Have you ever watched rain fall on the pavement? It makes a beautiful, seemingly random pattern. No drop is more or less likely to fall in a spot where another drop has fallen.
Let’s say you wanted to collect as much water as possible during a 30-minute rainfall. What kind of bucket would you make? Tall, short… wide, narrow… orange, green… hot, cold… raised above the ground, in a hole… what would you do?
This is the exact situation astronomers face when designing telescopes. Only instead of rain, we are trying to collect drops of light – called photons. And instead of setting a bucket in a rainstorm, we put a mirror in a dark location and hope for clear skies.
If you took a minute to think about it, you probably settled on using as big of a bucket as possible to collect the most rain. The width of the bucket, or its area on the ground, is more important than its depth, so long as it isn’t going to overflow. And the color, temperature, and height above the ground don’t really matter. This is exactly why astronomers are partial to huge telescopes! The most important part of a telescope is its primary mirror, which is like a bucket for light. Giant mirrors don’t really give us a more “zoomed in” view of the cosmos, but they do let us collect more light – just like a big bucket will collect more rain. Photons of light are always raining down from the cosmos. Bigger mirrors mean more photons, and more photons means fainter stars and galaxies are visible.
There is another way to get even more rain, or photons, too, of course: leave your bucket out for more than 30 minutes. Maybe even leave it out for hours on end, and carefully set aside all the water – or light – you collect until you can add it all up later. The faintest, most distant galaxies are only visible to those with a big light-bucket and a lot of patience.
As it turns out, falling rain and incoming photons can both be described by a special set of mathematical rules called Poisson statistics. Each drop hits the ground in a random spot. But the sum total of all of these random events is predictable. So, If you make a graph of raindrops hitting a bucket, or photons hitting a telescope mirror, you get a special shape: a Poisson distribution.
Astronomers use this to know how long we need to stare at a distant star or galaxy, or how big a telescope we need to use. Poisson statistics tells us that the quality of telescope data for a star emitting N photons will be 1/√N. (We like to say the uncertainty, or “standard deviation,” is √N.) This is great news! If you spend some time looking at a star and collect 100 photons, your uncertainty will be 10 photons, which is 10% of 100. That’s not very precise. But if you stare at it longer – or trade up to a bigger telescope – and collect 1000 photons, the uncertainty will be about 32 photons, which is only 3%. Much better.
The next time you look up at the night sky, remember that your eyes are miniature telescopes. Or perhaps fun-sized light-buckets. How much starlight can you collect?