National Academies Press: OpenBook

A Science Strategy for Space Physics (1995)

Chapter: A Science Strategy for Space Physics: Chapter 5

« Previous: A Science Strategy for Space Physics: Chapter 4
Suggested Citation:"A Science Strategy for Space Physics: Chapter 5." National Research Council. 1995. A Science Strategy for Space Physics. Washington, DC: The National Academies Press. doi: 10.17226/12286.
×
Page 82
Suggested Citation:"A Science Strategy for Space Physics: Chapter 5." National Research Council. 1995. A Science Strategy for Space Physics. Washington, DC: The National Academies Press. doi: 10.17226/12286.
×
Page 83
Suggested Citation:"A Science Strategy for Space Physics: Chapter 5." National Research Council. 1995. A Science Strategy for Space Physics. Washington, DC: The National Academies Press. doi: 10.17226/12286.
×
Page 84
Suggested Citation:"A Science Strategy for Space Physics: Chapter 5." National Research Council. 1995. A Science Strategy for Space Physics. Washington, DC: The National Academies Press. doi: 10.17226/12286.
×
Page 85
Suggested Citation:"A Science Strategy for Space Physics: Chapter 5." National Research Council. 1995. A Science Strategy for Space Physics. Washington, DC: The National Academies Press. doi: 10.17226/12286.
×
Page 86
Suggested Citation:"A Science Strategy for Space Physics: Chapter 5." National Research Council. 1995. A Science Strategy for Space Physics. Washington, DC: The National Academies Press. doi: 10.17226/12286.
×
Page 87
Suggested Citation:"A Science Strategy for Space Physics: Chapter 5." National Research Council. 1995. A Science Strategy for Space Physics. Washington, DC: The National Academies Press. doi: 10.17226/12286.
×
Page 88
Suggested Citation:"A Science Strategy for Space Physics: Chapter 5." National Research Council. 1995. A Science Strategy for Space Physics. Washington, DC: The National Academies Press. doi: 10.17226/12286.
×
Page 89
Suggested Citation:"A Science Strategy for Space Physics: Chapter 5." National Research Council. 1995. A Science Strategy for Space Physics. Washington, DC: The National Academies Press. doi: 10.17226/12286.
×
Page 90

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

A Science Strategy for Space Physics: Chapter 5 A Science Strategy for Space Physics 5 Plasma Processes That Accelerate Very Energetic Particles and Control Their Propagation SCIENTIFIC BACKGROUND Energetic particles appear to be accelerated wherever plasma, magnetic fields, and motion are observed. Figure 20 summarizes the many sources of energetic particles in the heliosphere. The energies reached seem to depend on the scale of the object that accelerates them, although nowhere is the process fully understood. Because energetic electrons emit observable radio frequency synchrotron radiation, researchers know that energetic electrons and magnetic fields are common features of the Sun's corona, the planets, and galaxies everywhere. Solar energetic particles and galactic cosmic rays have much in common. They include electrons and nuclei over the entire periodic table accelerated to a wide range of energies-from less than 1 MeV to over 1020 eV. The study REPORT MENU of these particles provides a vital bridge between space plasma physics using in situ NOTICE measurements and remote sensing of astrophysical objects where cosmic rays may have MEMBERSHIP important dynamical consequences. Studies of point sources of gamma rays (e.g., active SUMMARY galactic nuclei and pulsars) have already led and will continue to lead to increased PART I understanding of particle acceleration in other space environments. Science demands that PART II we understand the acceleration of cosmic rays, the most extraordinary nonthermal CHAPTER 1 CHAPTER 2 process in the universe. CHAPTER 3 CHAPTER 4 CHAPTER 5 PART III APPENDIX file:///C|/SSB_old_web/strach5.html (1 of 10) [6/18/2004 2:20:29 PM]

