THE GREEK TRADITION

Human beings have long looked up at the sky and pondered its mysteries. Evidence of the long struggle to understand its secrets may be seen in remnants of cultures around the world: the great Stonehenge monument in England, the structures and the writings of the Maya and Aztecs, and the medicine wheels of the Native Americans. However, our modern scientific view of the universe traces its beginnings to the ancient Greek tradition of natural philosophy. Pythagoras (ca. 550 b.c.) first demonstrated the fundamental relationship between numbers and nature through his study of musical intervals and through his investigation of the geometry of the right angle. The Greeks continued their study of the universe for hundreds of years using the natural language of mathematics employed by Pythagoras. The modern discipline of astronomy depends heavily on a mathematical formulation of its physical theories, following the process begun by the ancient Greeks.

In an initial investigation of the night sky, perhaps its most obvious feature to a careful observer is the fact that it is constantly changing. Not only do the stars move steadily from east to west during the course of a night, but different stars are visible in the evening sky, depending upon the season. Of course the Moon also changes, both in its position in the sky and in its phase. More subtle and more complex are the movements of the planets, or “wandering stars.”

The Geocentric Universe

Plato (ca. 350 b.c.) suggested that to understand the motions of the heavens, one must first begin with a set of workable assumptions, or hypotheses. It seemed obvious that the stars of the night sky revolved about a fixed Earth and that the heavens ought to obey the purest possible form of motion. Plato therefore proposed that celestial bodies should move about Earth with a uniform (or constant) speed and follow a circular motion with Earth at the center of that motion. This concept of a geocentric universe was a natural consequence of the apparently unchanging relationship of the stars to one another in fixed constellations.

Barred spiral galaxies raise the question of what differentiates them from normal spiral galaxies. In this chapter, special features of barred spirals are explained, which indicate dependence of their forms on time.

THE CLASSIFICATION OF BARRED SPIRALS

Barred spiral galaxies contain, in contrast to normal spiral galaxies, a straight stellar bar which is symmetrical about the core and whose ends connect to the spiral arms. The term “bar” goes back to Edwin Hubble, who in 1936 introduced the classification “SB” for “spiral barred”, in order to distinguish between S and SB types. The classification of barred spirals is the same as that of normal spirals. For example, an SB type classified as SBa is a galaxy with a tight spiral pattern and bright nucleus. Moving to “later” SB types, the pitch angle increases and the core at the middle of the bar becomes more compact and less prominent.

In the galaxy classification introduced by Gerard de Vaucouleurs in 1959, the Hubble classification was extended by the SAB type. In this system, galaxies with weak bars are classified as SAB. In addition, de Vaucouleurs introduced the supplementary classifications (s), (r), and (rs) to describe the transition region between bar and spiral arms. This made it possible to distinguish between pure spiral patterns and galaxies with an inner ring connected to the bar region.

Bars often have a diffuse appearance and show less structure than spiral arms. Thus, there is no finer classification based on the bar. Only with the advent of modern methods of astronomical research was it determined that there are measurable differences in the bar structures. For example, the form of the bar can be more boxy or more disc-like. An important quantity for the assessment of the dynamics of a barred spiral galaxy is the axial ratio of the bar, i.e. the ratio of width to length. In the earlier Hubble types SBa to SBb, the relative length of the bar is greater than in the later types (SBc to SBd).

NEWTONIAN COSMOLOGY

On December 27, 1831, a ship sailed out of Plymouth, England, on a voyage around the world that would last nearly five years. Only 90 feet long, the Beagle was crowded with 74 people, one of whom was Charles Darwin. During stops in South America, the Galapagos Islands, Tahiti, New Zealand, and Australia, he exercised his formidable powers of observation. In 1859, after two decades of careful study and reflection, Darwin published On the Origin of Species by Means of Natural Selection, or the Preservation of Favored Races in the Struggle for Life. For the first time, people began to comprehend their own origins.

