The cosmic "dark ages"

In brief, "dark ages" refers to the period after recombination occurred, about 380,000 years after the big bang, creating the cosmic microwave background (CMB), up to and partly including the time that the first stars had formed, perhaps as early as four hundred million years later, and caused the reionization of much of the neutral hydrogen in the universe.

That's a mouthful, but it's important to understand in order to have a useful discussion of the conditions that existed when the first stars and first galaxies in the universe formed. Many important open questions in astrophysics right now have to do with the nature of these events. Since I expect to discuss some of these questions, it's necessary to say some things about the "dark ages". That's what this note is about.

Let's start with the CMB. I'm going to give just a sketch. You might want to consult other references if you need more detail.

The period of time in which the CMB emerged is also known as the period of recombination. This was not an instantaneous process, but it did proceed relatively quickly, and is often thought of as a single event.

Basically, before recombination matter (mostly hydrogen and helium) and energy (light, i. e. photons) existed in thermal equilibrium. That is, the following reaction could occur with equal probability in either direction:

H + γ ⇄ p + e^-

Here, H stands for a hydrogen atom (with one electron), γ is a photon, p is a proton, and e^- is an electron. (We'll ignore helium, for simplicity.) What this formula says is that a photon of sufficient energy could dislodge an electron from a hydrogen atom to form a proton and a free electron, and with equal probability protons and free electrons could combine to form a hydrogen atom and a photon.

As the universe cooled after the big bang, the average temperature of the matter-energy plasma steadily dropped. Before the period of recombination, hydrogen atoms could exist, but not for very long, because most photons had enough energy to completely dislodge an electron, so the reaction went from left to right as often as from right to left.

Over a period of time lasting a few tens of thousands of years the situation changed so that most photons no longer had enough energy to dislodge an electron. (A low energy photon could still interact or "scatter" with a hydrogen atom by raising an electron to a higher energy level, but we can gloss over that detail.) Note that the average or "typical" photon energy may be a lot lower than what's needed to dislodge an electron, as long as there are still enough higher-energy photons around. This is a statistical situation governed by the Maxwell-Boltzmann equation, but all that really matters is that eventually photons and neutral hydrogen atoms "decouple" statistically.

So at some point you have recombination, when electrons combine with protons to make neutral hydrogen, and the process (mostly) doesn't reverse. Occasionally, a photon and a hydrogen atom may still interact, but as the universe expands, it's increasingly less likely for a photon and an atom to come close enough to interact, until the probability of interaction is essentially zero. This second stage is sometimes referred to as "decoupling" of matter and photons.

Thus the period of "dark ages" began right after the relatively brief process of recombination and decoupling. For simplicity, we date this point to a single time when the process was about half complete, roughly 380,000 years after the big bang.

This period is termed "dark", even though there were plenty of photons around, because there were as yet no stars or other compact sources of illumination. (There's another reasons for calling it "dark", which we'll get to in a moment.)

CMB photons have a nearly perfect black-body distribution. There is a clear peak of maximum energy in this distribution. What we observe is that this peak occurs at about 2 mm, in the microwave part of the spectrum. But the time of decoupling, 380,000 years after the big bang, corresponds to a redshift of z≈1100, so at the time of decoupling the peak photon energy was around a wavelength of just 2.2 μm (2200 nm) in the infrared part of the electromagnetic spectrum. (If you need to refresh your memory about how redshift works, check here.) So "dark" is not exactly the right term to use, but compared to abundant light from stars, it's not unreasonable.

After the time of recombination/decoupling, most hydrogen and helium atoms were neutral and un-ionized. This went on for several hundred million years. One of the most interesting open questions is about determining more exactly how long this lasted. We can reasonably guess what probably brought the dark ages to an end: formation of the first stars in the universe. But we don't have a good idea of just when this started, or how long the process took.

In this period, matter was beginning slowly to come together in higher-density clumps under the force of gravity. Dark matter, which outweighed ordinary matter then (as now), by a ratio of about 5.5:1 speeded up this process.

It was precisely this formation of regions of higher matter density that enabled the first stars to form. But because of this same higher density of matter around newborn stars, the abundant high-energy photons produced by these stars were again likely to interact with the nearby un-ionized matter, which scattered them and reduced their energy – dimming the light of these first stars.