A Science Strategy for Space Physics: Chapter 5 FIGURE 20 Sources of energetic particles in the heliosphere. (Courtesy of Marcia Neugebauer, Jet Propulsion Laboratory.) Solar energetic particles have been observed since before the dawn of the space era. As our ability grew to launch satellites outside of the Earth's local space environment, our knowledge of these solar-related events increased enormously. These solar particles are now known to span the energy range from solar wind plasma to greater than 10 GeV, have variable abundance and charge states, and appear to be accelerated by more than one process. There are short-lived, low-intensity events with widely varying compositional signatures associated with solar flares. There are also long-lived, very high intensity events with moderately similar compositional signatures associated with coronal shocks. In addition, energetic particles are further accelerated and their spatial distribution modified by shocks propagating through the heliosphere. From balloon and satellite observations over the last 25 years, researchers know that cosmic rays fill our galaxy with an energy density comparable to that in the turbulent motion of the interstellar gas and in magnetic fields. Gamma-ray measurements by the Compton Gamma Ray Observatory (CGRO) and earlier satellites and ground-based radio observations have mapped their distribution throughout the galaxy. The high degree of isotropy of the cosmic rays as measured by ground-based air shower arrays at energies above 1012 eV is an important constraint. Cosmic rays are hypothesized to originate in a large number of sources, probably supernova remnants, in a thin disk near the plane of the galaxy. Once accelerated they become highly mixed as they diffuse through the galactic magnetic fields and into the galactic halo. file:///C|/SSB_old_web/strach5.html (2 of 10) [6/18/2004 2:20:29 PM]

A Science Strategy for Space Physics: Chapter 5 Theories of stellar evolution and the synthesis of the elements reveal that most of the nuclei heavier than helium are formed in the interiors of stars. The energy released when lighter elements fuse into heavier ones supports stars against gravitational collapse. When this source of energy is exhausted, stars explode, hurling heavy elements into the interstellar medium. The explosions create additional, even heavier elements that can be subsequently accelerated, perhaps by shocks from those same explosions, to cosmic-ray energies. Supernova explosions are the only sources capable of supplying the energy required to balance the leakage of cosmic rays from the galaxy as determined by estimating the lifetime of cosmic rays from the surviving fraction of radioactive 10Be and other radioactive isotopes. The energies of the galactic cosmic rays cover a range of more than 14 orders of magnitude, but how they are accelerated is unknown. Solar energetic particles are accelerated by solar flares and coronal shocks, processes believed to involve more than one mechanism. At the higher energies the processes of acceleration and propagation must involve interactions with the large-scale magnetic structures of the system. Measurements of the energy spectrum of each individual component of the solar energetic particles have been made by a variety of spacecraft throughout the solar system (IMPs, OGOs, Helios, ICE/ISEE-3, Pioneers, Voyagers, and so on). The spectra of galactic cosmic rays have been measured on space missions such as HEAO-3 and Spacelab-2 up to about 1012 eV; exploratory measurements by the JACEE group and on Russian satellites have been made up to approximately 1014 eV. For the higher-energy cosmic rays, the principal information is the composite "all particle" spectrum, which comes from ground-based air shower detectors that measure the total energy arriving at ground level. Inference of composition from these measurements is currently only statistical; identification on an event-by-event basis is not possible. New knowledge of the highly inhomogeneous nature of the galaxy (e.g., molecular clouds, supernova bubbles, and the highly variable plasma environment) from satellites like EUVE, Rosat, and CGRO has given rise to a new generation of models for the origin and acceleration of galactic cosmic rays. The models are based on the idea that particles are confined by magnetic fields to remain in the vicinity of shock waves produced by converging or overtaking plasma flows. These theories were developed to explain in situ observations of energetic particles near planetary bow shocks and shocks in interplanetary space; it has been demonstrated that heavy ions can gain significant amounts of energy in such an environment. Shock acceleration is probably important in the solar corona, but a different mechanism is probably responsible for accelerating solar flare particles in a magnetically closed environment. In some space environments, magnetic reconnection may be important in removing energy from the plasma and giving it to individual particles. On a galactic scale, hydromagnetic motion and reconnection must have a role in determining the evolution and shape of the magnetic fields, and the release of energy by reconnection is a candidate acceleration mechanism. The spatial scales of interplanetary shocks are quite different from those in interstellar space. The question is whether or not the scale of interstellar shocks is sufficient to produce the observed cosmic rays. The detailed answers are believed to be accessible by extending the detailed composition measurements to cover the whole energy regime over which the mechanism is expected to operate. The critical features are expected to be significant deviations from power law spectra and predictable upper- energy cutoffs that are different for different species. file:///C|/SSB_old_web/strach5.html (3 of 10) [6/18/2004 2:20:29 PM]

