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:

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.

## Monday, August 30, 2010

## Friday, August 20, 2010

### 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.

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.

Labels:
CMB,
fourier analysis,
WMAP

### A little more about me and the blog

I've talked to a few people in the last few weeks who asked me to write a bit more of an introduction to both me and what I'm trying to do with this blog, so here goes:

My parents are both extremely intelligent people. Before he retired, my father was in academic publishing as an editor for several years before running the Princeton University Press for the last 20 years of his career. My mother is a writer, author of several books on a rather wide-ranging list of subjects including gardening, architecture, biographies of several people and two novels. I grew up surrounded by books on history, literature, politics, etc. Despite this rather literary background, however, all through school I somehow found myself doing my best work in math and science. I graduated college with a physics degree, but I did not then know what I wanted to do (nor did I have a job). Fortunately, my thesis advisor in college, Dan McKinsey, was hired as a professor at Yale University that summer and asked me to come work for him while I figured things out. Seven years later, I left Yale with a PhD in physics and I think it's pretty safe to say that I am now trying to make a career as a practicing physicist.

Although my family has gotten used to this idea during the (many) years spent lost in graduate school without a real job, I think it's still a bit of a mystery to them how I ended up as a scientist. And perhaps more importantly, I've often felt that they (and in particular, my mom) really don't know what I do nor how I do it. While the question of how I ended up here is sometimes a mystery to me (as far as I can tell, I like doing the physics I do and figure I should keep at it as long as people let me), the second mystery is something I should be able to do something about, especially if I want to be a good physicist. Hence this blog.

I truly do want to try to explain my work so that my family, and my mom in particular, understands. As I said before, my mom is a very intelligent woman, but she tends to be a touch skittish around mathematical ideas. And if I can explain things like dark matter in an understandable way to her, it will mean that I myself understand what I'm doing. More generally, I've found over the years that people I meet really have a lot of interest in physics, but they always say, “I was no good at it” or even worse, “my teacher was terrible.” In the blog, therefore, I'm trying to write about what I'm doing and why it's interesting in a way that does not require any background while simultaneously not underestimating the audience.

Once I started writing, I quickly discovered the particular format I wanted the blog to take, which I outlined at the bottom of this post: Update and future plans. So that's the summary.

Also, here's a picture of me at my sister's wedding. I'm trying to be funny here.

My parents are both extremely intelligent people. Before he retired, my father was in academic publishing as an editor for several years before running the Princeton University Press for the last 20 years of his career. My mother is a writer, author of several books on a rather wide-ranging list of subjects including gardening, architecture, biographies of several people and two novels. I grew up surrounded by books on history, literature, politics, etc. Despite this rather literary background, however, all through school I somehow found myself doing my best work in math and science. I graduated college with a physics degree, but I did not then know what I wanted to do (nor did I have a job). Fortunately, my thesis advisor in college, Dan McKinsey, was hired as a professor at Yale University that summer and asked me to come work for him while I figured things out. Seven years later, I left Yale with a PhD in physics and I think it's pretty safe to say that I am now trying to make a career as a practicing physicist.

Although my family has gotten used to this idea during the (many) years spent lost in graduate school without a real job, I think it's still a bit of a mystery to them how I ended up as a scientist. And perhaps more importantly, I've often felt that they (and in particular, my mom) really don't know what I do nor how I do it. While the question of how I ended up here is sometimes a mystery to me (as far as I can tell, I like doing the physics I do and figure I should keep at it as long as people let me), the second mystery is something I should be able to do something about, especially if I want to be a good physicist. Hence this blog.

I truly do want to try to explain my work so that my family, and my mom in particular, understands. As I said before, my mom is a very intelligent woman, but she tends to be a touch skittish around mathematical ideas. And if I can explain things like dark matter in an understandable way to her, it will mean that I myself understand what I'm doing. More generally, I've found over the years that people I meet really have a lot of interest in physics, but they always say, “I was no good at it” or even worse, “my teacher was terrible.” In the blog, therefore, I'm trying to write about what I'm doing and why it's interesting in a way that does not require any background while simultaneously not underestimating the audience.

Once I started writing, I quickly discovered the particular format I wanted the blog to take, which I outlined at the bottom of this post: Update and future plans. So that's the summary.

Also, here's a picture of me at my sister's wedding. I'm trying to be funny here.

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