Other discoveries followed during the next one hundred years, with careful observations and brilliant deductions uncovering more about our beginnings. The elucidation of DNA and plate tectonics revealed the mechanisms by which we and our planet evolved. The ideas of stellar nucleosynthesis explained the manufacture of the chemical elements by stars, implying the origin of our corporeal bodies and the ground on which we walk. Even the universe itself was found to be expanding. Then, in 1964, two researchers at Bell Laboratories measured the afterglow of the Big Bang, confirming the explosive origin of everything in existence. It is difficult to imagine a more breathtaking leap from ignorance to self-knowledge than that which occurred during this century of discovery.

Cosmology, taken as a whole, is the study of the origin and evolution of the universe. In this chapter, cosmology will be considered from several different perspectives. To help develop our intuition, this section will discuss the expansion of the universe from the point of view of Newtonian mechanics, without the complications (or insights) provided by general relativity or the modern ideas of particle physics. The discovery and implications of the cosmic microwave background radiation are described in Section 29.2, followed, in Section 29.3, by an introduction to the geometry of the universe as explained by general relativity. Section 29.4 describes how some of the key parameters of cosmology may be measured observationally. The intriguing theories and speculations provided by particle physics will be reserved for Chapter 30.

Elliptical galaxies cover a wide range in size. Thus some of the largest galaxies belong to the galaxy family discussed in this chapter.

THE CLASSIFICATION OF ELLIPTICAL GALAXIES

In the last few years, amateur astrophotography has become more professional. This allows interesting features to be seen even in the apparently uninteresting elliptical galaxies, making visible the results of current research. The high efficiency of sensitive CCDs, their large dynamic range and above all the possibilities of electronic image processing have played an enormous role in making these popular subjects for many photographers.

The classification of elliptical galaxies from E0 to E7 in the Hubble diagram describes their form, from the circular E0 to strongly flattened E7 types. The numbers from 0 to 7 following the E are computed according to the formula 10 × (a − b)/a, where a is the semimajor and b the semiminor axis of an ellipse. This allows one to quantify the ellipticity of galaxies. An ellipse also has two foci whose distance from the centre is known as the linear eccentricity, e. In the case of circular E0 types, the two foci coincide at the centre and the eccentricity is thus zero. With increasing distance of the foci and thus increasing flattening, the value of the linear eccentricity increases. The classification E0 to E7, however, has no physical background, since depending on the orientation the general triaxial form of a spindle-shaped elliptical galaxy could appear as a round E0 type. The almost circular E2 and E3 types are the most common in surveys.

Dwarf elliptical galaxies with low surface brightness are classified as dE. Some of the dwarf satellite galaxies of the Milky Way are classified as dwarf spheroidal, dSph, which are even dimmer than the dE. The Local Group containing the Milky Way also has irregular satellites. Relatively new are blue compact dwarfs, which are usually classified as irregular dwarf galaxies. At 15–20 per cent, their gas fraction is relatively large and explains their conspicuously large starformation rates.

THE CLASSIFICATION OF BINARY STARS

Adetailed understanding of the structure and evolution of stars (the goal of Part II) requires knowledge of their physical characteristics. We have seen that knowledge of blackbody radiation curves, spectra, and parallax enables us to determine a star's effective temperature, luminosity, radius, composition, and other parameters. However, the only direct way to determine the mass of a star is by studying its gravitational interaction with other objects.

In Chapter 2 Kepler's laws were used to calculate the masses of members of our Solar System. However, the universality of the gravitational force allows Kepler's laws to be generalized to include the orbits of stars about one another and even the orbital interactions of galaxies, as long as proper care is taken to refer all orbits to the center of mass of the system.

Fortunately, nature has provided ample opportunity for astronomers to observe binary star systems. At least half of all “stars” in the sky are actually multiple systems, two or more stars in orbit about a common center of mass. Analysis of the orbital parameters of these systems provides vital information about a variety of stellar characteristics, including mass.

The methods used to analyze the orbital data vary somewhat depending on the geometry of the system, its distance from the observer, and the relative masses and luminosities of the components. Consequently, binary star systems are classified according to their specific observational characteristics.