One of the large uncertainties concerns the characteristics of this first generation of stars. We have no direct evidence about them. What we think we know about them is based on theoretical models rather than direct observation. (We discussed formation of the first stars back here.) However, it's widely believed that these stars were unlike stars formed later, right up to the present time. The first stars were probably quite large (maybe as much as 200 solar masses), very hot, and very bright. Because they burned their fuel so rapidly, their lifetimes would be very short, perhaps less than a million years.

Some of the light from extremely hot, massive stars such as those of the first generation is well into the ultraviolet part of the spectrum, around 90 nm. Such photons have an energy above 13.6 eV (91.2 nm wavelength), enough to completely ionize hydrogen. If these stars formed, say, 400 million years after the big bang, at a redshift of z≈11, the wavelength of their light would be shifted to the area beyond 1100 nm, which is in the infrared. That's beyond the range of human eyes, or most astronomical instruments. Consequently, we would have a very hard time detecting light from the first stars, even if they weren't so far away (over 13 billion light-years) and obscured by clouds of atomic hydrogen. That time period would still seem "dark" to us – there would be very little we could "see".

However, the first stars radiated so much energy, especially at ultraviolet wavelengths, that over time they effectively reionized all of the hydrogen in their vicinity. And this is (probably) what brought about the epoch of reionization in the universe, effectively ending the "dark ages".

The first stars were probably not part of galaxies, though we don't know for sure. If that's the case, they would be even harder to observe. The first objects we will be able to detect from this period almost certainly will be galaxies or quasars (which are galaxies with a very active central black hole). So the question of when galaxies began to form is separate, but equally puzzling. There is evidence that the first galaxies in fact did form before the end of the dark ages – because we can actually observe a few that show evidence of un-ionized hydrogen.

What we can say for sure is that the first stars must have consisted only of the primordial elements hydrogen and helium, since heavier elements (except for a small trace of lithium) formed and dispersed only when the first stars exploded as supernovae. But that did happen rather quickly, since the first stars were very luminous, and consequently had very brief lives.

As noted, we aren't very sure about when this first generation of stars appeared, because we can't yet observe them directly. But we do have some evidence concerning the epoch of reionization, and hence we have some idea of when it ended.

One kind of evidence involves studying the spectra of some of the most distant objects we are currently able to observe – quasars. We have detected a number of quasars at redshifts between 6 and 7. This range represents a time period from about 780 to 950 million years after the big bang.

There are absorption lines in the spectra of these quasars, and they tell us not only about the redshift, but give other information as well. Among the most important lines are those due to hydrogen that's not fully ionized, such as lines of the Lyman series. For the most part these lines are due to hydrogen in the vicinity of the source, in which case the lines are quite sharp and distinct.

But suppose there is a substantial amount of incompletely ionized hydrogen between us and the source. If this gas is at a distance sufficiently less (in terms of redshift), the absorption lines will be fuzzy instead of sharp. This effect is called a Gunn-Peterson trough.

In 2001 a quasar was identified at z=6.28, which showed a Gunn-Peterson trough, while other quasars with z≤6 did not. This suggests that reionization was mostly complete by 950 million years after the big bang, but not by 900 million years. [1][2]

Quasars, by themselves, are a possible contributor to reionization, in addition to the earliest stars. Quasars certainly produce enough high-energy photons. However, the question is whether there were enough quasars in existence during the epoch of reionization to account for the effect. Since only the very brightest quasars can currently be observed at that distance (z≥6), it's not possible to reliably estimate how many quasars altogether were around then. Rough estimates suggest there weren't enough.

There is another source of evidence for reionization, one very different from the Gunn-Peterson trough. This involves a very detailed study of anisotropies (irregularities at small angular scales) in the CMB. The CMB has many anisotropies due to conditions existing from the earliest moments after the big bang. However, if reionization occurred, certain kinds of additional characteristic anisotropies will also be present. These result from polarization of CMB light due to Thomson scattering of photons by free electrons (if such exist in sufficient numbers). Since free electrons are a by-product of reionization, they provide a very good marker, if they can be detected.

