Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Astronomy

22.5 The Evolution of More Massive Stars

Astronomy22.5 The Evolution of More Massive Stars

Menu
Table of contents
  1. Preface
  2. 1 Science and the Universe: A Brief Tour
    1. Introduction
    2. 1.1 The Nature of Astronomy
    3. 1.2 The Nature of Science
    4. 1.3 The Laws of Nature
    5. 1.4 Numbers in Astronomy
    6. 1.5 Consequences of Light Travel Time
    7. 1.6 A Tour of the Universe
    8. 1.7 The Universe on the Large Scale
    9. 1.8 The Universe of the Very Small
    10. 1.9 A Conclusion and a Beginning
    11. For Further Exploration
  3. 2 Observing the Sky: The Birth of Astronomy
    1. Thinking Ahead
    2. 2.1 The Sky Above
    3. 2.2 Ancient Astronomy
    4. 2.3 Astrology and Astronomy
    5. 2.4 The Birth of Modern Astronomy
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  4. 3 Orbits and Gravity
    1. Thinking Ahead
    2. 3.1 The Laws of Planetary Motion
    3. 3.2 Newton’s Great Synthesis
    4. 3.3 Newton’s Universal Law of Gravitation
    5. 3.4 Orbits in the Solar System
    6. 3.5 Motions of Satellites and Spacecraft
    7. 3.6 Gravity with More Than Two Bodies
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  5. 4 Earth, Moon, and Sky
    1. Thinking Ahead
    2. 4.1 Earth and Sky
    3. 4.2 The Seasons
    4. 4.3 Keeping Time
    5. 4.4 The Calendar
    6. 4.5 Phases and Motions of the Moon
    7. 4.6 Ocean Tides and the Moon
    8. 4.7 Eclipses of the Sun and Moon
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  6. 5 Radiation and Spectra
    1. Thinking Ahead
    2. 5.1 The Behavior of Light
    3. 5.2 The Electromagnetic Spectrum
    4. 5.3 Spectroscopy in Astronomy
    5. 5.4 The Structure of the Atom
    6. 5.5 Formation of Spectral Lines
    7. 5.6 The Doppler Effect
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  7. 6 Astronomical Instruments
    1. Thinking Ahead
    2. 6.1 Telescopes
    3. 6.2 Telescopes Today
    4. 6.3 Visible-Light Detectors and Instruments
    5. 6.4 Radio Telescopes
    6. 6.5 Observations outside Earth’s Atmosphere
    7. 6.6 The Future of Large Telescopes
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  8. 7 Other Worlds: An Introduction to the Solar System
    1. Thinking Ahead
    2. 7.1 Overview of Our Planetary System
    3. 7.2 Composition and Structure of Planets
    4. 7.3 Dating Planetary Surfaces
    5. 7.4 Origin of the Solar System
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  9. 8 Earth as a Planet
    1. Thinking Ahead
    2. 8.1 The Global Perspective
    3. 8.2 Earth’s Crust
    4. 8.3 Earth’s Atmosphere
    5. 8.4 Life, Chemical Evolution, and Climate Change
    6. 8.5 Cosmic Influences on the Evolution of Earth
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  10. 9 Cratered Worlds
    1. Thinking Ahead
    2. 9.1 General Properties of the Moon
    3. 9.2 The Lunar Surface
    4. 9.3 Impact Craters
    5. 9.4 The Origin of the Moon
    6. 9.5 Mercury
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  11. 10 Earthlike Planets: Venus and Mars
    1. Thinking Ahead
    2. 10.1 The Nearest Planets: An Overview
    3. 10.2 The Geology of Venus
    4. 10.3 The Massive Atmosphere of Venus
    5. 10.4 The Geology of Mars
    6. 10.5 Water and Life on Mars
    7. 10.6 Divergent Planetary Evolution
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  12. 11 The Giant Planets
    1. Thinking Ahead
    2. 11.1 Exploring the Outer Planets
    3. 11.2 The Giant Planets
