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Summary

OBSERVATIONS OF ACTIVE GALAXIES

The story of modern astrophysics is one of a dynamically evolving universe. On every scale, from planets to stars to galaxies, the objects that are present in this era differ from what they were during previous epochs. As we study the ancient light that arrives from distant corners of the universe, we are able to examine how galaxies looked and behaved in their youth. These observations reveal a level of activity in the centers of young, remote galaxies that is rarely found in nearer galactic nuclei.

Seyfert Galaxies

The first hint of the violent heritage of today's galaxies was found by EdwardA. Fath (1880– 1959), who in 1908 was observing the spectra of “spiral nebulae.”Although most showed an absorption-line spectrum produced by the combined light of the galaxy's stars, NGC 1068 displayed six bright emission lines. In 1926 Edwin Hubble recorded the emission lines of this and two other galaxies. Seventeen years later Carl K. Seyfert (1911–1960) reported that a small percentage of galaxies have very bright nuclei that are the source of broad emission lines produced by atoms in a wide range of ionization states. These nuclei are nearly stellar in appearance.

Today these objects are known as Seyfert galaxies, with spectra that are categorized into one of two classes. Seyfert 1 galaxies have very broad emission lines that include both allowed lines (H I, He I, He II) and narrower forbidden lines (such as [O III]). Seyfert 1 galaxies generally have “narrow” allowed lines as well, although even the narrow lines are broad compared to the spectral lines exhibited by normal galaxies. The width of the lines is attributed to Doppler broadening, indicating that the allowed lines originate from sources with speeds typically between 1000 and 5000 km s−1, while the forbidden lines correspond to speeds of around 500 km s−1. Seyfert 2 galaxies have only narrow lines (both permitted and forbidden), with characteristic speeds of about 500 km s−1.

Summary

THE HUBBLE SEQUENCE

As was mentioned at the beginning of Chapter 24, it was in the middle of the eighteenth century that Kant and Wright first suggested that the Milky Way represents a finite-sized disk-like system of stars. In the two centuries of scientific investigation since their proposal, we have indeed come to learn that a major component of our Galaxy is well represented by a disk of stars that also contains a significant amount of gas and dust. As an extension of their philosophical argument about the nature of the Galaxy, Kant went on to suggest that if the MilkyWay is limited in extent, perhaps the diffuse and very faint “elliptical nebulae” seen in the night sky might actually be extremely distant disk-like systems, similar to our own but well beyond its boundary. He called these objects island universes.

Cataloging the Island Universes

The true nature of the island universes became a matter of much investigation, and extensive catalogs of these objects were collected. One such catalog we owe to Charles Messier (1730– 1817), who, while hunting for comets, recorded 103 fuzzy objects that could otherwise be confused with the intended targets of his search. Although many of the members of the Messier catalog are truly gaseous nebulae contained within the Milky Way (such as the Crab supernova remnant and the Orion Nebula, M1 and M42, respectively), and others are stellar clusters (for instance, the Pleiades open cluster is M45 and the great globular cluster in Hercules is M13), the nature of other nebulae, such as M31 in Andromeda (Fig. 24.7), was unknown.

Another catalog of nebulae was produced by William Herschel and subsequently expanded by his son, Sir John Herschel (1792–1871), to include the southern hemisphere. Later, J. L. E. Dreyer (1852–1926) published the New General Catalog (NGC), which was based on the work of the Herschels and contained almost 8000 objects. Like Messier's catalog, the NGC includes many entries that are either gaseous nebulae or stellar clusters located within the Milky Way. However, the true nature of other objects in the catalog remained in question.

Summary

MERCURY

The four terrestrial planets have a number of characteristics in common, such as being small, rocky, and slowly rotating (see Table 19.1). Our own Moon and several of the moons of the giant planets also share many of those same characteristics. In this chapter we shall focus our attention on the terrestrial planets and their moons, saving our discussion of the giant planets and their systems for Chapter 21.

The 3-to-2 Spin–Orbit Coupling of Mercury

As we learned in Section 17.1, the innermost planet, Mercury (Fig. 20.1), orbits so close to the Sun (0.39 AU) that Kepler's laws begin to break down. The reason is that spacetime in the vicinity of massive objects is affected in such a way that Newton's familiar inversesquare law (Eq. 2.11) is no longer a completely adequate description of gravity. It was the slow advance of the perihelion point of Mercury's rather eccentric orbit (e = 0.2056) that presented one of the first tests of Einstein's general theory of relativity.

