What Is Dark Matter?

WHAT IS DARK MATTER?

PRINCETON FRONTIERS IN PHYSICS

Abraham Loeb, How Did the First Stars and Galaxies Form?

Joshua Bloom, What Are Gamma-Ray Bursts?

Charles D. Bailyn, What Does a Black Hole Look like?

John Asher Jonson, How Do You Find an Exoplanet?

Paul Langacker, Can the Laws of Physics Be Unified?

Peter Fisher, What Is Dark Matter?

WHAT IS DARK MATTER?

PETER FISHER

PRINCETON UNIVERSITY PRESS

PRINCETON & OXFORD

Copyright © 2022 by Princeton University Press

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Library of Congress Cataloging-in-Publication Data

Names: Fisher, Peter, 1959- author.

Title: What is dark matter? / Peter Fisher.

Description: 1st. | Princeton: Princeton University Press, 2022. | Series: Princeton frontiers in physics | Includes bibliographical references and index.

Identifiers: LCCN 2021051624 (print) | LCCN 2021051625 (ebook) | ISBN 9780691148342 (hardback) | ISBN 9780691185910 (ebook)

Subjects: LCSH: Dark matter (Astronomy)

Classification: LCC QB791.3.F57 2022 (print) | LCC QB791.3 (ebook) | DDC 523.1/126–dc23/eng/20211217

LC record available at https://lccn.loc.gov/2021051624

LC ebook record available at https://lccn.loc.gov/2021051625

Version 1.0

British Library Cataloging-in-Publication Data is available

Editorial: Ingrid Gnerlich and Whitney Rauenhorst

Production Editorial: Mark Bellis

Text and Jacket Design: Jessica Massabrook

Production: Danielle Amatucci

Publicity: Matthew Taylor and Charlotte Coyne

Copyeditor: Cyd Westmoreland

This book is for

Jane Ann and Olympia,

my guiding lights.

CONTENTS

INTRODUCTION: THE DARK MATTER PROBLEM1

1. SOME BACKGROUND5

1.1 Mass, Weight, and Energy6

1.2 Distances in the Universe12

1.3 Measuring Speed Using Redshift16

1.4 Dark Energy and the Expansion of the Universe20

2. EVIDENCE FOR DARK MATTER FROM ASTRONOMY29

2.1 Observations of the Coma Cluster30

2.2 Orbits of Stars in Galaxies32

2.3 Numerical Simulations of Galaxy Formation38

2.4 Gravitational Lensing40

2.5 1E 0657-56 and the Bullet Cluster46

2.6 Light from the Big Bang51

3. NORMAL MATTER: THE STANDARD MODEL63

3.1 Particles and Interactions63

3.2 The Higgs Boson68

3.3 Testing the Standard Model71

4. WHAT DARK MATTER IS NOT75

4.1 Making Visible Matter: The Big Bang76

4.2 Neutrinos as Dark Matter86

4.3 Black Holes, White Dwarfs, Failed Stars, and Planets88

4.3.1 Baryonic Compact Objects88

4.3.2 Primordial Black Holes92

4.4 Modified Newtonian Dynamics96

5. SEARCHING FOR WIMPS ON EARTH98

5.1 Dark Matter in Galaxies99

5.2 Detecting WIMP Dark Matter from Elastic Scattering101

5.3 Measuring Two Kinds of Energy109

5.4 Detecting the Earth’s Motion through the Dark Matter Halo116

6. SEARCHING FOR DARK MATTER IN SPACE122

6.1 WIMP Annihilation in the Galaxy122

6.2 Detecting Cosmic Rays127

7. SEARCHING FOR AXIONS135

7.1 Why Do We Need Axions?135

7.2 The Axion Dark Matter Experiment137

7.3 The CERN Axion Solar Telescope (CAST) 141

8. EPILOGUE146

8.1 Looking Forward: Current and Upcoming Dark Matter Experiments146

8.2 Outlook149

GLOSSARY155

SUGGESTED READINGS167

INDEX169

WHAT IS DARK MATTER?

INTRODUCTION: THE DARK MATTER PROBLEM

Suppose you became aware that there were specters, invisible beings, living in your house. You cannot see, hear, or feel them, but you know they are there, because they move things around your home, open and close doors, and change the room temperature. You begin to notice patterns for these changes, as if they are governed by rules.

After a time, knowing their patterns, you begin to learn the rules. You learn how to predict what changes they will make, and when they will make them. As more time passes, you come to suspect that there are many specters—maybe ten for each person in your house. The specters have always dominated your environment, and you and your family have always responded to them without knowing it.

Your curiosity about the specters grows, and you try to learn more about them—what are they made of? Where did they come from? What do they want? Still, you never sense them directly, but only learn about them through the changes they make in your (their?) home. The specters shape your environment, but you do not shape theirs. They are completely unresponsive to anything you do to communicate with or learn about them. You imagine that the specters have always been there. They are not intruders, but part of the natural order of things.

Most of us would find such a circumstance very strange, perhaps troubling, and certainly very frustrating. How could we have coexisted with so many specters for so long without knowing it? Why is it so difficult to learn about them? Where did they come from?

Over the twentieth century, astronomers¹ gradually became aware of specters in our universe in the form of a new substance first called missing mass and later dark matter. This book uses the term dark matter. Dark matter created the shape and structure of galaxies, clusters of galaxies, and the universe itself.

The goal of this book is to make sense of the specters that represent dark matter: to explain how astronomers came to know about it; how theoreticians uncovered how dark matter shaped the largest structures in our universe through gravity; and how physicists and astronomers are navigating the complex, frustrating hunt to understand more about dark matter.

