Transiting exoplanets are a great boon because it's the only way to measure their size. And then if you can also measure their mass, you've got the density and the size which is the first step towards finding out what they're made out of, what's going on on the inside. The problem is as we talked about, finding a transiting planet is pretty hard. You go and you look at all of the stars that you can observe with that radial velocity that wobble of the star going back and forth. And if you get lucky, one of those happens to be transiting. Early on it was realized that there's another approach you could take. You could actually just go look up in the sky and wait for planets to transit. Just stare at one patch of the sky, look at one star, and if by chance the planetary system or the planet in that star happens to be perfectly aligned with you and you're watching it just the right time, you'll see a dip. And if you continue to watch, you'll continue to see dips time and time again at the right period. People tried this for a while with at first no success, and then limited success and then pretty good success. And so as the years went by, new transiting planets appeared which were discovered in transit and then people went back and found them- then people went back and measured their velocities to figure out their masses. And so the number of transiting planets kept building and building. The biggest boon in discovering transiting planets came not because people realized that this is an important way to get their masses in their sizes and understand the densities of these these giant Jupiter like planets because it was realized that the discovery of transiting planets gave the best opportunity for discovering something that was Earth-like rather than Jupiter-like. Remember, everything that we had talked about so far were these giant transiting planets, these giant planets that were close into their stars, these hot Jupiters. But if you could measure those dips in the brightness accurately enough, even something like the earth going front of a planet would give a little bit of dip. This was the motivation behind it the Kepler mission that NASA launched, which looks something like this. And what you have is a telescope, the light comes in right here and all it does is goes on to this huge array of digital cameras in the back here, and it's got solar panels and everything else that normal telescopes in space does, but it stares at one spot in the sky all the time. And this is critical because if you wanted to find something like the earth, and by like the earth it was meant something about the size and mass of the earth and something that was about the right distance away from the star, to be about the same temperature of the earth, to be potentially in the habitable zone- we'll talk a lot more about that in the last part of this class- but if you wanted to find something like that, well, how often is that going to go in front of the star? Even if you get lucky enough that it's lined up, it's going to go something like once a year. So if you're flitting around between different stars and different patches of the sky and you're looking for something that happens once a year, chances are you're going to miss it. If you stare at one spot in the sky for- the original plan was three years in a row- there's a good chance that if there's something like the Earth you'll see three dips with the same amount of time between each one and that would tell you that there's something the size of the earth there. Let me show you where in the sky they were looking. And if you've done much staring up at the stars you might actually recognize this. This is a very recognizable constellation Cygnus, the Swan, the head of the Swan is the long neck going off in this direction, this is the rest of the swan. Deneb is a nice bright star down here the edge of star. This is the Milky Way galaxy, the summertime- northern hemisphere summertime Milky Way Galaxy and the constellations Lyra and Aquila the eagle. And where Kepler is looking is right here. This whole big swath of the sky. Each of these little rectangles is one essentially one digital camera and it has an array of a bunch of these different digital cameras. And notice what they did. They didn't look right down here in the Milky Way where there are tons and tons and tons of stars, and the reason is there'll be too many stars packed too closely together to be able to see them very distinctly. They also didn't look up here really far away from the Milky Way galaxy where there just aren't that many stars. And the reason is there aren't that many stars. So they took a compromise between a lot of stars, but not too many stars and looked a little bit off the Milky Way galaxy. Let's think about what Kepler was most likely to find. Well, we know that if we have a star and we have planets going around it the ones that you're going to be most likely to have transiting are these ones that are very close to the parent star. And these things like hot Jupiters that have periods of say three days not only would that transit reoccur time and time and time and time again, but Jupiter is big. And so you'll see these big dips in the brightness of the star that occur over and over and over and over. And indeed, Kepler has found a ton of these transiting hot Jupiters. You would less likely to find Jupiters that are further away because the probability of having a transit of just a randomly aligned star is significantly lower. But of course, when the transit does happen, something that's the size of Jupiter again makes a very big transit. Of course, finding Jupiters that was not the main goal here. The goal was to find Earth like things, and an Earth like thing is so much smaller than Jupiter that when it passes in front of the star you almost don't see it. We can not detect Earth like things in front of sun like stars from the ground, because when you look at a star, there's the amount of light wobbles and you can't get something stable enough to see a dip like that in space. There was a chance of seeing something like that. And did they see it? Yes. They actually detected things that were the size of the earth and things that were even smaller than the size of the earth, but mostly ones that are close in. Not ones that are out here at one year orbits like the Earth has, at least not yet. The data are still being analyzed. But it sounds to me like that Kepler will not have discovered the main thing that was its alleged goal to begin with, which was to find a second earth. But I think that some people were disappointed that this was not in the cards to make this discovery that it was just a little bit too hard to find three miniscule dips over the course of three years. And you can imagine people might even have considered Kepler only semi-successful because it didn't actually discover this thing it said or defined, but the universe was kind. Kepler got lucky, we got lucky. The universe put planets in place that were really easy to find. There were Earth like planets that were incredibly close to the star, there were planets strewn throughout this region here. This region where they were incredibly easy to detect. This region by the way- this region in our drawing is significantly close in the Earth, orbit of Mercury. So in a lot of planetary systems, there are planets inside of where Mercury is in our planetary system. We knew about hot Jupiter is like that, but we didn't know that there were planets from very small to very large occupying these regions. It's really good there are because it makes them a lot easier to detect. They have a higher probability of detection, they transit many more times and so you can look at them over and over and over again and get very precise measurements