A Science Strategy for Space Physics: Chapter 5 There are limits to these theories, however. They inadequately explain the acceleration of electrons, even though electrons are clearly accelerated in a variety of space plasma environments from planetary magnetospheres, to solar and interplanetary environments, to supernova remnants, pulsar winds, and active galactic nuclei. In addition, these theories are probably not sufficient to explain the origin of the most energetic particles-those above 1015 eV where there is a kink in the observed energy spectrum, suggesting a significant change in the physics of the cosmic rays. The sources of cosmic rays in the galactic disk have an important role in providing the energy that affects the dynamics of the galactic plasma. For example, the energy density of galactic cosmic rays is sufficiently high that they must have an important dynamical role in the generation of the galactic magnetic field. They inflate this magnetic field and the plasma linked to it to form a galactic halo and possibly drive a galactic wind (Figure 21), analogous to the manner in which the Sun provides the energy to drive the solar wind. Parallels can be drawn between the two systems, the heliospheric system consisting of the Sun located in interstellar space and the Milky Way galaxy located in intergalactic space. In both cases, there are important sources that input energy, extended magnetic field structures, traveling shocks that accelerate particles, and plasma pressure which drives winds. Are there also, in both cases, escape of particles from the system and entry of particles from outside the system? The loss of particles from the "galactic magnetosphere" is energy dependent, affecting the interpretation of source spectra and hence acceleration mechanisms. New theoretical work shows that the consequences of the storage and diffusion of energetic particles in the galactic halo have an observable effect on the lifetime of cosmic rays in the galaxy. The abundances of radioactive isotopes such as 10Be and 26Al, at energies where the relativistic time dilation effects are important (>1 GeV/nucleon), increase in a manner that depends on the speed of a galactic wind, thus allowing one to distinguish between convective and diffusive losses of particles from the galaxy. FIGURE 21 Exchange of material between a galactic halo and intergalactic space. (Galaxy image courtesy of Eric Christian, NASA/GSFC.) Space physicists have little knowledge of the low-energy end of the cosmic-ray spectrum (below 100 MeV/nucleon) in the galaxy because those particles are strongly affected by their interactions with the interplanetary magnetic field and the boundary structures of the heliosphere. Better understanding of those interactions is required to infer the interstellar spectrum, especially at energies from 1 to 300 MeV/nucleon, and to apply that knowledge to models of cosmic ray transport elsewhere in the galaxy. In situ studies beyond the heliopause would measure directly the unmodulated spectrum and energy density of cosmic rays in interstellar space, and thereby establish their contributions to the file:///C|/SSB_old_web/strach5.html (4 of 10) [6/18/2004 2:20:29 PM]

