Monday, August 30, 2010

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

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:

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.

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