    4. 11.3 Atmospheres of the Giant Planets
    5. Key Terms
    6. Summary
    7. For Further Exploration
    8. Collaborative Group Activities
    9. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  13. 12 Rings, Moons, and Pluto
    1. Thinking Ahead
    2. 12.1 Ring and Moon Systems Introduced
    3. 12.2 The Galilean Moons of Jupiter
    4. 12.3 Titan and Triton
    5. 12.4 Pluto and Charon
    6. 12.5 Planetary Rings (and Enceladus)
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  14. 13 Comets and Asteroids: Debris of the Solar System
    1. Thinking Ahead
    2. 13.1 Asteroids
    3. 13.2 Asteroids and Planetary Defense
    4. 13.3 The “Long-Haired” Comets
    5. 13.4 The Origin and Fate of Comets and Related Objects
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  15. 14 Cosmic Samples and the Origin of the Solar System
    1. Thinking Ahead
    2. 14.1 Meteors
    3. 14.2 Meteorites: Stones from Heaven
    4. 14.3 Formation of the Solar System
    5. 14.4 Comparison with Other Planetary Systems
    6. 14.5 Planetary Evolution
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  16. 15 The Sun: A Garden-Variety Star
    1. Thinking Ahead
    2. 15.1 The Structure and Composition of the Sun
    3. 15.2 The Solar Cycle
    4. 15.3 Solar Activity above the Photosphere
    5. 15.4 Space Weather
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  17. 16 The Sun: A Nuclear Powerhouse
    1. Thinking Ahead
    2. 16.1 Sources of Sunshine: Thermal and Gravitational Energy
    3. 16.2 Mass, Energy, and the Theory of Relativity
    4. 16.3 The Solar Interior: Theory
    5. 16.4 The Solar Interior: Observations
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  18. 17 Analyzing Starlight
    1. Thinking Ahead
    2. 17.1 The Brightness of Stars
    3. 17.2 Colors of Stars
    4. 17.3 The Spectra of Stars (and Brown Dwarfs)
    5. 17.4 Using Spectra to Measure Stellar Radius, Composition, and Motion
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  19. 18 The Stars: A Celestial Census
    1. Thinking Ahead
    2. 18.1 A Stellar Census
    3. 18.2 Measuring Stellar Masses
    4. 18.3 Diameters of Stars
    5. 18.4 The H–R Diagram
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  20. 19 Celestial Distances
    1. Thinking Ahead
    2. 19.1 Fundamental Units of Distance
    3. 19.2 Surveying the Stars
    4. 19.3 Variable Stars: One Key to Cosmic Distances
    5. 19.4 The H–R Diagram and Cosmic Distances
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  21. 20 Between the Stars: Gas and Dust in Space
    1. Thinking Ahead
    2. 20.1 The Interstellar Medium
    3. 20.2 Interstellar Gas
    4. 20.3 Cosmic Dust
    5. 20.4 Cosmic Rays
    6. 20.5 The Life Cycle of Cosmic Material
    7. 20.6 Interstellar Matter around the Sun
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  22. 21 The Birth of Stars and the Discovery of Planets outside the Solar System
    1. Thinking Ahead
    2. 21.1 Star Formation
    3. 21.2 The H–R Diagram and the Study of Stellar Evolution
    4. 21.3 Evidence That Planets Form around Other Stars
    5. 21.4 Planets beyond the Solar System: Search and Discovery
    6. 21.5 Exoplanets Everywhere: What We Are Learning
    7. 21.6 New Perspectives on Planet Formation
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  23. 22 Stars from Adolescence to Old Age
    1. Thinking Ahead
    2. 22.1 Evolution from the Main Sequence to Red Giants
    3. 22.2 Star Clusters
    4. 22.3 Checking Out the Theory