A Science Strategy for Space Physics: Chapter 5 ionization and heating of the interstellar medium, to the production of rare isotopes of cosmological interest, and to processes that include star production. Such studies could be carried out by an interstellar probe designed to pass through the termination shock and heliopause to explore the interstellar medium directly. Cosmic rays enter the solar system carrying information about their origin and propagation through the galactic magnetic fields and interstellar matter. They are an accessible sample of matter from outside the immediate solar neighborhood. Similarly, solar energetic particles provide a sample of solar material that contrasts with that obtained from the solar wind. In all cases, systematic and intriguing patterns emerge in the differences in elemental and isotopic abundance patterns between these samples and those observed in planetary and meteoritic material. Much has already been learned about these patterns from HEAO-3 experiments and from isotope measurements, first on ISEE-3 and now on SAMPEX and Ulysses. The high statistical accuracy of the measurements of solar flare particles, the anomalous component, and galactic cosmic rays on ACE will round out these studies for nuclei with atomic numbers less than 30 and kinetic energies less than 400 MeV/nucleon. Understanding abundance differences in these samples of matter is vital to the study of solar system evolution and to answering questions relating to the uniqueness of the terrestrial environment. Following ACE, it is important to extend high-resolution composition studies to the upper two-thirds of the periodic table. Cosmic rays with atomic numbers greater than 30 (often called the ultraheavy nuclei) are made predominately by the "r" (rapid) and "s" (slow) neutron capture processes that occur in markedly different stellar environments. The r-process occurs in explosive environments where the neutrons are added more rapidly than the time scale for decay, and the s-process occurs where neutrons are added more slowly. Measurements of individual elements and isotopes of these nuclei are required to establish the relative contributions of these processes to the nucleosynthesis of cosmic ray material and to study the evolution of the galaxy. Studies with HEAO-3 and Ariel 6 found an overabundance of r-process nuclei made primarily in supernova explosions. An accurate measurement of the uranium-to-thorium ratio would give a mean age of the heaviest cosmic rays from the time of nucleosynthesis in much the same way that those nuclei are used to measure the age of rocks on Earth. The presence of other transuranic elements with shorter half-lives would be the signature of a recently synthesized r-process component in the cosmic rays. The composition of the source of cosmic rays cannot be understood without understanding preferential acceleration, fractionation, and propagation processes. For example, one process that appears to be important in explaining the differences between the elemental composition of cosmic rays and solar-system material, and also between the solar wind and the solar photosphere (to the extent that such differences have been measured), depends on the first ionization potential (FIP) of the elements. Easily ionized material has an enhanced abundance in both the cosmic radiation and some types of solar wind flows. But the FIP effect is probably not the whole story. As they traverse the matter in the acceleration region and in the interstellar medium, the cosmic-ray nuclei may undergo nuclear interactions that fragment them and change the composition of the sample. These effects can be calculated if the necessary nuclear parameters are known and if a suitable model is adopted for the propagation of the particles. Strong experimental and theoretical efforts are needed to resolve the major uncertainties that still exist in making such calculations. Important information about cosmic ray acceleration is obtained from the study of file:///C|/SSB_old_web/strach5.html (5 of 10) [6/18/2004 2:20:29 PM]

A Science Strategy for Space Physics: Chapter 5 the energy spectra of secondary cosmic rays, which are energetic particles produced by collisions with interstellar material. Both the spatial distribution and energy spectra at "injection" of secondary cosmic rays can be calculated with far fewer assumptions than are required for the cosmic rays in general. Much work has been done with secondary nuclei, such as lithium, beryllium and boron, but the results to date have not been conclusive, and more data on heavier secondary particles are clearly needed. Positrons and antiprotons are the least studied of the light secondary particles, and are unique in that they cannot coexist with matter of any significant density. Therefore they cannot be produced by some two-stage processes proposed for the generation of heavier secondaries. Initial observations of antiprotons suggest an abundance larger than that expected from the studies of heavier nuclei. If confirmed, this result will indeed challenge the simple expectation (Occam's razor) that all cosmic rays are accelerated by the same mechanism. In any event, the antiproton flux must be measured over an extended energy range because it will yield information on cosmic ray propagation that cannot be obtained from heavier nuclei alone. The only fact clearly established about cosmic ray positrons is that, over a significant energy range, they are less abundant than electrons. This, however, is a fundamental observation, since an origin solely from interstellar interactions would produce a composition dominated by positrons. The implication is that electrons are indeed accelerated to cosmic ray energies. Explaining energetic electrons remains a major problem for theories of cosmic ray acceleration, even as radio observations of distant galaxies confirm that they are ubiquitous. Detailed determination of the spectra of electrons and positrons of all energies is greatly needed. Positrons can also contribute to cosmic rays as primary particles. Decay of radioactive supernova ejecta releases a large number of positrons at energies well above the injection threshold of most cosmic ray acceleration models. The composition and distribution of this radioactive material can be determined through observation of the gamma rays that it emits. Either detection or nondetection of these positrons as energetic cosmic rays will make a fundamental statement regarding the cosmic accelerator. Pulsar winds could also produce energetic positrons. It is thought that the plasma in such winds is produced by an electromagnetic cascade in the ultrastrong fields in the pulsar magnetosphere and therefore consists of positive and negative electrons in equal numbers. The energy in the wind flow itself could be at the TeV level, with even higher energies possible in subsequent acceleration at a termination shock. Apart from interaction products, antibaryons have never been observed in nature. No fully satisfactory theory has been advanced to support the extension of this relatively local (i.e., local cluster of galaxies) observation to the universe as a whole. Direct experimental tests for the existence of large domains of antimatter in the universe are possible by searching for antimatter in the small fraction of the cosmic radiation that could be of extragalactic origin. The most sensitive current searches from balloon experiments place upper limits in the range of a few antiparticles in 104 or 105 helium nuclei, whereas if there are equal numbers of matter and antimatter galaxies within 30 to 300 Mpc of Earth, we might expect to find antinuclei in the cosmic rays at a level of a few parts in 105 or 106. This number is highly uncertain; it depends on whether or not there is strong galactic modulation that excludes low-energy particles in a manner analogous to the way the solar wind excludes low-energy galactic particles. file:///C|/SSB_old_web/strach5.html (6 of 10) [6/18/2004 2:20:29 PM]

