volume is aimed at students, novice users, and all the rest of us who wish to learn more of the details of how a CCD operates. Topics include the various types of CCD; the process of data taking and reduction; photometric, astrometric, and spectroscopic methods; and CCD applications outside of the optical band-pass.