    5. 22.4 Further Evolution of Stars
    6. 22.5 The Evolution of More Massive Stars
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  24. 23 The Death of Stars
    1. Thinking Ahead
    2. 23.1 The Death of Low-Mass Stars
    3. 23.2 Evolution of Massive Stars: An Explosive Finish
    4. 23.3 Supernova Observations
    5. 23.4 Pulsars and the Discovery of Neutron Stars
    6. 23.5 The Evolution of Binary Star Systems
    7. 23.6 The Mystery of the Gamma-Ray Bursts
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  25. 24 Black Holes and Curved Spacetime
    1. Thinking Ahead
    2. 24.1 Introducing General Relativity
    3. 24.2 Spacetime and Gravity
    4. 24.3 Tests of General Relativity
    5. 24.4 Time in General Relativity
    6. 24.5 Black Holes
    7. 24.6 Evidence for Black Holes
    8. 24.7 Gravitational Wave Astronomy
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  26. 25 The Milky Way Galaxy
    1. Thinking Ahead
    2. 25.1 The Architecture of the Galaxy
    3. 25.2 Spiral Structure
    4. 25.3 The Mass of the Galaxy
    5. 25.4 The Center of the Galaxy
    6. 25.5 Stellar Populations in the Galaxy
    7. 25.6 The Formation of the Galaxy
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  27. 26 Galaxies
    1. Thinking Ahead
    2. 26.1 The Discovery of Galaxies
    3. 26.2 Types of Galaxies
    4. 26.3 Properties of Galaxies
    5. 26.4 The Extragalactic Distance Scale
    6. 26.5 The Expanding Universe
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  28. 27 Active Galaxies, Quasars, and Supermassive Black Holes
    1. Thinking Ahead
    2. 27.1 Quasars
    3. 27.2 Supermassive Black Holes: What Quasars Really Are
    4. 27.3 Quasars as Probes of Evolution in the Universe
    5. Key Terms
    6. Summary
    7. For Further Exploration
    8. Collaborative Group Activities
    9. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  29. 28 The Evolution and Distribution of Galaxies
    1. Thinking Ahead
    2. 28.1 Observations of Distant Galaxies
    3. 28.2 Galaxy Mergers and Active Galactic Nuclei
    4. 28.3 The Distribution of Galaxies in Space
    5. 28.4 The Challenge of Dark Matter
    6. 28.5 The Formation and Evolution of Galaxies and Structure in the Universe
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  30. 29 The Big Bang
    1. Thinking Ahead
    2. 29.1 The Age of the Universe
    3. 29.2 A Model of the Universe
    4. 29.3 The Beginning of the Universe
    5. 29.4 The Cosmic Microwave Background
    6. 29.5 What Is the Universe Really Made Of?
    7. 29.6 The Inflationary Universe
    8. 29.7 The Anthropic Principle
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  31. 30 Life in the Universe
    1. Thinking Ahead
    2. 30.1 The Cosmic Context for Life
    3. 30.2 Astrobiology
    4. 30.3 Searching for Life beyond Earth
    5. 30.4 The Search for Extraterrestrial Intelligence
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  32. A | How to Study for an Introductory Astronomy Class
  33. B | Astronomy Websites, Images, and Apps
  34. C | Scientific Notation
  35. D | Units Used in Science
  36. E | Some Useful Constants for Astronomy
  37. F | Physical and Orbital Data for the Planets
  38. G | Selected Moons of the Planets
  39. H | Future Total Eclipses
  40. I | The Nearest Stars, Brown Dwarfs, and White Dwarfs
  41. J | The Brightest Twenty Stars
  42. K | The Chemical Elements
  43. L | The Constellations
  44. M | Star Chart and Sky Event Resources
  45. Index