The first hint that Mercury's orbit also exhibits another curious feature came in 1965 when Rolf B. Dyce and Gordon H. Pettengill successfully bounced radar signals off the planet using the Arecibo radio telescope. The reflected signals had a spread of wavelengths that revealed Mercury's rotation speed; because of the Doppler effect, radio waves that hit the approaching limb were blueshifted and those that struck the receding limb were redshifted. These observations indicated that Mercury's rotation period was approximately 59 days. More precise measurements made by the Mariner 10 spacecraft during its repeated flybys of the planet in 1974 and 1975 showed that the rotation period was actually 58.6462 days, exactly two-thirds the length of its sidereal orbital period of 87.95 days.

How this peculiar 3-to-2 relationship between rotation and orbital periods developed can be understood in light of the process of tidal evolution discussed in Section 19.2. At perihelion, Mercury experiences the strongest tidal force, causing the planet to try to align its bulge axis along the line connecting the planet's center of mass to the center of mass of the Sun.

Summary

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.

Summary

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.

Summary

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.

Summary

Since the first edition of An Introduction to Modern Astrophysics and its abbreviated companion text, An Introduction to Modern Stellar Astrophysics, first appeared in 1996, there has been an incredible explosion in our knowledge of the heavens. It was just two months before the printing of the first editions that Michel Mayor and Didier Queloz announced the discovery of an extrasolar planet around 51 Pegasi, the first planet found orbiting a main-sequence star. In the next eleven years, the number of known extrasolar planets has grown to over 193. Not only do these discoveries shed new light on how stars and planetary systems form, but they also inform us about formation and planetary evolution in our own Solar System.

In addition, within the past decade important discoveries have been made of objects, within our Solar System but beyond Pluto, that are similar in size to that diminutive planet. In fact, one of the newly discovered Kuiper belt objects, currently referred to as 2003 UB313 (until the International Astronomical Union makes an official determination), appears to be larger than Pluto, challenging our definition of what a planet is and how many planets our Solar System is home to.

Explorations by robotic spacecraft and landers throughout our Solar System have also yielded a tremendous amount of new information about our celestial neighborhood. The armada of orbiters, along with the remarkable rovers, Spirit and Opportunity, have confirmed that liquid water has existed on the surface of Mars in the past. We have also had robotic emissaries visit Jupiter and Saturn, touch down on the surfaces of Titan and asteroids, crash into cometary nuclei, and even return cometary dust to Earth.

Missions such as Swift have enabled us to close in on the solutions to the mysterious gamma-ray bursts that were such an enigma at the time An Introduction to Modern Astrophysics first appeared.We now know that one class of gamma-ray bursts is associated with core-collapse supernovae and that the other class is probably associated with the merger of two neutron stars, or a neutron star and a black hole, in a binary system.

Summary

BASIC OPTICS

From the beginning, astronomy has been an observational science. In comparison with what was previously possible with the naked eye, Galileo's use of the new optical device known as the telescope greatly improved our ability to observe the universe (see Section 2.2). Today we continue to enhance our ability to “see” faint objects and to resolve them in greater detail. As a result, modern observational astronomy continues to supply scientists with more clues to the physical nature of our universe.

Although observational astronomy now covers the entire range of the electromagnetic spectrum, along with many areas of particle physics, the most familiar part of the field remains in the optical regime of the human eye (approximately 400 nm to 700 nm). Consequently, telescopes and detectors designed to investigate optical-wavelength radiation will be discussed in some detail. Furthermore, much of what we learn in studying telescopes and detectors in the optical regime will apply to other wavelength regions as well.

Refraction and Reflection

Galileo's telescope was a refracting telescope that made use of lenses through which light would pass, ultimately forming an image. Later, Newton designed and built a reflecting telescope that made use of mirrors as the principal optical component. Both refractors and reflectors remain in use today.

