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25644 results in Astronomy: General Interest

Page 231 of 1283

  • 29 - Cosmology

  • from IV - GALAXIES AND THE UNIVERSE
  • Bradley W. Carroll, Weber State University, Utah, Dale A. Ostlie, Weber State University, Utah
  • Book:
    An Introduction to Modern Astrophysics
    Published online:
    16 August 2019
    Print publication:
    07 September 2017, pp 1144-1229

  • 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.

  • 7 - Binary Systems and Stellar Parameters

  • from II - THE NATURE OF STARS
  • Bradley W. Carroll, Weber State University, Utah, Dale A. Ostlie, Weber State University, Utah
  • Book:
    An Introduction to Modern Astrophysics
    Published online:
    16 August 2019
    Print publication:
    07 September 2017, pp 180-201

  • 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.

  • • Optical double. These systems are not actually binaries at all but simply two stars that lie along the same line of sight (i.e., they have similar right ascensions and declinations). As a consequence of their large physical separations, the stars are not gravitationally bound, and hence the system is not useful in determining stellar masses.

  • • Visual binary. Both stars in the binary can be resolved independently, and if the orbital period is not prohibitively long, it is possible to monitor the motion of each member of the system. These systems provide important information about the angular separation of the stars from their mutual center of mass. If the distance to the binary is also known, the linear separations of the stars can then be calculated.

  • Preface

  • Bradley W. Carroll, Weber State University, Utah, Dale A. Ostlie, Weber State University, Utah
  • Book:
    An Introduction to Modern Astrophysics
    Published online:
    16 August 2019
    Print publication:
    07 September 2017, pp xiii-xviii

  • 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.

  • 6 - Telescopes

  • from I - THE TOOLS OF ASTRONOMY
  • Bradley W. Carroll, Weber State University, Utah, Dale A. Ostlie, Weber State University, Utah
  • Book:
    An Introduction to Modern Astrophysics
    Published online:
    16 August 2019
    Print publication:
    07 September 2017, pp 141-178

  • 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)].

  • J - Orbit, A Planetary Orbit Code

  • Bradley W. Carroll, Weber State University, Utah, Dale A. Ostlie, Weber State University, Utah
  • Book:
    An Introduction to Modern Astrophysics
    Published online:
    16 August 2019
    Print publication:
    07 September 2017, pp 1295-1295

  • 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

  • 26 - Galactic Evolution

  • from IV - GALAXIES AND THE UNIVERSE
  • Bradley W. Carroll, Weber State University, Utah, Dale A. Ostlie, Weber State University, Utah
  • Book:
    An Introduction to Modern Astrophysics
    Published online:
    16 August 2019
    Print publication:
    07 September 2017, pp 999-1037

  • 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.

  • I - Constants, A Programming Module

  • Bradley W. Carroll, Weber State University, Utah, Dale A. Ostlie, Weber State University, Utah
  • Book:
    An Introduction to Modern Astrophysics
    Published online:
    16 August 2019
    Print publication:
    07 September 2017, pp 1294-1294

  • Summary

    Constants is a Fortran 95 module implementation of the astronomical and physical constants data given in Appendix A (a C++ header file version is also available). Constants also includes high-precision values of mathematical constants (π, e) and conversion factors between degrees and radians. In addition, Constants provides various machine constants characteristic of the particular platform that a code is running on. For example, in the Fortran 95 implementation, Constants includes machine-queried KIND designations for single, double, and quadruple precision, the smallest and largest numbers that can be represented by the computer for a specific precision, and the number of significant figures that can be represented for each level of precision.

    Constants is employed by the other codes described in the appendices that follow. The source code is available for download from the resources tab on following

  • 5 - The Interaction of Light and Matter

  • from I - THE TOOLS OF ASTRONOMY
  • Bradley W. Carroll, Weber State University, Utah, Dale A. Ostlie, Weber State University, Utah
  • Book:
    An Introduction to Modern Astrophysics
    Published online:
    16 August 2019
    Print publication:
    07 September 2017, pp 111-140

  • Summary

    SPECTRAL LINES

    In 1835 a French philosopher, Auguste Comte (1798–1857), considered the limits of human knowledge. In his book Positive Philosophy, Comte wrote of the stars, “We see how we may determine their forms, their distances, their bulk, their motions, but we can never know anything of their chemical or mineralogical structure.” Thirty-three years earlier, however, WilliamWollaston (1766–1828), like Newton before him, passed sunlight through a prism to produce a rainbow-like spectrum. He discovered that a number of dark spectral lines were superimposed on the continuous spectrum where the Sun's light had been absorbed at certain discrete wavelengths. By 1814, the German optician Joseph von Fraunhofer (1787–1826) had cataloged 475 of these dark lines (today called Fraunhofer lines) in the solar spectrum. While measuring the wavelengths of these lines, Fraunhofer made the first observation capable of proving Comte wrong. Fraunhofer determined that the wavelength of one prominent dark line in the Sun's spectrum corresponds to the wavelength of the yellow light emitted when salt is sprinkled in a flame. The new science of spectroscopy was born with the identification of this sodium line.

