Time as we use it in our ordinary lives is based on the rotation and revolution of the Earth with respect to the Sun. These combined motions cause the Sun to appear to move continually around the heavens, and we define solar noon as the moment each day when the Sun crosses an observer's meridian. We could easily use the interval from one noon to the next to define the day, but in order to make all of the daylight hours part of the same calendar day, we start and end our days at midnight. The division of the day into twenty-four hours is strictly arbitrary and dates back to ancient Egypt, perhaps even earlier. The Greeks divided the periods of daylight and darkness into twelve equal parts to make twenty-four divisions in each day. The length of the hour defined in this way gradually changes throughout the year as the length of day and night varies with the seasons. The custom of dividing the hour into sixty minutes and the minute into sixty seconds is one of the last vestiges of the sexagesimal system of counting developed by the ancient Babylonians.

Today we keep track of time with a variety of clocks that range in complexity from sundials of the simplest sort to atomic clocks of the greatest precision.

We live on the surface of a planet that permits us to observe the distant Universe through a narrow window of the electromagnetic spectrum. While astronomers have expanded their vision with telescopes in Earth orbit, they still carry out most astronomical observations from the ground. As such, astronomers have to take into account the effects of the atmosphere on their observations. In this chapter we will discuss the five distinct ways the atmosphere affects the light from astronomical sources: extinction, refraction, seeing, scintillation, and dispersion.

Extinction

The Earth's atmosphere blocks most of the electromagnetic radiation arriving from space. Astronomers look through two “windows” in the electromagnetic spectrum to learn about extraterrestrial sources, the optical/near infrared (Figure 7.1) and radio. The optical window covers wavelengths from about 3000 Å to about 9000 Å. Several windows of moderately high transmission continue through the infrared up to about 26 microns. The windows in the radio band begin near 1 mm and end near 20 m. We will focus on the optical to near-IR window in this chapter.

We noted in Chapter 5 that the Johnson U bandpass is partly determined by the atmosphere's ultraviolet cutoff. Other bandpasses in the optical are determined by the filter transmission curves. The infrared JHKLM system (shown in Figure 7.1) is determined by the narrow windows between the deep molecular absorption bands.

Stars

When we wish to study the characteristics of a star, it is crucial that we be able to identify it with absolute certainty. Many resources are available to the astronomer to assist in star identification, and the method of choice depends largely on the brightness of the star. If the star is brighter than about fourth magnitude, the problem is quite simple, for there are not very many stars of comparable brightness. Once we set our telescope to the proper coordinates, there will probably be only one sufficiently bright star in the typical field of view. On the other hand, when we try to locate a star of eighth or ninth magnitude, there may be six or more stars in a field 30 arcmin in diameter. The numbers of progressively fainter stars in a given field increases dramatically. There are so many sources of error involved in setting a telescope that it is not reasonable to expect that the desired star will always be the one nearest the center of the field even if the coordinates are known and the telescope is set with great precision. Therefore, when trying to identify faint stars we must usually rely on maps or charts on which each star has been identified in some reliable manner. The observer can then compare the pattern of stars depicted on the chart with the pattern actually seen in the telescope and make a positive identification.

The development of spectacles (eyeglasses) was a tremendous impetus to the eventual development of the telescope. We do not know who first invented spectacles, but it is thought that they first appeared in Italy between 1285 and 1300. As eyeglasses became more common and more refined, it was perhaps inevitable that someone would figure out how to use lenses to form the first telescope. That happened in 1608, when the German-born Dutch eyeglass maker Hans Lippershey (1570–1619) built the first crude telescopes, not for astronomy, but for military uses.

In May of 1609, the Italian scientist Galileo Galilei (1564–1642) received word of this new magnifying instrument constructed using two lenses and a tube, and at once set about to build his own. In his Sidereus Nuncius (The Starry Messenger; 1610), Galileo describes his first telescope.

