Abraham Loeb is Frank B. Baird, Jr. Professor of Science, chair of the Astronomy Department, and director of the Institute for Theory and Computation at Harvard University. Loeb is a member of the American Academy of Arts and Sciences. He is the author of How Did the First Stars and Galaxies Form? (Princeton). Steven R. Furlanetto is associate professor of physics and astronomy at the University of California, Los Angeles.

The First Galaxies in The Universe

By Abraham Loeb Steven R. Furlanetto

PRINCETON UNIVERSITY PRESS

Copyright © 2013 Princeton University Press
All right reserved.
ISBN: 978-0-691-14491-7

Contents

Preface…………………………………………………………………xiPART I. FUNDAMENTALS OF STRUCTURE FORMATION………………………………..1Chapter 1 Introduction and Cosmological Background………………………….3Chapter 2 Linear Growth of Cosmological Perturbations……………………….25Chapter 3 Nonlinear Structure and Halo Formation……………………………41Chapter 4 The Intergalactic Medium………………………………………..92PART II. THE FIRST STRUCTURES…………………………………………….131Chapter 5 The First Stars………………………………………………..133Chapter 6 Stellar Feedback and Galaxy Formation…………………………….174Chapter 7 Supermassive Black Holes………………………………………..217Chapter 8 Physics of Galaxy Evolution……………………………………..251Chapter 9 The Reionization of Intergalactic Hydrogen………………………..283PART III. OBSERVATIONS OF THE COSMIC DAWN………………………………….335Chapter 10 Surveys of High-Redshift Galaxies……………………………….337Chapter 11 The Lyman-a Line as a Probe of the Early Universe…………………367Chapter 12 The 21-cm Line………………………………………………..408Chapter 13 Other Probes of the First Galaxies………………………………459Appendix A Useful Numbers…………………………………………………495Appendix B Cosmological Parameters…………………………………………497Notes…………………………………………………………………..499Further Reading………………………………………………………….509Index…………………………………………………………………..513

Chapter One

Introduction and Cosmological Background

1.1 Preliminary Remarks

On large scales, the Universe is observed to be expanding. As it expands, galaxies separate from one another, and the density of matter (averaged over a large volume of space) decreases. If we imagine playing the cosmic movie in reverse and tracing this evolution backward in time, we would infer that there must have been an instant when the density of matter was infinite. This moment in time is the Big Bang, before which we cannot reliably extrapolate our history. But even before we get all the way back to the Big Bang, there must have been a time when stars like our Sun and galaxies like our Milky Way did not exist, because the Universe was denser than they are. If so, how and when did the first stars and galaxies form?

Primitive versions of this question were considered by humans for thousands of years, long before it was realized that the Universe is expanding. Religious and philosophical texts attempted to provide a sketch of the big picture from which people could derive the answer. In retrospect, these attempts appear heroic in view of the scarcity of scientific data about the Universe prior to the twentieth century. To appreciate the progress made over the past century, consider, for example, the biblical story of Genesis. The opening chapter of the Bible asserts the following sequence of events: first, the Universe was created, then light was separated from darkness, water was separated from the sky, continents were separated from water, vegetation appeared spontaneously, stars formed, life emerged, and finally humans appeared on the scene. Instead, the modern scientific order of events begins with the Big Bang, followed by an early period in which light (radiation) dominated and then a longer period in which matter was preeminent and led to the appearance of stars, planets, life on Earth, and eventually humans. Interestingly, the starting and end points of both versions are the same.

Cosmology is by now a mature empirical science. We are privileged to live in a time when the story of genesis (how the Universe started and developed) can be critically explored by direct observations. Because light takes a finite time to travel to us from distant sources, we can see images of the Universe when it was younger by looking deep into space through powerful telescopes.

Existing data sets include an image of the Universe when it was 400,000 years old (in the form of the cosmic microwave background in Figure 1.1), as well as images of individual galaxies when the Universe was older than a billion years. But there is a serious challenge: between these two epochs was a period when the Universe was dark, stars had not yet formed, and the cosmic microwave background no longer traced the distribution of matter. And this is precisely the most interesting period, when the primordial soup evolved into the rich zoo of objects we now see. How can astronomers see this dark yet crucial time?

The situation is similar to having a photo album of a person that begins with the first ultrasound image of him or her as an unborn baby and then skips to some additional photos of his or her years as teenager and adult. The later photos do not simply show a scaled-up version of the first image. We are currently searching for the missing pages of the cosmic photo album that will tell us how the Universe evolved during its infancy to eventually make galaxies like our own Milky Way.

