Overview

When we look at photographs of the Milky Way (see Fig. 16.1), we note large regions where no light is seen. We think that these are due to dust blocking the light between us and the stars. We can see the same effect on a smaller scale (Fig. 14.1). Note that there is a high density of stars near the edges of the image. As one moves close to the center, the density of stars declines sharply. Near the center, no stars can be seen. This apparent hole in the distribution of stars is really caused by a small dust cloud, called a globule. The more dust there is in the globule, the fewer background stars we can see through the globule. We can use images like this to trace out the interstellar dust. We find that it is not uniformly distributed. Rather, it is mostly confined to concentrations or interstellar clouds.

We detect the presence of the gas by observing absorption or emission lines from the gas. By tracing these lines, we find that the gas also has an irregular distribution. Often the gas appears along the same lines of sight as the dust clouds. From this apparent coincidence we form the idea that the gas and dust are generally well mixed, with the gas having about 99% of the mass in a given cloud. In this chapter, we will see how the masses of different types of clouds are determined.

The past decades have seen dramatic improvements in our observing capabilities. There have been improvements in our ability to detect visible radiation, and there have also been exciting extensions to other parts of the spectrum. These improved observing capabilities have had a major impact on astronomy and astrophysics. In this chapter we will first discuss the basic concepts behind optical observations. We will then discuss observations in other parts of the spectrum.

What a telescope does

An optical telescope provides two important capabilities:

1. (1) It provides us with light-gathering power. This means that we can see fainter objects with a telescope than we can see with our naked eye.

2. (2) It provides us with angular resolution. This means that we can see greater detail with a telescope than without.

For ground-based optical telescopes, light-gathering power is usually the most important feature.

Light gathering

We can think of light from a star as a steady stream of photons striking the ground with a certain number of photons per unit area per second. If we look straight at a star, we will see only the photons that directly strike our eyes. If we can somehow collect photons over an area much larger than our eye, and concentrate them on the eye, then the eye will receive more photons per second than the unaided eye. A telescope provides us with a large collecting area to intercept as much of the beam of incoming photons as possible, and then has the optics to focus those photons on the eye, or a camera, or onto some detector.

Overview

Throughout this book we have discussed the components of our galaxy: stars, clusters of stars, interstellar gas and dust. We now look at how these components are arranged in the galaxy. The study of the large scale structure of our galaxy is difficult from our particular viewing point. We are in the plane of the galaxy, so all we see is a band of light (Fig. 16.1). The interstellar dust prevents us from seeing very far into the galaxy. We see a distorted view.

The first evidence on our true position in the galaxy came from the work of Harlow Shapley, who studied the distribution of globular clusters (Fig. 16.2). He found the distances to the clusters from observations of Cepheids and RR Lyrae stars. Shapley found that the globular clusters form a spherical distribution. The center of this distribution is some 10 kpc from the Sun. Presumably, the center of the globular cluster distribution is the center of the galaxy. This means that we are about 10 kpc from the galactic center.

In Chapter 13, when we studied HR diagrams for clusters, we introduced the concept of stellar populations I and II. The distribution of these populations in the galaxy can help us understand how the galaxy has evolved. Population I material is loosely thought of as being the young material in the galaxy.

Now that we know the basic properties of stars, we look at how the laws of physics determine those properties, and then how stars change with time – how they evolve. Stars go through a recurring full life cycle. They are born, they live through middle age, and they die. In their death, they distribute material into interstellar space to be incorporated into the next generation of stars.

In describing the life cycle, we can start anywhere in the process. In Chapter 9, we discuss the most stable part of their life cycle, life on the main sequence – stellar middle age. In Chapters 10, 11 and 12 we will look at the deaths of different types of stars. After discussing the interstellar medium in Chapter 14, we will look at star formation in Chapter 15.

Brightness of starlight

When we look at the sky, we note that some stars appear brighter than others. At this point we are not concerned with what causes these brightness differences. (They may result from stars actually having different power outputs, or from stars being at different distances.) All we know at first glance is that stars appear to have different brightnesses.

We would like to have some way of quantifying the observed brightnesses of stars. When we speak loosely of brightness, we are really talking about the energy flux, f, which is the energy per unit area per unit time received from the star. This can be measured with current instruments (as we will discuss in Chapter 4). However, the study of stellar brightness started long before such instruments, or even telescopes, were available. Ancient astronomers made naked eye estimates of brightness. Hipparchus, the Greek astronomer, and later Ptolemy, a Greek living in Alexandria, Egypt, around 150 BC, divided stars into six classes of brightness. These classes were called magnitudes. This was an ordinal arrangement, with first-magnitude stars being the brightest and sixth-magnitude stars being the faintest.

When quantitative measurements were made, it was found that each jump of one magnitude corresponded to a fixed flux ratio, not a flux difference. Because of this, the magnitude scale is essentially a logarithmic one. This is not too surprising, since the eye is approximately logarithmic in its response to light.

