So, Paul, this is really neat stuff. So we've found some things, but are we able to make any conclusions
based on a statistical basis so we know how frequent these things are?
Well, here's the data on what we've currently seen.
So, the red dots over here are the planets discovered and confirmed by the transit method,
so we're plotting the mass here against separation and, of course, the ones found by transit are all very close in.
This is not including most of the Kepler ones because they are not confirmed, but they'll be down around here,
and we've seen the radial velocity, which finds some of these hot Jupiters
but it's finding more and more of these eccentric giants up here.
The green dots over here, I hope you don't have red/green colour blindness like Brian does and discriminate them,
they're about what you'd expect these things to be, so that in this region over here,
so about the Einstein Radius out, a few astronomical units out,
and you can see things down to quite low masses and also quite high mass ones. We are indeed finding things where you'd expect.
So, we know we have different selection effects here,
and so we think that the selection effects for the green points are pretty much just how far away they are,
so the fact that they scatter down further down here tells us that maybe the blue points are a little biased because,
of course, the blue points don't find things down there.
Yes, so we've already talked about how we go about working out biases, whether we do a Monte Carlo simulation
or try and work out for each bin here what the odds are of seeing things,
and so we can try and recreate what the true population is. Given we only have seven or eight points here, it's pretty hard.
However, basically about half of the high magnification events are followed up,
the other half is just bad weather or they don't find them early enough for something like this,
and of those half that are followed up, about half show planets with different deviations,
and the half that don't could still have them, they're just too small
or just happen to fit in the gaps in the data which wasn't very well sampled or something.
It's looking like of all the half of all these, typically dwarf stars that were in the foreground of our line of sight to the bulge,
have planets big enough to see out in this sort of range.
Okay, so we can make some preliminary conclusions.
We should compare the radial velocities. Remember, this is just the radial velocity plot now,
and they're now getting to the stage where they can see Jupiter mass things out at Jupiter-like orbits,
and a recent paper by Robert Wittenmyer concluded that they are seeing
baby Jupiter-like things in about 3.3 percent of the stars they study.
However, that's almost certainly a gross underestimate of how many are out there
because they haven't got that many years of data, a lot of them you can't measure enough precision,
so he estimated that for every one they see, they've missed at least a few,
maybe as many as 10 but it can't be much more than 10 they've missed.
So, they have to potentially correct up their 3.3 percent by a factor of 10.
Maybe as much as 10, 12 or so but it could well be less than that. It's very uncertain given that they've only got, like, three of these things.
But, fortunately, we have microlensing which doesn't have that selection bias.
It's much better at doing it, we just don't have as many objects. So, what do we get if we compare the two results?
Well, let's compare this and we find that here the data on the radial velocity surveys is mostly close in,
so this is the number of these big planets as a function of distance, and here's a snow line,
and the radial velocity is mostly telling you about the ones closer in and it's going up as we went down as we said earlier.
So, it's very uncertain when you get out here.
Because we're extrapolating the data where you've only got a very small number of the things out here, and that's the microlensing data.
They're probably consistent, given the the large uncertainties on both of these things.
Okay, so they are consistent, although the microlensing is saying maybe there's even more than suggested by the radial velocities.
It looks like the number of planets really does keep on climbing as you get out here.
But we're really looking at 20, 30, 40 percent so 30, 40 percent seem to have Jupiter analogues.
It can't be much more than that because of the radial velocity there we've just been talking about.
If we try and work out the overall exoplanet populations, this is very rubbery.
We've got the classic hot Jupiters, the ones that were discovered first, and then maybe half a percent, one percent,
depending quite on where you draw the boundaries around them. (So, they really are an aberration.)
Yes, they were seen first because they're easy because they're so big and so close in, but they're not a large fraction.
The eccentric giants are about seven percent,
but then we've got the close-in Super-Earths seen by Kepler which is maybe 30 percent.
So, those are very common and we didn't know at all about them a few years ago.
Yes, and of course these ones are often the same stars as this one, for example, Epsilon and Andromeda has one of these and one of those.
Now, we're seeing the Jupiter analogues that are also maybe no more than 40 percent,
but probably at least 10 to 20 percent so maybe 30 percent is a good guess we're getting.
Numbers are very rubbery at the moment.
But these objects, let's just be clear, can these objects occur in these solar systems as well
and we just wouldn't know about them simultaneously?
It could be because, bare in mind, these are most typically seen by Kepler
whereas these are being seen mostly by galactic bulge micro-lenses,
not at the same stars, we can't look at the same stars and see both of these things.
It would be lovely if you could do microlensing in the Kepler field or point Kepler at the galactic bulge or something like that,
but that's not happened so it could be that these 30 percent are the same as this 30 percent or it could be different.
Maybe 30 percent here are 30 percent like that and they don't overlap.
Yes, the fact that microlensing only happens to one in a million stars means that even if you looked at Kepler,
the chances of getting luckier is almost zero, so...
But maybe, with future big telescopes, we could look for one of these events
and then wait until the foreground dwarf stars drifted away from the background star and then try and nail it for radial velocity
and see if you can work out what else is there, so we'd do transit observations.
So, there are ways forward, but we are getting, I think, a kind of an interesting picture here,
where solar systems seem to come in a variety of flavours and it may well be that they are mixed,
but certainly our own solar system does not appear to be grossly atypical.
Though it's not dominant. (Yes.)