Observers are moving ahead along several fronts. The first involves the construction of large infrared telescopes on the ground and in space that will provide us with new (although rather expensive!) photos of galaxies in the Universe at intermediate ages. Current plans include ground-based telescopes 24–42m in diameter and NASA’s successor to the Hubble Space Telescope, the James Webb Space Telescope (JWST). In addition, several observational groups around the globe are constructing radio arrays that will be capable of mapping the three-dimensional distribution of cosmic hydrogen left over from the Big Bang in the infant Universe. These arrays are aiming to detect the long-wavelength (redshifted 21-cm) radio emission from hydrogen atoms. Coincidentally, this long wavelength (or low frequency) overlaps the band used for radio and television broadcasting, and so these telescopes include arrays of regular radio antennas that one can find in electronics stores. These antennas will reveal how the clumpy distribution of neutral hydrogen evolved with cosmic time. By the time the Universe was a few hundreds of millions of years old, the hydrogen distribution had been punched with holes and resembled Swiss cheese. These holes were created by the ultraviolet radiation from the first galaxies and black holes, which ionized the cosmic hydrogen in their vicinity.

Theoretical research has focused in recent years on predicting the signals expected from the telescopes described and on providing motivation for these ambitious observational projects.

All these predictions are generated in the context of the modern cosmological paradigm, which turns the Big Bang model into a quantitative tool for understanding our Universe. In the remainder of this chapter, we briefly describe the essential aspects of this paradigm for understanding the formation of the first galaxies in the Universe.

1.2 Standard Cosmological Model

1.2.1 Cosmic Perspective

In 1915 Einstein formulated the general theory of relativity. He was inspired by the fact that all objects follow the same trajectories under the influence of gravity (the so-called equivalence principle, which by now has been tested to better than one part in a trillion), and realized that this would be a natural result if space–time is curved under the influence of matter. He wrote an equation describing how the distribution of matter (on one side of his equation) determines the curvature of space–time (on the other side of his equation). Einstein then applied his equation to describe the global dynamics of the Universe.

There were no computers available in 1915, and Einstein’s equations for the Universe were particularly difficult to solve in the most general case. To get around this obstacle Einstein considered the simplest possible Universe, one that is homogeneous and isotropic. Homogeneity means uniform conditions everywhere (at any given time), and isotropy means the same conditions in all directions seen from one vantage point. The combination of these two simplifying assumptions is known as the cosmological principle.

The Universe can be homogeneous but not isotropic: for example, the expansion rate could vary with direction. It can also be isotropic and not homogeneous: for example, we could be at the center of a spherically symmetric mass distribution. But if it is isotropic around every point, then it must also be homogeneous.

Under the simplifying assumptions associated with the cosmological principle, Einstein and his contemporaries were able to solve the equations. They were looking for their “lost keys” (solutions) under a convenient “lamppost” (simplifying assumptions), but the real Universe is not bound by any contract to be the simplest that we can imagine. In fact, it is truly remarkable in the first place that we dare describe the conditions across vast regions of space based on the blueprint of the laws of physics that describe the conditions here on Earth. Our daily life teaches us too often that we fail to appreciate complexity, and that an elegant model for reality is often too idealized for describing the truth (along the lines of approximating a cow as a spherical object).

In 1915 Einstein had the wrong notion of the Universe; at the time people associated the Universe with the Milky Way galaxy and regarded all the “spiral nebulae,” which we now know are distant galaxies, as constituents of our own Milky Way galaxy. Because the Milky Way is not expanding, Einstein attempted to reproduce a static universe with his equations. This turned out to be possible only after he added a cosmological constant, whose negative gravity would exactly counteract that of matter. However, Einstein later realized that this solution is unstable: a slight enhancement in density would make the density grow even further. As it turns out, there are no stable static solutions to Einstein’s equations for a homogeneous and isotropic Universe. The Universe must be either expanding or contracting. Less than a decade later, Edwin Hubble discovered that the nebulae previously considered to be constituents of the Milky Way galaxy are receding from us at a speed v that is proportional to their distance r, namely, v = H₀r, where H₀ is a spatial constant (which can evolve with time), commonly termed the Hubble constant. Hubble’s data indicated that the Universe is expanding. (Hubble also resolved individual bright stars in these nebulae, unambiguously determining their nature and their vast distances from the Milky Way.)

Einstein was remarkably successful in asserting the cosmological principle. As it turns out, our latest data indicate that the real Universe is homogeneous and isotropic on the largest observable scales to within one part in 10⁵. In particular, isotropy is well established for the distribution of faint radio sources, optical galaxies, the X-ray background, and most important, the cosmic microwave background (CMB). The constraints on homogeneity are less strict, but a cosmological model in which the Universe is isotropic and significantly inhomogeneous in spherical shells around our special location is also excluded based on surveys of galaxies and quasars. Fortuitously, Einstein’s simplifying assumptions turned out to be extremely accurate in describing reality: the keys were indeed lying next to the lamppost. Our Universe happens to be the simplest we could have imagined, for which Einstein’s equations can easily be solved.

Why was the Universe prepared to be in this special state? Cosmologists were able to go one step further and demonstrated that an early phase transition, called cosmic inflation—during which the expansion of the Universe accelerated exponentially—could have naturally produced the conditions postulated by the cosmological principle (although other explanations also may create such conditions). One is left to wonder whether the existence of inflation is just a fortunate consequence of the fundamental laws of nature, or whether perhaps the special conditions of the specific region of space–time we inhabit were selected out of many random possibilities elsewhere by the prerequisite that they allow our existence. The opinions of cosmologists on this question are split.

