What the WMAP image means

“It has been rightly said that nothing is unimportant, nothing powerless in the universe; a single atom can dissolve everything, and save everything! What terror! There lies the eternal distinction between good and evil.” –Gerard De Nerval

(For Rich C. and Sili, for their questions on this post.)

The humble hydrogen atom — one proton and one electron, bound together — is the most common form of normal matter in the entire Universe. When you look out at all the galaxies in the Universe, what you’re seeing is predominantly light coming from those simple hydrogen atoms fusing together at the cores of stars.

Image credit: Hubble Deep Field South, NASA/ESA.

Yet despite the huge amount of hydrogen, something like 1080 atoms in our observable Universe, there’s something far more abundant.

Light! If you want to understand where it comes from, we have to go back to the very early stages of the Big Bang. Not just back before there were atoms, but even before there were protons. The Universe was once so hot and dense that it was filled with what’s known as a quark-gluon plasma.

When you heat matter up to temperatures above two trillion Kelvin (!), the fundamental components of nuclei — quarks and gluons — become so energetic that calling groups of them things like “protons” and “neutrons” doesn’t make sense anymore.

Instead, quarks, gluons, and anything else that’s energetically allowed, simply exists in an unbound state.

Well, the Early Universe had temperatures that put two trillion Kelvin to shame! And the hotter you turn up the furnace, the more stuff you make! In fact, in the earliest times, you not only made all the particles in the standard model…

…you also made all the anti-particles in the standard model!

All told, in the very early stages of the Universe, what you think of today as radiation — namely, photons, or particles of light — was less than 2% of the total amount of particles present. (And if there’s new physics at high energies, like supersymmetry, extra dimensions, or grand unification, it might be even less than that!)

But remember the most important property of the Universe in the cosmological standard model: it’s expanding and cooling as it ages.

One result of this is that less and less energy is available, so it gets harder and harder to make these heavy particles. Another result is that they’re progressively farther apart, meaning that they start to condense into bound objects: baryons and mesons. And finally, because the Universe is aging all this time, the unstable particles that you’ve made decay!

Image credit: CERN.

Some of the particles that decay are (likely) responsible for creating the matter/antimatter asymmetry in our Universe, but the vast majority decay into truly stable radiation: photons and neutrinos.

The net result is that our Universe is filled with something like 1080 protons (and electrons), but something like 1090 photons. In other words, we have over a billion photons for every “atom” we’re going to wind up with. For many thousands of years, protons and electrons combine to form neutral atoms. But every time they do, an energetic enough photon comes along in very short order and kicks the electron out, keeping us in a plasma-like state. So we wait.

The Universe continues to expand and cool, and will do so until it’s cool enough to form neutral atoms for the first time.

What determines when this happens? Well, remember how I said that photons outnumber atoms by more than a billion to one? That means that not only does the average photon energy need to be unable to ionize a hydrogen atom, but that less than one out of every billion photons needs to have enough energy to ionize it.

Image credit: COsmic Background Explorer team.

So that very tail-end of the spectrum needs to drop below the ionization energy/temperature of hydrogen. This happens when the Universe cools to a temperature of about 3,000 Kelvin, almost two orders of magnitude lower than what it would need to cool to if the number of atoms and photons are the same.

When you finally cool down enough to form neutral atoms — when the Universe is about 380,000 years old — that radiation left over from the Big Bang can finally travel to you in a straight line, cooling as the Universe expands, and reaching our satellites and telescopes today, 13.7 billion years later.

Image credit: WMAP team, and NASA.

On average, we see that leftover radiation at 2.725 Kelvin, but when we look at even finer resolution, we can see what the fluctuations are in that radiation! That’s what this famous WMAP image shows us: how much hotter or cooler each individual place in the sky is from its “average” temperature of 2.725 Kelvin.

Now that you know what causes it and where it comes from, we can ask the big questions: what does this sky map mean, and what do we learn from it?

First off, this ellipse shows the entire sky. The plane of the galaxy has been subtracted out to the best of our abilities, and the minimum resolution of this image is between about 0.1 and 0.2 degrees, limited only by the sensitivity of our instruments.

What we then do is look at different sections of this map. For example, we might break it up into four equal chunks, and look at what the average temperature is in each of those four chunks, and see how far they deviate from the average. We might then try again, except this time, we break it up into twice as many chunks. And we do it again and again, seeing how the magnitude of the average fluctuations change as our scale changes.

And we do this up to the maximum resolution of our images, measuring what the average temperature fluctuations are on a whole slew of different scales. And, as we like, we can make a graph of what this looks like!

So when you see this graph, that’s what we’re looking at! For instance, the maximum average temperature fluctuations — of around 70-80 micro Kelvins — happen on scales of just about one square degree.

This is incredibly interesting for learning about the Universe! Why? Because, according to our leading theories, the Universe began with equal fluctuations on all scales! But by time the Universe is 380,000 years old, that is very clearly not the case anymore. Why not?

Because structure has started to form! The slightly overdense regions have started to grow; the slightly underdense regions have started to shrink. Radiation pressure has pushed small collapsing regions back outwards (in some small-enough regions, multiple times), but hasn’t had time to push large enough ones outwards even once!

In short, the patterns that come out of these fluctuations are very sensitive to the amount and type of matter and radiation both in the Universe at that time — when it’s 380,000 years old — and also how it’s been expanding since.

So when we analyze this data, we can learn how much matter (and of what different variety) exists in the Universe at any given time!

And this is what we find! For those of you who are curious about what percent of the Universe was in what form of energy at different epochs, I’ve taken the liberty of creating a chart for you that displays just that.

And that’s what the WMAP image means, where it comes from, and what we use it for!