To understand the effects of an optical system on the light coming from an astronomical object, we will focus first on refracting telescopes. The path of a light ray through a lens can be understood using Snell's law of refraction. Recall that as a light ray travels from one transparent medium to another, its path is bent at the interface. The amount that the ray is bent depends on the ratio of the wavelength-dependent indices of refraction of each material, where represents the speed of light within the specific medium. If

is the angle of incidence, measured with respect to the normal to the interface between the two media, and is the angle of refraction, also measured relative to the normal to the interface (see Fig. 6.1), then Snell's law is given by

If the surfaces of the lens are shaped properly, a beam of light rays of a given wavelength, originally traveling parallel to the axis of symmetry of the lens (called the optical axis of the system) can be brought to a focus at a point along that axis by a converging lens [Fig. 6.2(a)].

Summary

Orbit is a computer program designed to calculate the position of a planet orbiting a massive star (or, alternatively, the orbit of the reduced mass about the center of mass of the system). The program is based on Kepler's laws of planetary motion as derived in Chapter 2. References to the relevant equations are given in the comment sections of the code.

The user is asked to enter the mass of the parent star (in solar masses), the semimajor axis of the orbit (in AU), and the eccentricity of the orbit. The user is also asked to enter the number of time steps desired for the calculation (perhaps 1000 to 100,000) and the frequency with which the time steps are to be printed to the output file (Orbit.txt). If 1000 time steps are specified with a frequency of 10, then 100 evenly spaced (in time) time steps will be printed.

The output file can be imported directly into a graphics or spreadsheet program in order to generate a graph of the orbit. Note that it may be necessary to delete the header information in Orbit.txt prior to importing the data columns into the graphics or spreadsheet program.

The source code is available in both Fortran 95 and C++ versions. Compiled versions of the code are also available.

The code may be downloaded from the companion website at

Summary

INTERACTIONS OF GALAXIES

With the exquisite vision of the heavens provided by modern ground-based and space-based observatories, it has become increasingly apparent that galaxies are not “island universes”; they do not evolve in isolation.

Evidence of Interactions

Nearly all galaxies belong to clusters, and the galaxies take up a larger fraction of the cluster's volume than do the stars in a stellar cluster.We also know that the spacing between galaxies is typically only 100 times larger than the size of the galaxies themselves (see Section 27.3). Densely populated clusters, such as the Coma cluster (Figs. 26.1 and 26.2), have a higher proportion of early-type galaxies (ellipticals) in their centers than they do in their outer, less dense regions. As was already mentioned in Section 25.4, the central regions of these rich, regularly shaped clusters also have a higher proportion of early-type galaxies than the centers of less populated, amorphous-shaped irregular clusters, such as the Hercules cluster (Fig. 26.3). These observations seem to correlate with the increased probability of interactions and/or mergers between galaxies in regions of higher galaxy number density. Interactions tend to increase the velocity dispersions of stars in the galaxies involved, possibly destroying disk structures in late-type galaxies and causing the galaxies to relax to early-type r1/4 profiles (Eq. 25.2).

AVLA radio survey of the H I layer of galactic disks found that at least 50% of all disk galaxies display warped disks. Also, more than half of all elliptical galaxies harbor discrete shells of stars. Some disk warping may be due to tidal interactions with smaller satellite galaxies, and, as we shall see, shells in ellipticals are signatures of mergers.

Observations also suggest that hot, X-ray-emitting gas occupies much of the space between the galaxies in rich clusters and has a mass equal to or exceeding the mass of all of the cluster's stars (Section 27.3). It seems that the gravitational influence of interacting galaxies is largely responsible for removing the gas from the individual galaxies that make up the cluster, while still leaving the gas trapped in the cluster's overall gravitational well.

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14 - Stellar Pulsation

28 - Active Galaxies

Summary

A - Astronomical and Physical Constants

25 - The Nature of Galaxies

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20 - The Terrestrial Planets

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21 - The Realms of the Giant Planets

K - TwoStars, A Binary Star Code

H - The Messier Catalog

Dedication

16 - The Degenerate Remnants of Stars

1 - The Celestial Sphere

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29 - Cosmology

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7 - Binary Systems and Stellar Parameters

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I - THE TOOLS OF ASTRONOMY

4 - The Theory of Special Relativity

Preface

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6 - Telescopes

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J - Orbit, A Planetary Orbit Code

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26 - Galactic Evolution

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II - THE NATURE OF STARS

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