the simple science of rings around stars

I was intruiged by a recent astronomical discovery, not so much because of what was discovered, but how they discovered it. Some researchers used the Spitzer Space Telescope (like the Hubble, but for infrared instead of visible light) to look at the color of the heat being radiated from a young sun-like star 137 light-years away. What they ended up concluding is that the star has a band of rubble around it in an orbit that's similar to Jupiter's orbit around the sun. Like the asteroid belt, but a bit farther away. That's mildly interesting, since it's the first observation of an asteroid belt -- all the previous observed rings around stars have been much farther away, like Pluto's orbit or even farther. And so this discovery says something about how solar systems might form around stars like our own. Fine, that's great.

But what really interested me was how incredibly simple the science is. Figuring the distance out between a ring and a star turns out to be shockingly easy (well, the main idea is easy, but it's probably tricky in the details). The first thing you have to know is that hot things like stars and heated objects radiate heat in extremely predictible patterns. The top graph in the picture (click to see it bigger) shows the pattern, called the blackbody curve. The X axis is wavelength, which is inversely related to temperature. (Left is hotter, right is colder, confusingly.) So you get a hot peak, and then a smooth curve through colder and colder wavelengths. This curve is completely predictable, it seems. The other two graphs show the situation when you have a continuous disk of dust, and when you have a ring. With the continuous disk, all of the parts of the disk, both close and far way, absorb and re-radiate heat, so you get a flatter smooth curve, like the second graph. With the ring, though, all of the asteroids or dust or whatever are the same temperature, so it radiates in a pattern like a small, cold star. Subtract away the curve from the real star, and you have a curve that tells you how hot the ring is. In the case of the ring they just found, the debris was -262 degrees, which is much warmer than it would be if it were a Pluto-distance away. Given the amount of energy that star puts out, they can then calculate how far away from the star the ring must be to heat the ring that much, which turns out to be between 4 and 6 AU (astronomical units, distances from the Sun to the Earth).

That's pretty clever, and remarkably straightforward, all to figure out the details of something so far away...