I will use the terms visible matter or normal or luminous matter to refer to matter that forms stars and generates the light that we observe through telescopes. Dark matter’s invisibility means that it does not form stars or generate light (hence the term dark matter). More broadly, dark implies that dark matter does not significantly interact with visible or normal matter in any way other than through gravity.

Over the past 85 years, particle physicists, astronomers, and astrophysicists have shown through the process of elimination that no known substance can account for the effects of dark matter. That includes planets, extra gas in the universe, and anything else that is made of particles that we know about. This also includes the black holes made from the collapse of stars at the end of their lives. However, there is the idea that as-yet unobserved primordial black holes (PBHs) that formed in the early universe from matter fluctuations in space-time could explain dark matter.

In the 1930s, a few astronomers began to understand that the amount of visible matter in clusters of galaxies could not explain the motion of the galaxies in their cluster. The total mass of the newly discovered invisible matter appeared to be tens or hundreds of times the visible mass of the stars. In the 1970s, measurements of how stars move inside galaxies led to the idea that some unseen gravitating matter causes the visible stars to orbit around the center of their galaxy faster than predicted from just the mass of the stars alone. To explain this concept, and set the stage for the rest of the book, Chapter 1 provides some physics background. Chapter 2 then lays out the evidence for dark matter from astronomical observations.

In Chapter 3, we turn to what we do know. Four forces describe almost all the dynamics of matter. The weak force causes radioactive decays, the strong force binds quarks into protons and neutrons and binds protons and neutrons into atomic nuclei, the electromagnetic force determines the structure of matter, and all matter and energy feel the force of gravity. The weak, strong, and electromagnetic forces are all variants of quantum field theory and collectively make up the Standard Model of particle physics. The three Standard Model forces act on quarks and leptons that make up normal matter.

The Standard Model explains almost all the observed interactions between particles made since Henri Becquerel first observed radioactive decay in 1896. Albert Einstein and his successors left us with an excellent classical theory of gravity, but theorists have been unable to find a quantum theory of gravity, leaving us with a patchwork of theories: the quantum mechanical Standard Model for quarks and leptons, and classical gravity that acts on all matter. Dark matter does not fit anywhere in our patchwork: None of the known particles from the Standard Model have the properties of dark matter; and classical gravity does not predict particles, as gravity acts on all matter.

Chapter 4 follows the experiments that led to the conclusion that dark matter does not fit into our current view of particle physics, leaving the problem of finding out what dark matter is.

Over the past 30 years, many ideas have emerged to explain the effects of dark matter. This book focuses mostly on two hypothesized new particles, called Weakly Interacting Massive Particles (WIMPs) and axions, both of which could be dark matter particles. Chapters 5 and 6 explain some of the experiments searching for WIMPs on Earth and in space. Chapter 7 describes the idea behind axions, how axions could be dark matter, and how physicists search for axions.

This book does not end in Chapter 8 with a grand revelation of the properties of dark matter—these still elude my experimental colleagues and me. However, I hope that you will gain a deeper understanding of the dark matter problem and what a triumph it will be when we do learn something new about dark matter.

1. The glossary at the end of the book provides brief explanations of words in bold.

1

SOME BACKGROUND

Gravity plays a central role in everything that happens in the universe, and we will need to know a little about gravity to understand the dark matter story. The original ideas of gravity came from Galileo Galilei and Johannes Kepler in the early 1600s. Isaac Newton developed the full theory in 1687, explaining both the motion of objects acted on by a force and how massive bodies produce the forces that act on one another. In the nineteenth century, experiments began to show that Newton’s laws of motion were not strictly obeyed, leading to Albert Einstein’s Special Theory of Relativity in 1905, which gave universal laws of motion, with Newton’s laws as approximations for objects moving at much less than the speed of light. In 1916, Einstein’s General Theory of Relativity showed that gravity produced its effects through changes in the structure of space and time, with Newton’s law of gravitation giving an approximation for weak gravitational forces. Einstein’s theory has remained unmodified ever since.

We begin with essential background: Section 1.1 describes the relationship among mass, weight, and energy; Newton’s law of gravitation; and distance scales in the universe. Mass, weight, and energy have precise meanings that are necessary for understanding how gravity works. Next, we will look at how Newton’s law of gravitation exerts forces on distant objects, which will be essential for understanding how we know about dark matter. Since gravity works between distant bodies, Section 1.2 describes the typical sizes and separations of planets, stars, and galaxies in the expanding universe. Sections 1.3 and 1.4 describe the redshift phenomenon—crucial for measuring velocities in the cosmos—and dark energy.

1.1 MASS, WEIGHT, AND ENERGY

In 1687, Newton published Principia, in which he laid down three laws of motion. Newton’s first law defines inertia and why objects in motion will remain in motion. The second law defines force as a change in momentum. The second law says the force on an object is the product of the object’s mass and its acceleration:

force = mass ×acceleration. (1.1)

We can then measure the mass of something by computing the force acting on it, measuring its acceleration, and forming the ratio of force to acceleration:

mass = force acceleration.

The second law is a kinematic law, meaning it relates quantities of motion like velocity, force, mass, acceleration, and so on. A kinematic law tells us how objects respond to a force, while a dynamical law tells us what the forces are.

Figure 1.1. Two equal-mass bodies exert equal gravitational force on each other.

Figure 1.2. Doubling the mass of one body doubles the gravitational force felt by both bodies.

Newton’s third law explains how a force acting between two massive bodies causes an equal and opposite force on each body.

Principia also set forth Newton’s theory of gravity—a dynamic law of gravitational force between two bodies. While the same law applies whether