So, Paul, you've shown us that if we were to look at a solar system like our own,
with Jupiter going around the sun very nearby, 10 lightyears away, that the sun would be wiggling by 0.0016 arc seconds.
Now, an arc second is, there's 60 arc seconds in an arc minute, well an arc minute then has 60 of those to make a degree.
Now, a degree I think is something we understand, so an arc second is one 3600th of a degree, and this is almost a thousandth of that.
This is a very small angle, but of course we have big telescopes that are very precise.
How does that seem like we are going to be able to do that?
Well, in principle, you might think that you'd look at a star, you see the disk of a star, it looks pretty small but you can pick it out,
and then you'd go and observe it again a few years later and it would have moved.
So, you can try and look for something going from here to here. Not very big, but doable.
So, it moves by more than the star is wide across. (Yes.)
Yes, okay, so that may be doable, but there's a problem, it is that when I go out and I observe,
at least in the telescopes I use, stars don't look like that. They look more like that.
So, what we're actually trying to pick up is the difference between this and this.
Now, that looks a little harder.
So, why do your images of stars look so blurry?
Well, unfortunately, life is not quite as perfect as it might be, all those stars are very small,
the telescopes we use to observe them are very large.
Here's the Anglo-Australian telescope up near Coonabarabran, Siding Spring observatory,
and you can see that this four metre telescope is many, many tonnes of equipment
that all has to be lined up to a tenth of the wavelength of light you're looking at,
and a tenth of a wavelength of light you're looking at is like on order of a tenth of a micron, or 100 nanometers.
So, you have to have hundreds of tonnes of stuff lined up to a tenth of a nanometer and that's not so easy.
That's just the beginnings of the problems.
If there are any imperfections in the exact shape of any part of the telescope, that's going to blow your image.
But even if you had built a perfect telescope and we're fairly good at doing that, you've got this bloody thing up here called the atmosphere.
This is Mauna Kea Observatory, possibly the best observing site on Earth that we use,
and that's me in front of one of the telescopes up there.
But you can see that even at this high altitude, it's about 4200 metres up,
there's a lot of atmosphere above you and this atmosphere is not all uniform.
It's got bubbles of hot and cold air, which have a different refractive index, and they bend the light.
But this is called "astronomical seeing" and that was going to blow your image.
That's like the worst problem we have, really, but, okay, we spend a lot of money, we build telescopes in space.
We get above the atmosphere, and the Hubble Space Telescope,
of course, really is lined up to a tenth of a wavelength, and it is above the atmosphere.
Clearly, this should solve our problem.
But the trouble is that even if you put the telescope in space, there's a fundamental problem that comes from the wave-nature of light.
This is refraction. As the light comes into the aperture of the telescope, it's refracted because of its wave-nature, and that blurs the images.
We'll talk more about this later in the course, when we get into direct imaging,
but it turns out that even if a telescope is in space, the images are going to be blurry at some level.
Not as bad as from the ground, but still pretty blurry.
Alright, but let's say we have our star, and it's blurry, I can take lots of data,
and if I can get enough data I should be able to maybe overcome my problem, right?
I just go through and I use the fact, the law of averages, and I just average, although it is really, really blurry.
Yes, so here's the blur, so this is a cut through the image,
so an image like this you might go across and even measure how much light is in each pixel as you go across here,
and you might get something like this and if it shifted, it might change into something like that.
So, it shifts a little bit and it doesn't shift much.
But let's say that instead of looking at a few photons, I look at billions of them.
Yes, see you might be able to see that it's gone up a little bit on the side and down a bit on that side
and so even though the shift is a tiny fraction of the blurring, you might be able to measure it.
But, even here, there's a fundamental problem, the problem is that we can't get perfect profiles like this.
The reason is that in this profile, this is where you'd expect light to arrive,
you expect lots of light in the middle and less going away, but quantum mechanics tells us that the arrival of light is a random process.
What this actually is is a curve of the probability of a photon arriving here.
Light comes in photons, they are more likely to be over here than down there, but the actual time when one arrives is a random process.
So, here's a simulation of that.
Here's what an image like that might look like as you built up over time, and what you'll see if photons randomly arriving,
and they're more likely to arrive randomly over here than over there, but still, it's random,
and as time goes on you start building up something.
But you can see that, because of the random arrival of photons, you're getting very noisy data. It's not a perfectly smooth curve.
Right, and so here we have the star emerging and here appears to be a bit of a background,
because the sky, of course, isn't completely dark.
You see on a dark, moonlit sky, there's a glow due to molecules in the upper atmosphere.
Even if you go into space, there's a glow due to dust in our own solar system.
So, you're going to get some background, and then on top of it you're going to get this thing coming along.
There's this little funny thing like that, and you might think, well that's funny, but that's just random, and that's the way life is.
It is that Poisson Process as we call it, it gives you funny-looking things.
But Paul, we've sort of cheated here. This is a pretty faint star, why don't we look at Sirius, the brightest star in the sky,
and then our telescopes should be literally able to detect billions of photons a second,
and so we should be able to get something that looks pretty close to our ideal case.
Yes, what you saw here is when we had the very few photons like here, it looked like all this complete noise,
but as the number of photons builds up and up it gets better and better,
and sure enough you can get your hundreds of billions of photons, which you certainly can looking at a bright star like Sirius,
then you will get back that very sharp image.
The trouble is that you've got a picture, and you've got that very sharp image, but how do you know where a telescope is pointing exactly?
You may be able to measure it very precisely, say pixel number 47.539 on my detector,
but when you go back and observe 10 years later, which you need to because this is in 10 year periods,
your telescope is always suddenly pointing a little bit off, so the pixel will change even if it hasn't moved.
So, you'll know exactly where this star is in your picture, but you wont actually have any idea where it sits exactly on the sky.
The way you normally solve this is you reference it against some other stars in the field.
If you had two bright stars and connect those together,
you may not know exactly where they are but you'll know where one is relative to the other one.
The trouble is that the really bright stars where you get beautiful smooth data, like Sirius,
there isn't another Sirius an arc second away from it.
Oh, okay so the fact that we have Betelgeuse 25 degrees away isn't going to help us too much.
No, we need the two to be so close that they'd be on the same part of the same image.
If they're even further apart, even the atmospheric blurring will move them differently around to muck you up.
Okay, so this sounds almost hopeless, so maybe we should look at the fact that the other idea when the star is coming towards you,
it has a velocity we might be able to measure. Maybe we can do better that way.
So, let's calculate how big the shift in the lines, due to the doppler effect, is going to be.