Unfortunately, the earliest data analysis (in 2003) from the Wilkinson Microwave Anisotropy Probe suggested that reionization occurred in the range 11<z<30, which corresponds to a mere 100 million to 420 million years after the big bang. This is not compatible with the quasar evidence. It's also rather implausible at the high z end, if reionization was caused by the first stars.

Fortunately, however, later data analysis (released in 2008) restated the range for reionization to 7≤z≤11. [3] z=7 still doesn't quite mesh with the quasar data, but it's pretty close. z=11 corresponds to 420 million years after the big bang, which is quite plausible for appearance of the first stars. Note that if this range is correct, then the reionization process took a lot of time, maybe 400 to 500 million years. First generation stars almost certainly weren't around that long. Such stars have very short lifetimes, and new stars of this kind can't form, because the gas from which they could form would contain considerable amounts of elements heavier than helium, precluding the formation of more stars like those of the first generation.

A third possible source of evidence comes from surveys looking for very faint, high-redshift galaxies (not quasars). Some objects have been found up to z=7.5 – about 710 million years after the big bang. [4] What isn't clear is whether these objects were either abundant enough or had hot enough stars to contribute significantly to reionization. But when the James Webb Space Telescope goes to work, sometime after mid-2013, we should be able to find many more early galaxies. The planned upgrade to the Hubble Space Telescope this year would also help – if it occurs.

Further reading:

[1] Evidence for Reionization at z ~ 6: Detection of a Gunn-Peterson Trough in a z = 6.28 Quasar – 2001 research article on first evidence for reionization (open access)

[2] First Light: Astronomers Use Distant Quasar To Probe Cosmic "Dark Age," Universe Origins (8/8/01) – press release describing the preceding research

[3] A New Day in Precision Cosmology (3/11/08) – news article describing analysis of WMAP data, including information on reionization

[4] Largest Sample Of Very Distant Galaxies Ever Seen Provide New Insights Into Early Universe (7/24/08) – press release

Tags: cosmology, cosmic dark ages

Searching for dark energy... at the South Pole

Not all experimental astrophysical studies require elaborate, incredibly expensive equipment deployed at the L2 Sun-Earth Lagrangian point, like WMAP. A lot can be done with a microwave antenna just 10 meters across... if it's located at the South Pole.

Cosmologists Probe Mystery Of Dark Energy With South Pole Telescope

What can the SPT tell us about the past and future of dark energy? John E. Carlstrom, director of KICP and the S. Chandrasekhar Distinguished Professor in Astronomy and Astrophysics at the University of Chicago, says the telescope is examining clusters of galaxies to learn what role dark energy played in their evolution. “One of the important things we need to learn about dark energy is what influence it has had on structure,” Carlstrom says. If scientists can learn how the density of clusters changed over time, he says they can determine “constraints on the equation of state of dark energy.” That is, they can get a more precise idea of whether dark energy is taking us toward a big rip, a big crunch or something in between.

The telescope is looking specifically for the Sunyaev-Zel’dovich (SZ) effect, a distortion of the CMB radiation caused by the highly energized gas of galaxy clusters. When photons originating from the CMB traverse the clusters, they interact with electrons and tend to scatter, creating slight variations in temperature -- shadows against the microwave background – that the SPT detects with a battery of 1,000 sensors chilled to near absolute zero.

The SPT will survey about a fifth of the entire southern sky and is expected to detect thousands of clusters. Analyzing follow-up data from optical telescopes, the scientists will determine the mass, distance and age of the clusters. They will then map the clusters in space and time to see how their density and structure evolved over billions of years under the competing pulls of gravity and dark energy. They hope to learn how much power dark energy exerted in the early universe, how it evolved to dominate the universe now, and by extension, how much power it may wield in the future.

But the SPT isn't adapted only for studies of dark energy. As a sensitive microwave telescope, it can also make detailed observations of the cosmic microwave background, much as WMAP does.

The SPT’s activity will not end with this survey of galaxy clusters. Another project in the works will use the telescope to scan the CMB for tiny fluctuations in its polarization. Like visible light, the microwave radiation from the Big Bang has waves moving in electromagnetic fields at different angles, some up-and-down and other side-to-side. Observations with another South Pole instrument, the degree angular scale interferometer (DASI), have confirmed that the CMB is polarized as expected from prevailing theories about the physics of the Big Bang. Researchers now want to use the more sensitive SPT to look for minute variations in the CMB polarization that mark the presence of huge gravity waves.

