Understanding the CMB

How do scientists understand the CMB? At this stage, I think we can try to outline the whole process. Over a year ago, I described the CMB as a sea of photons streaming through the universe, not interacting with anything until they reach us on earth. These photons are microwaves and can be picked up by radio antennas; at one point in time, the snow that people saw on their old television sets with bunny-ear antennas contained a component of the CMB. As I described here, the first group to observe the CMB initially interpreted it as an unexplained source of noise in their state of the art radio equipment.

To make the very sensitive measurements necessary to understand this today, we need to measure the CMB in space, where there is less interference from man-made radio backgrounds and the atmosphere. Therefore, in the 1990s, a group of scientists developed the WMAP satellite, which was flown by NASA at the beginning of the 2000s and has been collecting great data ever since.

(Personal aside: the WMAP satellite was originally the MAP satellite. The W was added in honor of Prof. David Wilkinson of Princeton University who passed away in 2002. I had the good fortune of being taught by Dave as a sophomore in college when I didn't know the first thing about experimental physics, and I also worked with him for a summer on the Search For Extraterrestrial Intelligence project [a topic for another time, perhaps]. He was a really great teacher, a wonderful man and one of the reasons I am a physicist today. It's nice that his work has had such a profound influence on physics research today.)

The WMAP satellite detects the CMB as it streams in from all directions, and the data can be used to produce the lovely CMB map that I keep showing. But what is this map? Essentially, it's sort of the inverse of a world map. As we know, the earth is a sphere and flat world maps are projections of that sphere onto a flat surface, as in this nice illustration taken from www.nationalatlas.gov:

The CMB map is very similar. If you look out into the sky the same distance in every direction, you would map out the inside of a spherical surface. Then you could project what you saw onto a flat surface just like the globe projects onto a flat world map. The result is the CMB map.


Ok, now what? We have a map of all the little temperature fluctuations in the CMB photons coming from all directions of the sky. Well, the CMB scientists use a version of Fourier analysis to find correlations in these temperature fluctuations. For those who want more mathematical detail, in the series on Fourier analysis, I stated that any function could be obtained by summing sine functions of different frequencies. Well, there are a class of functions similar to the sine function called Spherical Harmonics that can in most cases recreate any two dimensional function, and the spherical harmonics have many of the same properties as the sine function when it comes to integration. Therefore, one can multiply the two-dimensional signal by a spherical harmonic of a given "frequency" and integrate just as one would in Fourier analysis to find the amount of the signal described by that particular frequency. And the result is something that looks like the following:

Courtesy WMAP/NASA Science Team

This is analogous to the breakdown of the A chord into frequencies, with the difference that "l" or the "multipole moment" refers to the way frequencies are understood in spherical harmonics. Just as the Fourier transform shows us how much of a signal is contained in different frequencies, this plot shows us how much of the CMB are correlated over different angular scales (the lower x-axis in the plot). For example, much of the CMB signal is contained around an angular scale of between 2 and 0.5 degrees. What does that mean? It means that the map is not just a random collection of fluctuations, but that regions separated by about 1 degree are related to each other.

This is a fairly dense post, so I'll leave it at that for now and come back later if I get questions. Next, we'll talk about how the angular correlations tell us about the universe.

Back to the CMB

Over a year ago now (I have been really delinquent), I started talking about the CMB. If you recall, the CMB was like a picture of the universe as it was very early on after the Big Bang. And in this post, I said the following: "using the [noise in the] CMB, we can understand the age of the universe (13 and a half billion years), the geometry of the universe (flat), the amount of energy and density in the universe (the pie charts in the first post of this blog, including the 23% accounted for by dark matter [there is a connection between this and what I have been talking about until now, after all]), the rate of expansion of the universe, and other things."



Now that we've been through the whole sequence on Fourier analysis, we can start to understand how we extract that kind of information from a map that looks completely random to the eye. The key is that by applying a variation of Fourier analysis to the map in the picture, we can look for correlations between the fluctuations in the noise. As I explained it, Fourier analysis was able to extract how much of an apparently noisy and random signal was contained in different frequencies - for example, it could pull the individual notes out of the idealized A chord.

An artificially noisy A-chord.


The Fourier transform of the A-chord, with constituent frequencies easily visible.

In that example, the Fourier analysis effectively looks for correlations in time. Because the signal was made up of discrete frequencies, different parts of the signal were related to each other. For example, the A note has a root frequency of 440 Hz, or 440 cycles per second. What that means, although it can be hard to see by eye, is that two parts of the signal separated by 1/440 seconds are related in the way they appear, and the Fourier transform picks up on that. The premise of the CMB analysis is that two areas on the CMB map are also related in the way they appear (just not by eye). Instead of looking for time correlations, they look for spatial correlations in the map using a similar algorithm to the Fourier transform described above. In the next post, I'll show how they decompose the map shown above into its underlying angular or spatial frequencies.

CMB Anisotropies (part 2)

The Dipole
The above picture is an image of the temperature variation in the CMB with the contrast turned up to 1 part in 1000. Therefore, there is about 0.1% difference between the left side and the right side. This particular pattern appears fairly often in physics and is known as a dipole (there are two "poles" where the temperature is hotter or colder and the rest of the distribution stems from those two centers). Why is there such a distinct pattern in the temperature distribution?

The answer lies in the Doppler effect, which we've talked about at length before. In fact, we've talked about everything we need to explain this pattern. I've mentioned that the temperature is similar to the energy, so that we're effectively showing the energy of the CMB photons as a function of where they are coming from. And we know that the energy of a photon is related to its frequency. Therefore, the above picture shows the change in frequency of photons coming from one direction or another. We know that galaxies rotate, including our own. And finally, we know from the Doppler effect that the relative velocities of a source and an observer can change the observed frequency of light.

Mom, can you now guess why this pattern looks the way it does (I'm not sure how I feel about directly addressing anyone in this blog, since there's clearly no possibility of a direct response, but I'll leave it for now)? If you guessed that the Earth's motion through the galaxy resulted in a Doppler shift of the CMB photons depending on whether they are coming from in front of us or behind us, you would be exactly right. In effect, the Earth (and the Sun and the entire solar system) is moving towards one of those poles and away from the other, and thus we see the Doppler shifted dipole pattern shown above.

That is pretty interesting, but not revolutionary. We understand the Doppler effect and we know our galaxy is rotating, so if that were the only thing in the CMB anisotropy, it wouldn't be that big a deal. The real excitement (I keep pushing it forward, don't I?) arrives when we subtract the dipole effect (it's fully understood, so we can do that), leaving the smaller part in one hundred thousand variations.



Tiny variations
Finally (finally!), I will talk about what the CMB is showing us. The above is a map with the contrast turned up to that part in 100,000. And now there's no obvious pattern, which is good, because the universe is supposed to look the same in all directions. Basically, these little fluctuations are the imprint of noise in the very early universe (remember, at one point I described the CMB as a snapshot of the universe at 400,000 years old). And by studying the distribution of this noise, we can infer things about the properties of the universe.

I plan on going into this in more detail (with a detour through something called Fourier analysis), but using the CMB, we can understand the age of the universe (13 and a half billion years), the geometry of the universe (flat), the amount of energy and density in the universe (the pie charts in the first post of this blog, including the 23% accounted for by dark matter [there is a connection between this and what I have been talking about until now, after all]), the rate of expansion of the universe, and other things. I think (and I hope you agree with me) that this is really impressive - this one measurement has answered several deeply fundamental cosmological questions about how the universe works all in one go, just by carefully studying the snow picked up by the rabbit ears on my mom's now useless analog television set.