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.

## Sunday, July 12, 2009

## Sunday, July 5, 2009

### CMB Anisotropies (part 1: tricks with figures)

Now that we've had a week since the last post for us all to calm down about how exciting we found the giant map of pink representing the CMB and the implications that single color had for our understanding of the universe, I want to start talking about "anisotropy." Last week, I defined isotropy as meaning that everything looks the same in all directions. My mother, being a woman of letters, will immediately recognize that anisotropy must be the opposite - everything is not the same in all directions. In the last twenty years, it's been the anisotropy of the CMB that has really changed the physics world.

First, let's talk about the pink map one more time. What is actually being shown in that map is the temperature of the photons coming from that particular region of the sky (the map is elliptical because we are projecting a spherical surface [the sky around the earth] onto a flat space, much like flat maps of the globe are elliptical). The temperature is in this case a proxy for energy, and recall that the energy of a photon is related to its wavelength. Therefore, we can think of the pink map as showing the wavelengths of photons coming from different parts of the sky, and they all have about the same wavelength or temperature (about -270 degrees Celsius if you're interested).

Now, there's a subtlety here regarding contrast, because I never told you what the color actually represents in terms of temperature. If pink means any temperature between 0 and 4000 C, then no wonder the universe looks the same everywhere! To illustrate what I mean, I'm going to once again draw some of my own really high quality images. I have a gas stove in my apartment with 4 burners. When I turn those burners on, there are four hot spots on my stove. Let's assume the main part of the stove always stays at room temperature (70 degrees Fahrenheit or 21 C). Let's further assume that the temperature in the flame of my burners is 3500 F or 2500 C. I can represent this graphically in two different ways:

In the plot to the left, I've used a reasonable contrast, and we can clearly see the white that represents the room temperature part of the stove and the red that represents the hot part. But in the plot to the right, I've used such a big scale (or a small contrast), that the stove looks the same color, just like the map of the CMB.

Hopefully, you're now all asking the question, "so just how isotropic is the CMB?" since I can apparently make a plot that looks uniform just by changing the scale. The answer is that it is very isotropic, but not perfectly. The pink map is accurate up to 1 part in 1000. Basically, all the photons have the same temperature to within 0.1%. Which is pretty uniform. But, suppose we turned up the contrast, so that colors varied with that 0.1% (this would be analogous to switching from the right plot to the left). Now the CMB looks like this:

What about if we went even further, to a contrast of 1 part in 100,000 (this would be like looking for the difference between adding or subtracting a penny from 1,000 dollars)? Here is where the excitement really enters, but I'll talk about that in the next post (CMB plots courtesy of the WMAP homepage, as usual).

First, let's talk about the pink map one more time. What is actually being shown in that map is the temperature of the photons coming from that particular region of the sky (the map is elliptical because we are projecting a spherical surface [the sky around the earth] onto a flat space, much like flat maps of the globe are elliptical). The temperature is in this case a proxy for energy, and recall that the energy of a photon is related to its wavelength. Therefore, we can think of the pink map as showing the wavelengths of photons coming from different parts of the sky, and they all have about the same wavelength or temperature (about -270 degrees Celsius if you're interested).

Now, there's a subtlety here regarding contrast, because I never told you what the color actually represents in terms of temperature. If pink means any temperature between 0 and 4000 C, then no wonder the universe looks the same everywhere! To illustrate what I mean, I'm going to once again draw some of my own really high quality images. I have a gas stove in my apartment with 4 burners. When I turn those burners on, there are four hot spots on my stove. Let's assume the main part of the stove always stays at room temperature (70 degrees Fahrenheit or 21 C). Let's further assume that the temperature in the flame of my burners is 3500 F or 2500 C. I can represent this graphically in two different ways:

In the plot to the left, I've used a reasonable contrast, and we can clearly see the white that represents the room temperature part of the stove and the red that represents the hot part. But in the plot to the right, I've used such a big scale (or a small contrast), that the stove looks the same color, just like the map of the CMB.

Hopefully, you're now all asking the question, "so just how isotropic is the CMB?" since I can apparently make a plot that looks uniform just by changing the scale. The answer is that it is very isotropic, but not perfectly. The pink map is accurate up to 1 part in 1000. Basically, all the photons have the same temperature to within 0.1%. Which is pretty uniform. But, suppose we turned up the contrast, so that colors varied with that 0.1% (this would be analogous to switching from the right plot to the left). Now the CMB looks like this:

What about if we went even further, to a contrast of 1 part in 100,000 (this would be like looking for the difference between adding or subtracting a penny from 1,000 dollars)? Here is where the excitement really enters, but I'll talk about that in the next post (CMB plots courtesy of the WMAP homepage, as usual).

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