Introduction

In this book we have derived a number of equations of motion to study the rotational and orbital motion of solar system objects. These equations have described either conservative systems, such as the two- and three-body problems, or dissipative systems, such as the equations governing tidal evolution or the dynamical effects of drag forces. However, all have a common characteristic: They describe systems that are deterministic. This means that the current state of the system allows us to calculate its past and future state providing we know all the forces that are acting on it. In the case of the two-body problem we were able to solve the equations of motion and calculate the behaviour of the system at all past and future times. A complete analytical solution was not possible in the case of the three-body problem and we had to rely on numerical solutions if we wanted to follow the orbital evolution of a test particle. However, there was an implicit assumption that, given the initial state of the system, we should be able to calculate its future state by obtaining solutions of the equations of motion. Unfortunately this assumption is not valid for some of the systems we have investigated and this is because of the phenomenon called chaos.

More and more investigators are being attracted to work in the infrared spectral region. My intention in this book is to introduce the infrared, its peculiarities and its special techniques, to a new audience that may include established astronomers as well as new students. Basic facts and figures are emphasized and I have not tried to cover all current research. The approach usually avoids the historical and the reader is referred instead to recent books and papers. The origins of ideas are always complex and, with something like 104 papers published, it is impossible to do justice to every individual in the field.

The first chapter deals with the basic facts of blackbody radiation, which plays a dominant role in infrared astronomy. A short review of atomic and molecular physics follows in order to provide a convenient reminder of the meaning of spectroscopic nomenclature. The second chapter covers the general properties of the Earth's atmosphere and outlines the main infrared surveys that have taken place or will shortly do so. Chapter 3 is devoted to photometry, emphasizing its fundamental aspects and the importance of traceability and calibration. Chapter 4 is an introduction to spectroscopy, treating firstly the stars. Photodissociation regions, which are of great interest in the infrared and millimeter region, are followed by HII regions and some “Rosetta Stone” spectra of representative objects. Chapter 5 is devoted to dust and its central role in star formation. Finally, because an understanding of the technology is important in obtaining reliable results, the last chapter covers the basics of infrared instrumentation.

Introduction

The central astronomical role of dust is at its most evident in the infrared. Protostars form from dusty clouds of molecular gas; the cool condensing dust around them emits copiously at sub-millimeter and far-infrared wavelengths. Even fully developed stars such as Vega may be found to be surrounded by remnant dust particles (see Habing et al., 1996), causing excess emission at long wavelengths. Near the end of their existence, a new generation of dust is formed by evolved stars, for example, in the atmospheres of asymptotic giant branch objects and in the ejecta of supernovae.

As in the visible region, dust scatters and absorbs light, giving rise to extinction, though its effects are much smaller in the infrared than in the visible. A dramatic example is the Galactic Center, which suffers 30 mag of extinction at V, so that only about one photon in 1012 comes through, whereas AK (2.2 μm) is about 2.5 mag and ∼10% of the photons can penetrate. Figure 5.1 shows the distribution of several types of objects with cool dust in an IRAS color-color diagram.

Dust also polarizes the light from distant stars and some properties of the polarization are found to be related to the extinction.

Even when the extinction is quite moderate, by observing in the infrared, the effects of interstellar absorption, which bedevil the use of the cepheid and RR Lyrae period-luminosity relations for distance determination, may be greatly reduced (e.g., Laney and Stobie, 1993, in the case of cepheids).

Introduction

We can consider spectroscopy at several different resolution levels.

The crudest resolution amounts to photometry, where the wavelength scale is divided into a small number of regions, or wide bands, to give an indication of a spectral energy distribution (SED). Examples might include the U(0.37), B(0.44), V(0.55), R(0.64) and I(0.80 μm) system in the visible region and the J(1.25), H(1.65), K (2.2), L(3.5), M(4.8), N(10), and Q(20 μm) system of ground-based infrared, as well as the 12, 25, 60 and 100 μm IRAS bands.

Many data with Δλ/λ ∼ 0.01 exist from spectrometers that used circular variable filters (CVFs). This is usually considered to be the least resolution which can really be called spectroscopy.

The next level might be called medium-resolution spectroscopy, where the detailed lines that usually compose molecular bands are not seen, but the bands are treated in an averaged manner. Most infrared spectroscopy falls into this category.

With high-resolution spectroscopy the individual molecular lines can be examined. Sensitivity considerations have limited this type of work hitherto to the study of the Sun, bright stars and planets. With the advent of large infrared array detectors and large telescopes, it is reasonable to predict that fainter objects will soon receive attention. High resolution has in the past been obtained through the use of Fabry–Perot etalons or Michelson interferometers, also called Fourier–transform spectrometers.

Stellar spectra

The theoretical study of stars is usually divided into stellar interiors and stellar atmospheres. The output of the interior can be regarded as something like a blackbody, but the atmosphere modifies the emergent flux according to its temperature structure, pressure structure and composition.

If the polar axis of an equatorial mount is misaligned, three kinds of errors result:

1. • Hour angle error (the object appears to drift in right ascension, or putting it another way, the drive rate appears to be wrong);

2. • Declination error (the object appears to drift in declination);

3. • Field rotation (the object appears to rotate). The hour angle error is entirely absorbed into guiding corrections that are needed for other reasons. In this appendix I shall analyze the remaining two. As far as I can determine, no one in the twentieth century has published a full analysis of this matter, although it is discussed by Chauvenet (1876, vol. 2, pp. 367–390) and Pickering (1886, pp. 195–201). Their equipment was quite different from that now in use, and their aim was to build perfect equatorial mounts rather than to analyze the effect of making guiding corrections with portable equipment whose alignment is never perfect. On the related problem of tracking the stars with an altazimuth mount and field-de-rotator, see Trueblood and Genet (1985, p. 109 ff.) and Pouplier (1992).

Precaution for calculators Many of the calculations described here require a large number of significant digits in order to yield useful results. For example, in Example 1, a number is multiplied by 0.999 990 480 7, and if this were rounded to 1.0 the entire significance of the number would be lost.