Stephan Meyer, associate director of KICP and Professor in Astronomy and Astrophysics at the University of Chicago, says these waves are “a reasonable fraction of the size of the universe” in length and would have been generated in the “inflationary epoch” of the Big Bang. This was the time when the universe was just 10^-50 seconds old and matter had not yet coalesced into neutrons and protons. “We don’t really understand the physics of that era,” Meyer says. A new set of sensors, able to detect polarization as well as heat, is being built by the University of Chicago and should be ready for installation on the SPT by the austral summer (the northern winter) of 2009-10.

Tags: dark energy, cosmic inflation

Inflation and the cosmic microwave background

About three weeks ago I wrote a little about the cosmic microwave background (CMB), and talked about writing more. So here's a little more. The CMB is microwave radiation we can (almost) literally "see" even though it originated only about 350,000 years after the big bang. (I'll explain more in a minute about what "originated" means in this context.)

There are a number of things very wonderful and remarkable about the CMB. Not only is it one of the major pieces of evidence supporting the big bang theory in general, but it also gives us much information about things as diverse as the relative proportions of ordinary matter and dark matter in the universe, the overall curvature of the universe ("flat", "convex", or "concave"), and the ratio of the number of baryons (protons and neutrons) to photons in the universe.

Further, of particular concern here, the CMB provides a means of testing a theory – the theory of cosmic inflation – that describes a much different period of time than that of the CMB itself, a period of time that began only about 10^-35 seconds after the big bang itself. The theory of inflation comprises a range of models describing what may have happened at that time. If there is any truth at all to the theory, the CMB can help narrow the range of acceptable models.

I have a couple of older articles on this from back in March/April here and here. These deal with the announcement back then of analysis of data from the Wilkinson Microwave Anisotropy Probe (WMAP) that, among several other things, gave the first reasonable evidence for inflation.

Rather than dive right away into further explanation of that, I'm going to refer you first to this excellent recent article on the subject by Sean Carroll: Reconstructing Inflation.

What's that, you say? It sounds impressive, but you don't quite follow the details? OK, let's step back for a moment and review the basics. The picture below is a graphical representation of the main data obtained from WMAP:

This picture shows slight variations in temperature across the entire sky, at microwave frequencies, where blue represents coolest and red represents warmest. The variations are actually very small: the whole range is ± 200 microKelvins (millionths of a degree K).

Temperature differences correspond directly to differences in matter density – because a gas under higher pressure is warmer and denser than the same gas under lower pressure (the "combined gas law"). So what we see here are minute ripples of higher and lower pressure in the matter of the universe at roughly 350,000 years after the big bang. What has caused these pressure waves? Carroll's article explains

The same basic mechanism works in both cases — quantum fluctuations (due ultimately to Heisenberg’s uncertainty principle) at very small wavelengths are amplified by the process of inflation to macroscopic scales, where they are temporarily frozen-in until the expansion of the universe relaxes sufficiently to allow them to dynamically evolve.

The spots and blotches you see in this picture are shadows on the wall, as it were, of quantum fluctuations that actually occurred 10^-35 seconds after the big bang. At first, in a period that lasted perhaps only 10^-33 seconds, these fluctuations were inflated at an incredible rate. Thereafter, they continued to expand along with the rest of spacetime itself, until we see them projected on the CMB wall 350,000 years later.

To be more precise, we should note that this metaphorical CMB "wall" did not form at some single precise time. Instead, the CMB itself is a result of most of the hydrogen and helium matter in the early universe making the transition from an ionised plasma to an ordinary gas of neutral atoms, as free electrons were "captured" by the hydrogen and helium ions. Consider, for simplicity, just the hydrogen. It takes 13.6 eV (electron volts) of energy to separate an electron from a hydrogen atom. In the early universe when the typical photon had much more than this energy, atomic hydrogen could not exist for long, as most passing photons could "liberate" the electrons. But when the energy of the typical photon dropped, as the universe expanded, to the equivalent of around 13.6 eV, hydrogen atoms became stable for longer periods of time. This is known as the period of "recombination" (even though prior to this, protons and electrons had never been in a "combined" state). Once there was a lot of atomic hydrogen, photons of the most common energy levels "scattered" from the atomic hydrogen, and the universe was somewhat opaque to those photons.