Learning Objectives

By the end of this section, you will be able to:

  • Explain how and why massive stars evolve much more rapidly than lower-mass stars like our Sun
  • Discuss the origin of the elements heavier than carbon within stars

If what we have described so far were the whole story of the evolution of stars and elements, we would have a big problem on our hands. We will see in later chapters that in our best models of the first few minutes of the universe, everything starts with the two simplest elements—hydrogen and helium (plus a tiny bit of lithium). All the predictions of the models imply that no heavier elements were produced at the beginning of the universe. Yet when we look around us on Earth, we see lots of other elements besides hydrogen and helium. These elements must have been made (fused) somewhere in the universe, and the only place hot enough to make them is inside stars. One of the fundamental discoveries of twentieth-century astronomy is that the stars are the source of most of the chemical richness that characterizes our world and our lives.

We have already seen that carbon, oxygen, and some other elements are made inside lower-mass stars during the red-giant stage. But where do the heavier elements we know and love (such as the silicon and iron inside Earth, and the gold and silver in our jewelry) come from? The kinds of stars we have been discussing so far never get hot enough at their centers to make these elements. It turns out that these heavier elements are formed later in the lives more massive stars, as well as during explosions that can mark the end of the lives of some stars.

Making New Elements in Massive Stars

Massive stars evolve in much the same way that the Sun does (but always more quickly)—up to the formation of a carbon-oxygen core. One difference is that for stars with more than about twice the mass of the Sun, helium begins fusion more gradually, rather than with a sudden flash. Also, when more massive stars become red giants, they become so bright and large that we call them supergiants. Such stars can expand until their outer regions become as large as the orbit of Jupiter, which is precisely what the Hubble Space Telescope has shown for the star Betelgeuse (see Figure 22.4). They also lose mass very effectively, producing dramatic winds and outbursts as they age. Figure 22.20 shows a wonderful image of the very massive star Eta Carinae, with a great deal of ejected material clearly visible.

The Eta Carinae Ejection Nebula. At the center of this H S T image is the slightly obscured star Eta Carinae which is surrounded by two giant lobes and an equatorial disk of material.
Figure 22.20 Eta Carinae. With a mass at least 100 times that of the Sun, the hot supergiant Eta Carinae is one of the most massive stars known. This Hubble Space Telescope image records the two giant lobes and equatorial disk of material it has ejected in the course of its evolution. The pink outer region is material ejected in an outburst seen in 1843, the largest of such mass loss event that any star is known to have survived. Moving away from the star at a speed of about 1000 km/s, the material is rich in nitrogen and other elements formed in the interior of the star. The inner blue-white region is the material ejected at lower speeds and is thus still closer to the star. It appears blue-white because it contains dust and reflects the light of Eta Carinae, whose luminosity is 4 million times that of our Sun. (credit: modification of work by Jon Morse (University of Colorado) & NASA)

But the crucial way that massive stars diverge from the story we have outlined is that they can start additional kinds of fusion in their centers and in the shells surrounding their central regions. The outer layers of a star with a mass greater than about 8 solar masses have a weight that is enough to compress the carbon-oxygen core until it becomes hot enough to ignite fusion of carbon nuclei. Carbon can fuse into still more oxygen, and at still higher temperatures, oxygen and then neon, magnesium, and finally silicon can build even heavier elements. Iron is, however, the endpoint of this process. The fusion of iron atoms produces products that are more massive than the nuclei that are being fused and therefore the process requires energy, as opposed to releasing energy, which all fusion reactions up to this point have done. This required energy comes at the expense of the star itself, which is now on the brink of death (Figure 22.21). What happens next will be described in the chapter on The Death of Stars.

Interior Structure of a Massive Star before the End of its Life. The onion like layers of a massive star are illustrated as follows: the outermost layer is composed of hydrogen, followed by another hydrogen layer, a helium layer, an oxygen layer, a neon layer, a magnesium layer, a silicon layer, and culminating in a core of iron “ash”.
Figure 22.21 Interior Structure of a Massive Star Just before It Exhausts Its Nuclear Fuel. High-mass stars can fuse elements heavier than carbon. As a massive star nears the end of its evolution, its interior resembles an onion. Hydrogen fusion is taking place in an outer shell, and progressively heavier elements are undergoing fusion in the higher-temperature layers closer to the center. All of these fusion reactions generate energy and enable the star to continue shining. Iron is different. The fusion of iron requires energy, and when iron is finally created in the core, the star has only minutes to live.