Galileo's first telescope could magnify objects just three times, and it was only about an inch in diameter. He soon constructed several more powerful telescopes, beginning at eight times magnification and eventually achieving 30 times.

What are astronomical spectra good for? For nearly 100 years photographs of low-dispersion spectra have been used to classify stars according to spectral type and luminosity class, determine spectral energy distributions, determine the redshifts and properties of galaxies, and measure emission line ratios in nebulae. High-dispersion spectra have been used to determine precise radial velocities, chemical element abundances in stellar atmospheres and in the interstellar medium, rotational velocities in stars, and magnetic field strengths in stellar atmospheres. We will explore aspects of some of these applications in this chapter.

Low-dispersion spectra are usually presented with absolute flux units on the vertical axis, as we showed in Chapter 5. High-dispersion stellar spectra, however, are usually normalized with respect to the local continuum. The continuum consists of the regions of highest flux that appear continuous except for the intervening absorption lines. Continuum windows are usually available even over a span of a few ångströms in high-dispersion spectra of Sun-like stars. In order to normalize a spectrum, first it is necessary to fit a low-order function through the continuum windows. This can be done by manually selecting the windows or by using a routine that automatically rejects high and low points according to an objective criterion. We show in Figure 13.1 a sample 50 Å region of a high-dispersion spectrum prior to and after continuum normalization. Normalized spectra are used in several of the analysis methods described below.

Visual observations

For thousands of years people recorded what they saw in the sky on rock walls, clay tablets, ivory and papyrus. In more recent times astronomers tried to reproduce on paper the precise patterns of the stars they observed with and without optical aid, some producing accurate and beautiful sky charts. Until the mid nineteenth century the human eye was the only available light detector.

The eye is truly a remarkable organ. Let us describe its structure and the function of some of its important parts in the overall process of vision. Figure 8.1 is a sketch of the right eye as it would appear looking down through the top of the head. The eye is essentially a spherical object that maintains its form by means of its tough outer layer, the sclera. The front center portion of the sclera is the transparent cornea through which all light entering the eye must pass. Behind the cornea is the crystalline lens, and the two are separated by a small amount of clear liquid known as the aqueous humor. The eyeball is filled with a jelly-like substance, the vitreous humor, which also helps it maintain its shape.

Light refracts at the outside surface of the cornea and at all of the interfaces within the eye. In a very real way, then, the optical characteristics of the eye are determined by the cornea, aqueous humor, crystalline lens and the vitreous humor.

One of the important actions that is in nearly all of the foregoing chapters is measurement. We measure time, coordinates, proper motions, parallaxes, magnitudes, the positions of lines in spectra, and shifts in positions of spectral lines, for example. After a measurement has been made we want to know how good the measurement really is, and in order to evaluate our measurements, we must turn to statistics. We would also like to use our measured data to make predictions either within or beyond the range of the measurements. Here we shall describe some of the principles that permit us to achieve these two goals in practical situations.

As an example, let us assume that a student is asked to determine the position of a spectrum line by measuring the distance from some reference position to the line center with a ruler. The smallest divisions on the ruler are one mm apart. We should be able to read the position of the line to within one tenth of a millimeter (0.1 mm). Just as a check the student makes a second setting and reads a new value with the ruler. She tries again and again until she has made fifty tries, and she never makes quite the same reading twice. Which of these many readings should be adopted as the correct one?

In the night sky the stars appear as bright points on a dark spherical surface (Figure 1.1). No such surface really exists, of course, but the concept of a celestial sphere is a useful one that goes back thousands of years. Ptolemy described it and so did Pythagoras and many others. Today we no longer have to worry about the reality of that sphere, and so we eliminate the need for speculation on its composition, radius, thickness and so forth. On the other hand, even though the celestial sphere is not a physical entity, we have many practical uses for the concept. The observer is always at the center of it, and the direction from the observer to any star may be considered to be a radius of the celestial sphere.