A Science Strategy for Space Physics: Chapter 5 Questions about the origin of cosmic rays have become more focused and detailed over the past decade, even though there is still much to learn. Phenomenological models have begun to be replaced with more physical models. Space-based measurements have shown the power of making statistically significant measurements above the atmosphere. The nuclear interaction cross sections necessary for interpreting the data are being better measured. Spacecraft approaching the outer boundary and the polar regions of the heliosphere are acquiring new data with which to address the question of how cosmic rays enter the heliosphere. During the coming decade, studies of the galactic cosmic rays and their interactions with the underlying matter and plasma should lead to detailed understanding of their acceleration and propagation. The principal current questions in cosmic ray research are the following: How are solar energetic particles and galactic cosmic rays accelerated? Do supernova or stellar-wind shocks provide the bulk of the cosmic ray energy? Is there more than one mechanism operating? How are particles injected into the accelerator? What are the abundances of the sources of the cosmic ray elements and isotopes, and how do they differ from solar system abundances? What are the nuclear processes that produced this material? Do the abundances show evidence of galactic evolution since the formation of the solar system? What are the preferential selection and fractionation processes that modify the abundances? What time has elapsed between synthesis of the elements and their acceleration? How long has it been since the heaviest elements were synthesized? How do cosmic rays interact with matter and magnetic fields on galactic temporal and spatial scales? How are energetic particles confined in both ordered and chaotic magnetic fields? What are the mechanisms by which they leak out, and what determines the rate at which this escape occurs? Is there a galactic wind? If so, is it driven by cosmic ray pressure? Does it convect particles out of the galactic magnetosphere? Is there an extragalactic component of the cosmic radiation? If so, can researchers find evidence for primordial antimatter in this sample? CURRENT PROGRAM The elemental composition and the isotope ratios for all elements through nickel will be measured by a sequence of instruments on SAMPEX, Ulysses, Wind, and ACE at energies up to a few hundred MeV/nucleon. Those measurements should lead to a much file:///C|/SSB_old_web/strach5.html (7 of 10) [6/18/2004 2:20:29 PM]