Aristotle, observing the Greeks in the fourth century b.c., thought that man's natural proclivities were toward discourse and political activity. Adam Smith, observing the Scots in the eighteenth century a.d., saw instead a propensity to engage in economic exchange. From the observations of these two intellectual giants, two separate fields in the social sciences have developed: the science of politics and the science of economics.

Traditionally, these two fields have been separated by the types of questions they ask, the assumptions they make about individual motivation, and the methodologies they employ. Political science has studied man's behavior in the public arena; economics has studied man in the marketplace. Political science has often assumed that political man pursues the public interest.

The Bergson-Samuelson SWF has been constructed analogously to the individual's utility function. Just as the individual chooses bundles of commodities to maximize his utility, society must choose an allocation of commodities across individuals to maximize its welfare. That consumers make choices to maximize their utility follows almost tautologically from the definition of rationality. In extending the idea of maximizing an objective function to the level of society, however, more is involved than just rationality. Embedded in the characteristics of the welfare function and the nature of the data fed into it are the value judgments that give the SWF its normative content, as the discussions of Bergson (1938) and Samuelson (1947, ch. 8) make clear.

An alternative way of analyzing individual behavior from assuming that individuals maximize their utility is to assume various postulates about individual rationality that suffice to define a preference ordering, and allow one to predict which bundle an individual will choose from any environment. Again by analogy, one can make various postulates about social decision making and analyze society's decisions in terms of social preference orderings.

Two views of representation

Several alternatives to the majority rule have been proposed down through the years. Three of the newest and most complicated of these are presented in Chapter 8. Here we discuss some of the simpler proposals.

These voting procedures are usually not considered a means of revealing preferences on a public good issue, but a means of choosing a candidate for a given office. All issues cannot be chosen simultaneously. Only one of them can be. Although such choices are perhaps most easily envisaged in terms of a list of candidates for a vacant public office, the procedures might be thought of as being applied to a choice from among any set of mutually exclusive alternatives – such as points along the Pareto-possibility frontier.

The alternative voting procedures defined

In Part III we examine the properties of the different institutions of representative government that have been devised to supplement or replace direct democracy as a means of representing individual preferences. We begin with the United States's contribution to the evolution of representative government – federalism – because it is in some ways related to the theory of clubs reviewed in the preceding chapter.

Majority rule and redistribution

As Chapter 4 indicated, a committee concerned only with providing public goods and correcting for externalities might nevertheless choose as its voting rule the simple majority rule, if it placed enough weight on saving time. But speed is not the only property that majority rule possesses. Indeed, once issues can pass with less than unanimous agreement, the distinction between allocative efficiency and redistribution becomes blurred. Some individuals are inevitably worse off under the chosen outcome than they would be were some other outcome selected, and there is in effect a redistribution from those who are worse off because the issue has passed to those who are better off.

To see this point more clearly, consider Figure 5.1. The ordinal utilities of two groups of voters, the rich and the poor, are depicted on the vertical and horizontal axes. All of the members of both groups are assumed to have identical preference functions. In the absence of the provision of any public good, representative individuals from each group experience utility levels represented by S and T. The point of initial endowment on the Pareto-possibility frontier with only private good production is E. The provision of the public good can by assumption improve the utilities of both individuals.

With large numbers of voters and issues, direct democracy is impossible. Even in polities sufficiently small so that all individuals can actually come together to debate and decide issues – say, a polity of 500 – it is impossible for all individuals to present their own views, even rather briefly, on every issue. Thus the “chairman's problem” is to select individuals to represent the various positions most members of the polity are likely to hold (de Jouvenal, 1961). When the polity is too large to assemble together, representatives must be selected by some means.

The public choice literature has focused on three aspects of representative democracy: the behavior of representatives both during the campaign to be elected and while in office; the behavior of voters in choosing representatives; and the characteristics of the outcomes under representative democracy. The public choice approach assumes that representatives, like voters, are rational economic actors bent on maximizing their utilities. Although it is natural to assume that voters' utilities are functions of the baskets of public goods and services they consume, the “natural assumption” concerning what maximizes a representative's utility is not as easily made.

In this part of the book we present four applications of the public choice approach to explaining real-world phenomena. The first application tries to explain the macroeconomic policies of governments. To what extent are these determined by the competitive struggle for votes? To what extent do voters take into account the macroeconomic performance of a government when deciding how to vote? These questions have elicited a variety of theoretical models to explain governmental macroeconomic policies and a gigantic number of empirical studies. Indeed, probably no other area of public choice has witnessed as much empirical testing of its propositions as this area of politico-macroeconomic models. Alas, as too often happens with empirical work, not all authors reach the same conclusions as to what “the data show,” and the literature is therefore filled with often spirited exchanges. We shall not attempt to resolve all of the outstanding disagreements, but will try instead to give the reader a feel for the nature of the debate on various issues and the weight of the empirical support on each side of a question. We begin with the question that Harold Wilson obviously considered an established fact. Does the state of the economy affect how voters vote?