The stars are so far very away that we can consider the celestial sphere to be very large and the Earth very small. From the perspective of an observer on the celestial sphere looking back, the entire Earth would appear as a single point. And on the surface of the Earth, when we point to objects in the sky, we don't need to know how far away they are for the purposes of positional astronomy. We need only be concerned with the angles between points on the celestial sphere. That's why a good planetarium fools us into thinking that we are looking at the real sky.

Astronomers, both professional and amateur, have cataloged thousands of variable stars across the celestial sphere. Their periods range from a few minutes to hundreds of days. Some are visible to the naked eye, but most can only be detected with large telescopes. Some behave in an erratic fashion, while others are as predictable as the sunrise. Within this large group there is something for the interests and equipment of every observer, and serious contributions to the overall body of astronomical data can be made by anyone who is willing to exercise care in all phases of the collection of data.

Astronomers have found the study of variable stars to be both pleasant and rewarding. We shall begin this chapter with some information on nomenclature, reference materials and the various classes of variable star. We shall then proceed to discuss methods of analysis of variable star light curves and the determination of precise periods.

Naming variable stars

Variable stars are named in accordance with a scheme that was introduced in the middle of the nineteenth century when variability was first being recognized as a common phenomenon in stars. The originator of the current practice was the German astronomer, Friedrich Argelander, who was mentioned in Chapter 3 as the force behind the BD charts and catalog. In each constellation the first variable to be discovered was identified with the letter “R” followed by the possessive form of the Latin name.

It is safe to say that the spectrograph, a relatively simple instrument, brought about a virtual revolution in astronomy. Although Newton had examined the spectrum of sunlight and Fraunhofer had seen the spectra of a few stars, the spectroscope was not extensively used on telescopes until the latter half of the nineteenth century. Beginning in about 1860, Sir William Huggins in England and Fr. Angelo Secchi in Rome performed their first experiments on the light from the Moon, the planets and the brighter stars. The spectrograph was slowly refined and improved, and eventually it made possible a series of new understandings of the nature of the Sun and stars. First came the identification of a few absorption lines in solar and stellar spectra; then came recognition of several distinct classes of spectra. By the end of the century the construction of spectrographs had been refined to the point that radial velocities could be measured with confidence. Today we have a remarkable understanding of the physical processes that occur in nebulae and the atmospheres of the Sun and stars.

Since the nineteenth century several technological developments have increased the efficiency of the spectrograph, and there have been changes in the means by which the light is dispersed. The general principles of the spectrograph are not complicated, however, and we will outline them below. We shall discuss first the prism and then the grating as dispersive elements. Then we will describe the practical considerations in the design and use of a spectrograph.

Overview of exoplanet properties and theory

In the past ten years, 170 exoplanets have been discovered orbiting 130 normal stars by using the Doppler technique to monitor the gravitational wobble induced by a planet, as summarized by Marcy et al. (2004) and Mayor et al. (2004). Multipleplanet systems have been detected around 17 of the 130 planet-bearing stars, found by superimposed multiple Doppler periodicities (Mayor et al., 2004; Vogt et al., 2005). Another five exoplanets have been found photometrically by the dimming of the star as the planet transits across the visible hemisphere of the star (Bouchy et al., 2005; Torres et al., 2005).

The Doppler surveys for planets have revealed several properties:

• Planet mass distribution: dN/dM α M−1.5 (Fig. 11.1).

• Planet occurrence increases with semimajor axis (Fig. 11.2).

• Hot Jupiters (a < 0.1 AU) exist around 0.8% of FGK stars.

• Eccentric orbits are common (Fig. 11.3).

• Planet occurrence rises rapidly with stellar metallicity (Fig. 11.4).

• Multiple planets are common, often in resonant orbits.