1.2.2 Origin of Structure

Hubble’s discovery of the expansion of the Universe has immediate implications for the past and future of the Universe. If we reverse in our mind the expansion history back in time, we realize that the Universe must have been denser in its past. In fact, there must have been a point in time where the matter density was infinite, at the moment of the so-called Big Bang. Indeed, we do detect relics from a hotter, denser phase of the Universe in the form of light elements (such as deuterium, helium, and lithium) as well as the CMB. At early times, this radiation coupled extremely well to the cosmic gas and produced a spectrum known as a blackbody, a form predicted a century ago to characterize matter and radiation in equilibrium. The CMB provides the best example of a blackbody spectrum we have.

To get a rough estimate of when the Big Bang occurred, we may simply divide the distance of all galaxies by their recession velocity. This calculation gives a unique answer, ~ r/v ~ 1/H₀, that is independent of distance. The latest measurements of the Hubble constant give a value of H₀ [approximately equal to] 70kms^-1 Mpc^-1, which implies a current age for the Universe 1/H₀ of 14 billion years (or 5 × 10¹⁷ seconds).

The second implication concerns our future. A fortunate feature of a spherically symmetric Universe is that when considering a sphere of matter in it, we are allowed to ignore the gravitational influence of everything outside this sphere. If we empty the sphere and consider a test particle on the boundary of an empty void embedded in a uniform Universe, the particle will experience no net gravitational acceleration. This result, known as Birkhoff’s theorem, is reminiscent of Newton’s “iron sphere theorem.” It allows us to solve the equations of motion for matter on the boundary of the sphere through a local analysis without worrying about the rest of the Universe. Therefore, if the sphere has exactly the same conditions as the rest of the Universe, we may deduce the global expansion history of the Universe by examining its behavior. If the sphere is slightly denser than the mean, we will infer how its density contrast will evolve relative to the background Universe.

For the moment, let us ignore the energy density of the vacuum (which is always a good approximation at sufficiently early cosmic times, when matter was denser). Then, the equation describing the motion of a spherical shell of matter is identical with the equation of motion of a rocket launched from the surface of the earth. The rocket will escape to infinity if its kinetic energy exceeds its gravitational binding energy, making its total energy positive. However, if its total energy is negative, the rocket will reach a maximum height and then fall back. To deduce the future evolution of the Universe, we need to examine the energy of a spherical shell of matter relative to the origin. With a uniform density, ρ, a spherical shell of radius r has a total mass M = ρ × (4π r³/3 enclosed within it. Its energy per unit mass is the sum of the kinetic energy due to its expansion speed v = Hr, (1/2)v², and its potential gravitational energy, –GM/r (where G is Newton’s constant), namely, E = v²/2-GM/r. By substituting the preceding relations for v and M, we can easily show that E = (1/2)v²(1 – Ω), where Ω = ρ/ρ_c, and ρ_c = 3H²/8πG is defined as the critical density. We therefore find that there are three possible scenarios for the cosmic expansion. The Universe has either (i) Ω > 1, making it gravitationally bound with E <0—such a “closed Universe” will turn around and end up collapsing toward a “big crunch”; (ii) Ω <1, making it gravitationally unbound with E > 0—such an “open Universe” will expand forever; or the borderline case, (iii) Ω = 1, making the Universe marginally bound or “flat” with E = 0.

Einstein’s equations relate the geometry of space to its matter content through the value of Ω: an open Universe has the geometry of a saddle with a negative spatial curvature, a closed Universe has the geometry of a spherical globe with a positive curvature, and a flat Universe has a flat geometry with no curvature. Our observable section of the Universe appears to be flat.

Now we are in a position to understand how objects like the Milky Way galaxy formed out of small density inhomogeneities that are amplified by gravity.

Let us consider for simplicity the background of a marginally bound (flat) Universe dominated by matter. In such a background, only a slight enhancement in density is required to exceed the critical density ρ_c. Because of Birkhoff’s theorem, a spherical region denser than the mean will behave as if it is part of a closed Universe and will increase its density contrast with time, while an underdense spherical region will behave as if it is part of an open Universe and will appear more vacant with time relative to the background, as illustrated in Figure 1.2. Starting with slight density enhancements that bring them above the critical value, ρ_c, the overdense regions will initially expand, reach a maximum radius, and then collapse on themselves (like the trajectory of a rocket launched straight up, away from the center of the earth). An initially slightly inhomogeneous Universe will end up clumpy, with collapsed objects forming out of overdense regions. The material to make the objects is drained out of the intervening underdense regions, which end up as voids.

(Continues…)

Excerpted from The First Galaxies in The Universeby Abraham Loeb Steven R. Furlanetto Copyright © 2013 by Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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