Physicists have now found nuclear pathways whereby virtually all chemical elements of atomic weights up to that of iron can be built up by this nucleosynthesis (the making of new atomic nuclei) in the centers of the more massive red giant stars. This still leaves the question of where elements heavier than iron come from. We will see in the next chapter that when massive stars finally exhaust their nuclear fuel, they most often die in a spectacular explosion—a supernova. Heavier elements can be synthesized in the stunning violence of such explosions.

Not only can we explain in this way where the elements that make up our world and others come from, but our theories of nucleosynthesis inside stars are even able to predict the relative abundances with which the elements occur in nature. The way stars build up elements during various nuclear reactions really can explain why some elements (oxygen, carbon, and iron) are common and others are quite rare (gold, silver, and uranium).

Elements in Globular Clusters and Open Clusters Are Not the Same

The fact that the elements are made in stars over time explains an important difference between globular and open clusters. Hydrogen and helium, which are the most abundant elements in stars in the solar neighborhood, are also the most abundant constituents of stars in both kinds of clusters. However, the abundances of the elements heavier than helium are very different.

In the Sun and most of its neighboring stars, the combined abundance (by mass) of the elements heavier than hydrogen and helium is 1–4% of the star’s mass. Spectra show that most open-cluster stars also have 1–4% of their matter in the form of heavy elements. Globular clusters, however, are a different story. The heavy-element abundance of stars in typical globular clusters is found to be only 1/10 to 1/100 that of the Sun. A few very old stars not in clusters have been discovered with even lower abundances of heavy elements.

The differences in chemical composition are a direct consequence of the formation of a cluster of stars. The very first generation of stars initially contained only hydrogen and helium. We have seen that these stars, in order to generate energy, created heavier elements in their interiors. In the last stages of their lives, they ejected matter, now enriched in heavy elements, into the reservoirs of raw material between the stars. Such matter was then incorporated into a new generation of stars.

This means that the relative abundance of the heavy elements must be less and less as we look further into the past. We saw that the globular clusters are much older than the open clusters. Since globular-cluster stars formed much earlier (that is, they are an earlier generation of stars) than those in open clusters, they have only a relatively small abundance of elements heavier than hydrogen and helium.

As time passes, the proportion of heavier elements in the “raw material” that makes new stars and planets increases. This means that the first generation of stars that formed in our Galaxy would not have been accompanied by a planet like Earth, full of silicon, iron, and many other heavy elements. Earth (and the astronomy students who live on it) was possible only after generations of stars had a chance to make and recycle their heavier elements.

Now the search is on for true first-generation stars, made only of hydrogen and helium. Theories predict that such stars should be very massive, live fast, and die quickly. They should have lived and died long ago. The place to look for them is in very distant galaxies that formed when the universe was only a few hundred million years old, but whose light is only arriving at Earth now.

Approaching Death

Compared with the main-sequence lifetimes of stars, the events that characterize the last stages of stellar evolution pass very quickly (especially for massive stars). As the star’s luminosity increases, its rate of nuclear fuel consumption goes up rapidly—just at that point in its life when its fuel supply is beginning to run down.

After the prime fuel—hydrogen—is exhausted in a star’s core, we saw that other sources of nuclear energy are available to the star in the fusion of, first, helium, and then of other more complex elements. But the energy yield of these reactions is much less than that of the fusion of hydrogen to helium. And to trigger these reactions, the central temperature must be higher than that required for the fusion of hydrogen to helium, leading to even more rapid consumption of fuel. Clearly this is a losing game, and very quickly the star reaches its end. As it does so, however, some remarkable things can happen, as we will see in The Death of Stars.

Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/astronomy/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/astronomy/pages/1-introduction
Citation information

© Jan 28, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.