The transiting planets permit measurement of planet radius and mass, demonstrating that they are “gas giants”, as expected (Henry et al., 2000; Charbonneau et al., 2000). The properties of the 170 known exoplanets motivate theories of their formation and their dynamical interactions with both the protoplanetary disk and other planets (Bryden et al., 2000; Laughlin and Chambers, 2001; Rivera and Lissauer, 2001; Chiang and Murray, 2002; Lee and Peale, 2002; Ford et al., 2003; Ida and Lin, 2004).

With the words “Twas the night before Christmas…” does a good old story start. In December 2004, just a couple of days before Christmas, not three wise men but more than 60 wise men and women came to a castle in the Bavarian mountains. They traveled through a strong snow storm, but no-one turned back; all of them arrived. They had a noble goal in mind: to discuss the current understanding of the formation of planets. The meeting took place December 19–22, 2004 at the Ringberg castle of the Max-Planck-Society. Anyone who has had the chance to attend a meeting there knows what a friendly and stimulating atmosphere for a workshop it provides.

About a year beforehand we had called them, and now they came. The idea was to have a wonderful conference at the romantic Ringberg castle and to bring together theorists and observers, as well as meteoriticists and experimental astrophysicists. Only then, we thought, could we obtain a global picture of the ideas we have about how our planetary system came into life. We wanted to collect not only the accepted ideas, but also the speculative and competing ideas.

We were quickly convinced that this conference, unique in its composition, should generate a permanent record in the form of a proceedings book. But this book should not be just one more useless compendium of unrefereed papers, but should provide a concise and accurate picture of current planet formation theory, experiment, and observation.

Introduction

Directly after the discovery of the very first extrasolar planets around main-sequence stars it has become obvious that the new planetary systems differ substantially from our own Solar System. Amongst other properties one distinguishing feature is the close proximity of several planets to their host stars (hot Jupiters). As it is difficult to imagine scenarios to form planets so close to their parent star it is generally assumed that massive, Jupiter-like planets form further away, and then migrate inwards towards the star due to disk–planet tidal interactions. Hence, the mere existence of hot Jupiters can be taken as clear evidence of the occurence of migration. Interestingly, theoretically the possibility of migrating planets has long been predicted from the early 1980s.

Another observational indication that some migration of planets must have occured is the existence of planets in mean motion resonances. Due to converging differential migration of two planets both embedded in a protoplanetary disk they can be captured in a low-order mean motion resonance. The most prominent example is the system GJ 876 where the planets have orbital periods of roughly 30 and 60 days.

In this review we focus on the theoretical aspects of the disk–planet interaction which leads to a change in the orbital elements of the planet most notably its semimajor axis. We only treat systems with a single planet and do not consider planetery systems containing multiple planets.

Introduction

The count of extrasolar giant planets detected by radial velocity measurements is now well over a hundred, accounting for about 5% of F, G and K main-sequence stars in the Solar neighborhood; about 10% of the planets are in multiple systems. It thus seems an inescapable conclusion that giant planet formation is a ubiquitous and robust process. There is also strong observational evidence for a correlation between the occurrence rate of (detectable) planets and the metallicity of the parent star (Gonzalez, 1997; Fischer and Valenti, 2003). There are two possible explanations for this phenomenon: first, the planet formation process may tend to “pollute” the parent star with higher-metallicity material, as giant planets (Laughlin and Adams, 1997) or planetesimals (Murray et al., 2001) migrate in and are engulfed. If this is the case, higher-mass stars, which have thinner convective envelopes in which to preserve the pollution, ought to display a systematically higher metallicity. However, no such trend has been observed so far (Wilden et al., 2002; Dotter and Chaboyer, 2002; Quillen, 2002; Fischer and Valenti, 2003). Furthermore, Fischer and Valenti (2005) found no sign of various other potential accretion signatures, such as dilution of metallicity in subgiants with planets. The other explanation is that higher metallicity – and thus a higher fraction of solids in the protoplanetary disk – increases the chances of forming a giant planet.