Cosmic cats on the radio

Thanks to my Nuffield student Rose Yemelyanova for creating the great cat images as part of her project and letting me use them here. 

The title may not sound scientific but it turns out cosmic cats are a great way
to explain radio interferometry, a notoriously tricky topic, so I have good reason for the quirky wording.

It may not surprise you to know that radio telescopes see the world very differently to us. For many years astronomers have explored the Universe across the entire range of the electromagnetic spectrum, including the radio. A radio telescope is not, in fact, particularly different from a tv satellite dish, it's just pointed away from those signal-beaming satellites and out into space instead.

The world would look quite different to us if we could see in the radio. For one thing we'd be able to see through walls, but it'd also be terribly noisy with all those cell phone and tv signals bouncing around. But to our best type of radio telescopes, radio interferometers, the world looks very different indeed.

This is because interferometers are like broken telescopes. See, here's the problem in astronomy: bigger is always better. The bigger your telescope, the better your resolution. The largest single-dish radio telescope in the world is Arecibo in Puerto Rico. With a 300m diameter, it is so large it had to be built in a massive natural sinkhole. This is pretty much as big as it's going to get for telescopes, it's just not physically possible to support that much steel, especially if you want to actually be able to move it (something Arecibo can't do...). Fortunately, we can cheat. We can split up a gigantic telescope into lots of smaller ones, and it turns out to work just as well. 

This is called interferometry and it works a bit like your ears. A sound signal reaches each ear at a slightly different time, but instead of hearing a mess, your brain is clever enough to put the signals together and figure out roughly where the sound came from in the first place. Interferometers are like the ears of astronomy (and the brain bit is called a correlator, a complex and fast computer). The great thing about this, is with interferometry we can build telescopes that act like they're 36km wide, such as the VLA (which is an ingenious acronym for Very Large Array). This gives us exquisite resolution in radio astronomical images.

The problem with radio interferometry is that it can be tricky to understand if you want to go into a bit more detail than "they're like ears". The thing is, you now have a big telescope with lots of gaps, instead of having a single continuous dish. So the question is, what does a telescope like this actually see? If you make an image from radio data, do you see gaps like missing pieces of a puzzle or is it something else? 

The intuitive answer, that gaps between telescopes equals gaps in an image is not right, but then very little in interferometry is intuitive. What's important to a radio interferometer is scale. Two antennas far apart pick up the smallest scales (so very fine detail) whereas antennas close together see only the large scale, but pick up none of the details. It's like the difference between investigating the pattern on a single brick on the wall and looking at the entire cathedral (details on a single brick is small scale while the whole cathedral is large scale). The crucial quantity is the baseline: the distance between any two antennas is a baseline, and the limiting resolution of the instrument depends on its longest baseline. It's like if you had dozens of ears, the largest distance between any two would dictate how well you'd be able to pinpoint the exact location of any sound. Sort of.

The best explanation I've ever seen of how this works are in this (Maths-free!) description of the Fourier transform and this explanation of how interferometers work from the ALMA website. Since those websites do such a great job explaining how radio telescopes see the world, I'm going to talk about cats instead.

Have a look at this picture of an adorable kitten. What we did (because, well, we can) was take this picture of a cat, put it in the sky, and make a simulation of a telescope observing this cat and had a look at what it would see. So this picture can be seen as the "true sky", what you would see if you had a perfect telescope. But we don't have purrfect... sorry, perfect telescopes so we simulated some real, imperfect ones.

We looked at three telescopes: 

•  KAT-7: a 7-antenna array in South Africa, which a small precursor to the massive Square Kilometre Array (maximum baseline 185m).
• WSRT: a well-established 14-antenna array in Westerbork, Netherlands (maximum baseline 2.7km).
• VLA: a premier radio interferometer in New Mexico, with 27 antennas (maximum baseline 36km).

So, what happens if you put that kitten on the sky and observed it with KAT-7? Well you get an image that looks like this. If you're really creative (and you already know it's a cat), you can sort of make out a head and some ears. Other than that, it just looks like a lot of mess. Not at all cat-like. This is because you've got too many gaps and not long enough baselines. You can get a sense for the large scale information, but you lose all the details. So the problem here is both not enough antennas at different baselines, and also that the longest baseline is quite short so we're only getting large scales.

Now what happens if we look at the same kitten with the WSRT? This telescope has more baselines, because it has more antennas, and they're also farther apart than KAT-7. And indeed, it's starting to look like a cat. We can make out the basic shape, but still don't have any of the details. So we have more baselines (antennas at different distances), but we still don't have long enough baselines to pick out the details on the cat's face.

Ok, lets look at this cat with world's current best interferometer, the VLA. Suddenly, it actually looks like a cat! The extra and longer baselines of the VLA are able to fill in the details that the WSRT was missing, and so we finally are able to see our adorable cosmic kitten.

However, you may still notice some junk around the kitten. It's still not a perfect reconstruction and this is simply because by definition, you will always have gaps in an interferometer. We can't put them infinitely close together to fill in all the gaps, and we wouldn't want to because it would be expensive. If you only have 27 antennas, then you want to put them at a variety of distances apart to get a range of baselines, and hence be able to see both the detail of the cat's face and its general outline as well, although you don't see either one perfectly.

Some telescopes are designed to look at the large scale and do big surveys so they tend to cluster all the antennas close together (in fact, with its new technology LOFAR can see the entire sky at once). Some telescopes however are designed to go really deep and at high resolution on a small patch of sky and thus the antennas are place farther apart. The SKA is so great (and so expensive) because it's going to try and do both, with lots and lots (2000+) of antennas...

The conclusion: radio interferometry has heralded in a new age of incredibly high resolution radio astronomical images, generations of confused grad students (ploughing through Fourier transforms and dirty images) and now, a new generation of students putting cats in the sky for the sake of a blog post.