A Science Strategy for Space Physics: Chapter 5 better understanding of the systematics of fractionation processes and will provide new information on galactic evolution since the formation of the solar system. Balloon-borne experiments are making progress in a number of specific areas. Measurements are currently under way to study positrons and antiprotons over a limited energy range. Balloon-borne experiments for exploratory measurements of isotopic composition above 0.5 GeV/nucleon for elements up to oxygen, for studying trans-iron isotopes, and for studying ultraheavy elements are currently planned. Nuclei beyond iron in the periodic table have been studied previously on Ariel 6, HEAO-3, and LDEF. Measurements of the energy spectra of the few most abundant elements have been carried out to energies beyond 1014 eV on balloons, HEAO-3, and Spacelab-2. Searches for antihelium and heavier antinuclei are being carried out; the expected sensitivity would lead to detection of one antihelium nucleus per 105 to 106 helium nuclei. Extensive air shower experiments show that a major feature in the cosmic ray spectrum exists at an energy between 1015 eV and 1016 eV. So far, inconclusive but promising attempts are being made to derive the elemental composition in that energy range from air shower data. A program is currently under way to measure the nuclear parameters that describe the propagation of cosmic ray nuclei through the matter in the interstellar medium. Without the nuclear parameters, composition measurements are difficult to interpret or compare with model predictions. Recent work indicates that these parameters are energy dependent over a greater range than previously thought. Those cross sections are absolutely essential in order to deduce the true nature of the cosmic radiations as accelerated. They should be made with a precision that will allow the measurements being made on the satellites mentioned above to be interpreted without introducing significant additional error. FUTURE DIRECTIONS An important new generation of isotope spectrometers recently launched (Ulysses, SAMPEX, and Wind) or soon to be launched (ACE) will join those on Voyager in making extensive measurements of the elemental and isotopic compositions and charge states of cosmic rays throughout the heliosphere. This important new set of observations will satisfy long-standing recommendations of earlier National Research Council committees. The recently developed capability to fly high-altitude balloons for 10 days or more makes it possible to begin carrying out some of the important measurements that researchers can currently identify. Other objectives require measurements in space where they can be made without contamination by atmospheric background and where significant statistics can be gathered to make the precise measurements necessary to distinguish between models. The structure in the total cosmic ray energy spectrum at energies above 1014 eV is probably related to variations in composition. Furthermore, the energies at which that structure occurs are quite close to the energies expected on the basis of the lifetimes of supernova shocks. It is now technically feasible to extend cosmic ray composition measurements made from balloons up to energies approaching 1015 eV and similar file:///C|/SSB_old_web/strach5.html (8 of 10) [6/18/2004 2:20:29 PM]

A Science Strategy for Space Physics: Chapter 5 measurements made from ground-based (air shower) observatories down to energies of 1014 eV. By an aggressive but completely practical program of research, a full order of magnitude of overlap between those two techniques can be obtained in the coming decade. Observations using a large calorimeter on a space-based platform would test theories concerning the acceleration of galactic cosmic rays in supernovae shocks and provide details on the transformations of the source spectrum and composition that take place between the acceleration and the observation of the particles. A large magnetic spectrometer in space will be required to make isotope measurements at energies above 0.5 GeV/nucleon. In particular, measurements of the radioactive nuclides, 10Be, 26Al, and perhaps 36Cl, at energies above 1 GeV/nucleon will provide a test for the existence of a galactic wind and bound its velocity. Because of the relativistic time dilation, the energy dependence of the surviving fraction of those radioactive nuclei depends on whether the loss mechanism from the galaxy is purely diffusive or also includes convective terms. While the first steps toward this objective can be met by balloon-borne observations, completing the scientific objective ultimately requires measurements of high statistical precision made outside the atmosphere. It is important to complete the characterization of cosmic rays heavier than nickel, since abundances of only about a third of those nuclei have been measured. Of particular importance are the trans-iron elemental abundances of odd-Z nuclei and the very rare radioactive actinide elements that can be used to determine the age of this sample of matter. Long-duration balloon flights of detectors currently being developed should enable the measurement of abundances of the lower-charge trans-iron nuclei up through strontium (Z = 38). Instruments flown on satellites are required to make definitive measurements of the heaviest element abundances, in particular the actinides. The spectra of positrons (10 MeV to 100 GeV) and of antiprotons (100 MeV to 100 GeV) must be measured to determine where those particles are created and how they are accelerated. Between approximately 3 and 30 GeV, the necessary cosmic ray positron and antiproton measurements can be obtained by continued support of currently planned and new long-duration balloon instrumentation. For lower and higher energies, atmospheric secondary particles prevent definitive measurements from balloons, particularly for positrons at energies below 2 GeV. Technology has now evolved to the point that the required mass of a positron or antiproton detector is easily compatible with the payload capacity of small launch vehicles such as the Pegasus and the Taurus. Flights of instruments on long-duration balloons for 10 days should be capable of extending the search for antihelium nuclei to 1 part in 107. Measurements in space would extend the sensitivity by yet another factor of 30 or more. A positive detection, however unlikely, would have profound implications for fundamental physics and cosmology. file:///C|/SSB_old_web/strach5.html (9 of 10) [6/18/2004 2:20:29 PM]

Next: A Science Strategy for Space Physics: Part III »
A Science Strategy for Space Physics Get This Book
×
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF
  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!