## 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).