But as the temperature dropped further, most photons did not have enough energy to liberate electrons from hydrogen atoms. So most photons ceased to scatter from atomic hydrogen, and the universe effectively became transparent again. Although this happened over a relatively short period of time, it was not instantaneous. By the time that most hydrogen was in an unionized state, a typical photon never again scattered off a hydrogen atom. So around any present observer, there is a "surface of last scattering". Assuming what are currently considered the most likely cosmological parameters, this corresponds to a time about 13.3 billion years ago (equivalent to a red shift of about 1100), about 350,000 years after the big bang. This surface of last scattering is what we see today as the CMB. The temperature of the universe at this time of last scattering was about 3000° Kelvin, but due to the subsequent expansion of the universe, the CMB photons now have an energy that peaks around 2.725° K, in the microwave part of the spectrum.

There is another way to represent the WMAP data for the CMB. You've probably seen it in some form. (It's in Carroll's article, if you read that.)

The vertical scale on the left is a measure of the amplitude of temperature fluctuations. The top and bottom scales are measures of angular size. 90°, for instance, is one fourth of the whole sky. The "multipole moment" (l) is an integer that corresponds to an angular measure of 180°/l. So, for instance, the peak on the above graph occurs around l=200, which is slightly less than 1°. For comparison, the angular size of the full moon viewed from earth is about .5°. What the graph is saying, roughly, is that strongest temperature fluctuations (spots in the picture above the graph), if you could see them with your naked eyes, are almost twice the angular size of a full moon. (Astrophysicists use multipole moments, since they are the relevant identifiers of "spherical harmonic" functions that are used to construct a series representation of the function which describes theoretical temperature variations, similar to the way that a Fourier series can represent a function of one real variable.)

The small dots on the graph are WMAP measurements for various values of l. They come with error bars, which are mostly too small to see, because the WMAP measurements were mostly pretty precise. The red line through the measured values is the theoretically predicted values, assuming that the temperature variations are actually the result of quantum fluctuations that occurred in the inflationary period. The locations of the two peaks to the right of the main peak are especially important, and they correspond fairly well to theoretical predictions.

Carroll's article explains how there are actually two kinds of perturbations we might potentially observe in measured quantities: "scalar" and "tensor", reflecting the fact that Einstein's equation describing gravity waves (which result from the inflation-era quantum fluctuations) is a tensor differential equation. Further, all that we can readily measure from the WMAP data are scalar perturbations:

To date, we are quite sure that we have detected the influence of scalar perturbations; they are responsible for most, if not all, of the temperature fluctuations we observe in the Cosmic Microwave Background. We’re still looking for the gravity-wave/tensor perturbations. It may someday be possible to detect them directly as gravitational waves, with an ultra-sensitive dedicated satellite; at the moment, though, that’s still pie-in-the-sky (as it were). More optimistically, the stretching caused by the gravity waves can leave a distinctive imprint on the polarization of the CMB — in particular, in the type of polarization known as the B-modes. These haven’t been detected yet, but we’re trying.

Problem is, even if the tensor modes are there, they are probably quite tiny. Whether or not they are substantial enough to produce observable B-mode polarization in the CMB is a huge question, and one that theorists are presently unable to answer with any confidence.

The WMAP experiment was capable of studying polarization of CMB microwaves only rather crudely. But a new experiment is due for launch very soon (early 2007) in the form of the European Space Agency's Planck mission. Considering that it took several years to analyze WMAP data, we may not have better information right away – but it won't be too long, if everything goes reasonably well.

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Further information about CMB:

Wilkinson Microwave Anisotropy Probe

NASA web site of WMAP, containing background information, images, and graphs.

Wayne Hu's Home Page

One of the best collections of CMB information, including an introduction, explanation of the physics, and discussion of CMB polarization.

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Tags: astrophysics, cosmology, cosmic microwave background, CMB, Microwave Anisotropy Probe, WMAP, cosmic inflation