“I have an existential map. It has ‘You are here’ written all over it.” -Steven Wright
So just because the Ask Ethan series is becoming way more popular than I can handle — I’ve got more than 200 questions that I’m sitting on by now — doesn’t mean you should stop sending your questions! There are some really good ones, and today’s comes from Robert Plotner, who asks:
When maps of the CMB are depicted, they are shown as a flattened ovoid. How does this correlate to our view of the sky which is a sphere? For example, a global map of the Earth is either distorted to show it in two dimensions or sliced up. What actual part of the sky are we looking at when we see the CMB represented? Is it distorted to show it in two dimensions? If we are only seeing part of the sky represented, is there any missing information that could add to our understanding? Thank you.
Robert, of course, is talking about the famous pictures that look like this:
It might seem difficult to believe, but as unconventional as it may seem, there’s actually the entire sky encoded in that image.
Think about the Earth, if you will.
A map like this is probably what you’re used to when you visualize the Earth. Maybe if you live in the USA, you’re used to the Americas being centered; maybe if you live in the U.K., you’re used to the map being centered just so that France is cut off of both the left and right sides. In any case, this is the most common styling of maps of Earth that you’re likely to find.
It’s also wildly inaccurate. You might be surprised to learn that Africa is more than double the size of Antarctica, that South America is actually larger than Russia, and that Australia is more than three times the size of Greenland! This is due to the fact that the Earth isn’t a flat, 2D surface; the surface of the Earth resides on a sphere!
But if you take the surface of a sphere and try to “unroll” it, or create a flat surface out of it, it doesn’t work out nicely at all! Don’t believe me? Take an orange, peel it (carefully), and try to lay the peel down flat on a level surface. Chances are, if you do a really good job, you’ll end up with something like this.
The problem is, when you take a spherical surface and try to lay it out flat, something‘s going to give.
If you insist on making a flat map like you’re used to seeing for the surface of the Earth, you can make a completely connected map with nice grid-like (perpendicular) latitude and longitude lines, but you have to sacrifice the accuracy of area. (That type of map projection is called a Mercator projection.)
You can keep the accurate area and the perpendicular latitude/longitude lines if you’re willing to give up connectedness, like the Goode homolosine projection, above.
Or, you can do some sort of compromise, keeping a connected map with perpendicular latitudes/longitudes but compressing latitudes the higher they get, getting you closer to equal areas (but not quite there), as you can see below.
None of these are entirely satisfying, and they couldn’t possibly be! It’s impossible to keep perpendicular latitude/longitude lines, accurate areas, and a completely connected map without sacrificing something; that’s because the surface of a sphere isn’t flat, and it’s impossible for it to be accurately laid flat.
This is true for a map of the (almost plenispherical) Earth, and it’s true when we look up at the heavens, too.
So whenever we go to visualize the entire sky and present it in a two-dimensional format, we’ve got to sacrifice something. The only question is what it’s going to be!
Because size (or area) in astronomy is so important, that can’t be something we sacrifice. It’s also important to keep everything visually connected, because there are no gaps in space. So we wind up sacrificing the perpendicularity of latitude and longitude (or declination and right ascension, as we call their analogues in astronomy), and lose the accuracy of angles and shapes in order to preserve the things that are important to us. We could (but don’t usually) do the same thing to Earth!
This particular projection is known as a Mollweide projection, and if you remember those three things I told you about the Earth earlier:
- that Africa is more than double the size of Antarctica,
- that South America is actually larger than Russia, and
- that Australia is more than three times the size of Greenland,
they’re probably much easier to believe looking at a projection like this! Well, this is what we do to the sky — or simply how we project it — when we present it in a 2D visualization!
So rather than show you a shot of the galaxy like this, which is only part of the sky…
we show you the whole thing, as shown in a galacto-centric Mollweide projection!
When we look in the microwave portion of the spectrum, like the Planck spacecraft did, it sees everything from all the sources in the sky, including the galactic foregrounds, the zodiacal light and dust, as well as the primordial, cosmic light from the Big Bang.
And finally, when we subtract out those galactic foregrounds, the “average” 2.725 K blackbody temperature…
the CMB dipole, or our peculiar motion through the Universe,
that’s when we can finally see the important stuff from the CMB’s leftover glow.
We then break that up into its different components (using spherical harmonics), analyze it, and that’s how we learn about the Universe! But we do all of it in a Mollweide projection, and that’s why the maps of the sky appear in the shape they do! But there’s nothing missing; you’re seeing the whole sky all at once. It just takes a little getting used to.
So keep sending your questions, and I’ll keep teaching you about the Universe, or whatever it is you’re asking about!