Sometimes, you can learn a lot by what you cannot see. For example, if you are a night watchman at the Tower of London and you find you cannot see the Crown Jewels, you learn that you had better start looking for a a new job and a good lawyer. Or maybe you learn that the batteries in your flashlight have gone dead. However, if you go running out claiming that the Crown Jewels have been stolen when really you just needed new batteries, you are in a heap of trouble.
In astronomy, understanding a "non-detection" (in other words, understanding what you are not seeing) is often a crucial piece of evidence in solving a puzzle. The key is knowing when you could have seen something if it were there.
One easy example of this is the picture above. In the middle of the picture, you don't see any stars, while on the edges, you see hundreds of stars. If there were stars in the middle of the picture, could we have seen them? The answer is "Yes!" (or perhaps "Duh!") We know this is true because we can see stars on the edges of the picture. So, either there aren't any stars in the spot in the middle of the picture, or something is blocking the light from those stars. The answer is the latter -- a thick cloud of dust and gas is blocking the starlight. If we look at infrared light, which can pass through dust, we can see lots of stars all over the same patch of sky. And, by careful analysis of these pictures, we can learn a lot about the cloud of dust and gas, and the infant star or stars being formed inside it.
Okay, now a harder example. We astronomers are pretty sure we know how gravity works. After all, we use Newton's Law of Gravitation and Einstein's General Relativity to send space probes all over the Solar System. But when we apply these laws to clusters of galaxies, we run into a problem. The galaxies move around much faster than we think they should, at least when we add up all of the light that we see. This effect was first noticed by astronomer Fritz Zwicky in 1933, which led Zwicky to propose that there is additional material there that we can't see.
In the 1970s and 1980s, X-ray telescopes detected a glow of X-rays from these clusters of galaxies, indicating that the clusters had million-degree gas swirling around in them! This very hot gas would not be visible in optical light, and when astronomers added up how much gas was in this invisible hot phase, it ended up being more mass than in visible light. But even then, it was still not enough to account for the speeds at which the galaxies move around. For this reason (and others that I won't go into), astronomers came up with the idea that some other type of matter, "dark matter", must exist. There is still some controversy as to whether dark matter exists, or whether we just don't fully understand gravity (though most astronomers, myself included, are pretty sure that some invisible form of matter exists).
Another example of a non-detection being used is in black holes. In all cases we suspect there is a black hole, light from gas or stars in orbit around the black hole tells us that there is something big and unseen there. For example, this movie shows the observed (and predicted) positions of stars at the center of our Milky Way Galaxy. From the laws of gravity, we are certain that, at the center of the galaxy there is an object with a mass over two million times that of the sun. But, as you see from this movie, we don't see anything there! The only thing astronomers know about that is dense enough to have this much material and yet not be seen is a black hole. In the past, some other possibilities remained, like a dense cluster of white dwarfs or neutron stars -- these would be faint enough not to see. But as more evidence comes in, we have constrained the size of any such cluster to be so small that gravity would cause such a cluster to collapse into a black hole anyway.
But we have to be careful not to be fooled. Astronomy literature is full of mistakes people make when they messed up in calculating what they could see. For example, several years ago people were claiming that, in earlier ages of the Universe, there were not as many barred spiral galaxies as there are today. As it turns out, these claims are most likely wrong. When you look at distant galaxies, they appear smaller, so what is clearly a bar in a nearby galaxy can be invisible when seen from far away. And the people doing the study had a little too much confidence in their ability to be able to see these bars. In short, it's hard to see things that are far away, and, if you are wrong about how hard it is to see them, you make mistakes.
This week, I was reading a paper by an acquaintance who was looking for light from planets and brown dwarfs (stars that are too small to power themselves by nuclear fusion) around white dwarfs. He didn't find any. And so, the question becomes, why not? Are they too faint for us to see? Or were there never planets there? Or were any planets that were there get swallowed by the star as it grew into a red giant during its death throes? These are questions that the paper tried to address, and it all hinges on how well we know what we can and cannot see. If the planets are simply too faint to see, then not seeing them doesn't mean much. But if they should be visible and we don't see them, then we'll learn something about planets and the fates of solar systems. We'll just have to wait and see.