    Kirchhoff's Laws

    The foundations of spectroscopy were established by Robert Bunsen (1811–1899), a German chemist, and by Gustav Kirchhoff (1824–1887), a Prussian theoretical physicist. Bunsen's burner produced a colorless flame that was ideal for studying the spectra of heated substances. He and Kirchhoff then designed a spectroscope that passed the light of a flame spectrum through a prism to be analyzed. The wavelengths of light absorbed and emitted by an element were found to be the same; Kirchhoff determined that 70 dark lines in the solar spectrum correspond to 70 bright lines emitted by iron vapor. In 1860 Kirchhoff and Bunsen published their classic work Chemical Analysis by Spectral Observations, in which they developed the idea that every element produces its own pattern of spectral lines and thus may be identified by its unique spectral line “fingerprint.” Kirchhoff summarized the production of spectral lines in three laws, which are now known as Kirchhoff's laws:

  • • A hot, dense gas or hot solid object produces a continuous spectrum with no dark spectral lines.

  • • A hot, diffuse gas produces bright spectral lines (emission lines).

  • • Acool, diffuse gas in front of a source of a continuous spectrum produces dark spectral lines (absorption lines) in the continuous spectrum.

  • 24 - The Milky Way Galaxy

  • from IV - GALAXIES AND THE UNIVERSE
  • Bradley W. Carroll, Weber State University, Utah, Dale A. Ostlie, Weber State University, Utah
  • Book:
    An Introduction to Modern Astrophysics
    Published online:
    16 August 2019
    Print publication:
    07 September 2017, pp 874-939

  • Summary

    COUNTING THE STARS IN THE SKY

    As we learned in the first two chapters of this text, human beings have long looked up at the heavens and contemplated its vastness, proposing various models to explain its form. In some civilizations the stars were believed to be located on a celestial sphere that rotated majestically above a fixed, central Earth.WhenGalileo made his first telescopic observations of the night sky in 1610, we started down a long road that has dramatically expanded our view of the universe.

    In this chapter we will explore the complex system of stars, dust, gas, and dark matter known as the Milky Way Galaxy. Although it is possible to get at least a general idea about the nature of other galaxies from our external viewpoint, studying our own Galaxy has proved to be very challenging. As we will learn, we live in a disk of stars, dust, and gas that severely impacts our ability to “see” beyond our relative stellar neighborhood when we look along the plane of the disk. The problem is most severe when looking toward the center of the Galaxy in the constellation Sagittarius. In Section 24.1 we will discover that studying the distribution of stars while considering the effects of extinction provides us with our first hint of what the MilkyWay looks like from an outside perspective. In Section 24.2, a detailed description of the many varying components of the Galaxy will be presented.

    Much of what we know today about the formation and evolution of the Milky Way is encoded in the motions of the Galaxy's constituents, especially when combined with information about variations in composition. Unfortunately, measuring the motions of the stars and gas in the Galaxy is done from an observing platform (Earth) that is itself undergoing a complex motion that involves the orbit of Earth around the Sun and the Sun's elaborate path around the Galaxy. In Section 24.3 we will investigate these motions, allowing us to move from a description of motions relative to the Sun to motions relative to the center of the Galaxy.

  • 2 - Celestial Mechanics

  • from I - THE TOOLS OF ASTRONOMY
  • Bradley W. Carroll, Weber State University, Utah, Dale A. Ostlie, Weber State University, Utah
  • Book:
    An Introduction to Modern Astrophysics
    Published online:
    16 August 2019
    Print publication:
    07 September 2017, pp 23-56

  • Summary

    ELLIPTICAL ORBITS

    Although the inherent simplicity of the Copernican model was aesthetically pleasing, the idea of a heliocentric universe was not immediately accepted; it lacked the support of observations capable of unambiguously demonstrating that a geocentric model was wrong.

    Tycho Brahe: The Great Naked-Eye Observer

    After the death of Copernicus, Tycho Brahe (1546–1601), the foremost naked-eye observer, carefully followed the motions of the “wandering stars” and other celestial objects. He carried out his work at the observatory, Uraniborg, on the island of Hveen (a facility provided for him by King Frederick II of Denmark). To improve the accuracy of his observations, Tycho used large measuring instruments, such as the quadrant depicted in the mural in Fig. 2.1(a).Tycho's observations were so meticulous that he was able to measure the position of an object in the heavens to an accuracy of better than 4_, approximately one-eighth the angular diameter of a full moon. Through the accuracy of his observations he demonstrated for the first time that comets must be much farther away than the Moon, rather than being some form of atmospheric phenomenon.Tycho is also credited with observing the supernova of 1572, which clearly demonstrated that the heavens were not unchanging as Church doctrine held. (This observation prompted King Frederick to build Uraniborg.) Despite the great care with which he carried out his work, Tycho was not able to find any clear evidence of the motion of Earth through the heavens, and he therefore concluded that the Copernican model must be false (see Section 3.1).

    Kepler's Laws of Planetary Motion

    At Tycho's invitation, Johannes Kepler (1571–1630), a German mathematician, joined him later in Prague [Fig. 2.1(b)]. Unlike Tycho, Kepler was a heliocentrist, and it was his desire to find a geometrical model of the universe that would be consistent with the best observations then available, namely Tycho's. After Tycho's death, Kepler inherited the massof observations accumulated over the years and began a painstaking analysis of the data. His initial, almost mystic, idea was that the universe is arranged with five perfect solids, nested to support the six known naked-eye planets (including Earth) on crystalline spheres, with the entire system centered on the Sun. After this model proved unsuccessful, he attempted to devise an accurate set of circular planetary orbits about the Sun, focusing specifically on Mars.

Page 231 of 1283