of what's going on. So this is great. Let's take a look at what we know now about the numbers of planets in these relatively close in regions that were observed really well. After a lot of analysis of the data that had been returned from Kepler, this is how it was boiled down in one very nice paper. So again, these are all linked on the class website. You should take a read, it's a nice paper to read. Here is the fraction of stars having planets with periods between five and a hundred days. And mercury is 88 days so we'll call this mercury and inside. What is the fraction of stars? There's two lines there's this gray points here and then there's the orange points here. The orange points are because when the planets get small- two earth radii, 1.4, one earth radius, sometimes they're missed. They make such a small dip in the brightness of the star that they can be missed. And so the astronomers here worked hard to figure out how many were missed compared to how many were found, and what they found is that the maximum number comes right around here a little bit over two earth radii, and something like 18% of all stars in the Kepler field that were looked at. 18% have two earth radius planets with periods shorter than Mercury's orbit. 18%. There are two things that are astounding about this to me. One is that 18% have planets inside of Mercury's orbit. That's weird enough to begin with. 18% have two earth radius planets. What's a two earth radius planet? I don't know. Why don't I know? Because we don't have any. We have earth which has a radius of one earth radius. And what's next? Neptune, which is about 3.8 earth radii. What's in between? I don't know. We don't have anything like it. We have never seen anything like it. And yet, in between 1 and 3.8 let's look right here. That is everything in this region here is something the likes of which we don't have in the solar system 18% are in this band right here. But we have another 14% here, another 5% here, if we add all these together some large number of stars have these between Earth and Neptune planets inside the orbit of Mercury. And where are these planets? Well, the other thing you can look at is the orbital period, and remember that mercury is in here at 88 days and there's a peak somewhere between 25 and 15, it goes down. And this is- notice that there's still a correction, there's orange correction. But things that are in shorter periods actually are easier to detect because they occur over and over and over again. So this peak is presumably quite real. There's a peak at somewhere between 25 and 50 days of planets. Again, the most common, if you look at the two of these together, the most common thing in the universe appears to be planets at this period inside the orbit of Mercury and planets that are bigger than the Earth and smaller than Neptune. What are those things? Well, we can guess that they are either larger rocky bodies- we would call those super-Earths, or smaller gaseous body, mini-Neptunes or something else entirely in the next lecture you'll hear about some of the possibilities of something else entirely can. But let's for now talk mostly about super-Earths and mini-Neptunes. How do we distinguish between super-Earths and mini-Neptunes? Well, that's a pretty obvious one. Super-Earths rocky things are going to have densities like that of the earth, very high densities, rock like iron like densities. Neptunes are going to have densities of the much lower sort like Neptune and Uranus. So let's go measure the densities. You can't. We can't measure densities of all these planets because we don't know their masses. In particular, measuring the masses of these small planets is particularly hard because the small planets presumably have small masses and the small masses make very small impacts on their parent star. Remember the mass is measured as the planet goes around the star, it makes a little wobble on the star itself, Jupiter sized planets make nice big wobbles. Easy to measure. Smaller planets, much harder to measure. This is one other way in which the universe was exceedingly kind to Kepler and to the rest of us who are excited about looking at the Kepler data because it turns out that there are other ways of measuring the masses of some of these objects. And one of the most important has been a way that's been called transit timing variation. Here's how it works. Here's the star. Here is a planet going around the star. Let's say like this. And you're way over here watching the star and every time the planet goes in front there's a little dip and it happens at a nice periodic fashion. What if there was a second planet going around star? We'll put in a slightly different place. Second planet going around the stars is going to have a longer period because it's further away. It too is going to cause little dips in the brightness of the star. When that happens you can do an exceedingly cool thing which is, as this is going around it's on a nice periodic orbit, this is going around its on its nice periodic orbit also. But these two planets exert a little bit of a gravitational tug on each other. When this planet is right here, it pulls this planet in this direction just a little bit and speeds it along in its orbit just a little bit. Of course, this planet then gets to here while this planet is here and it slows it back down just a little bit. So on average nothing happens, but from orbit to orbit to orbit to orbit, this thing speeds up and slows down depending on the position of this. Same thing happens here as this is being sped up a little bit, this is being slowed down a little bit, sped up a little bit. And so instead of having these planets go in front of the star like clockwork tick tick tick tick tick. And then the other one maybe going tick tick tick tick instead of doing that there are slight variations. This one happens a little bit later. This one happened a little earlier. This one happens exactly right on time, later, earlier on time. And these have variations to a little bit later, a little bit earlier, and you can actually take all those variations to a fairly sophisticated analysis and figure out exactly, very precisely what the masses of these two planets are. You do not need to measure the velocity of the star and its effect on the wobble here, you can do it directly. This is great because in some of these cases there were tiny tiny tiny planets packed in really close and in one case up to six planets that were packed in very tightly and each one interacting with the other ever so slightly, and all of these planets can be measured. Truly just astounding. I would never have predicted that the universe would have been so kind to have given so many planets so close to their stars, so many planets lined up perfectly. Remember, you could imagine that if one planet orbits like this, and one planet orbits like this, and like this and they're not exactly all on the same plane, that they're not all going to transit at the same time, and it's not going to work but it does. Most planetary systems at least ones that have planets in close like this are very flat planes, even flatter in some cases than the solar system is. So these transit timing variations have been able to measure the masses. For some of the other systems there has indeed been radial velocity measurements, these measurements of the wobble of the star. So we do know some of the masses of some of the planets too. And now we can give you an overall view of what the masses of these planets are from the things that are about the size of the earth of which there are a few that are known, to things that are more like the size of Neptune and those things between, and let's take a look at what it looks like. Here are all the planets with measured radii and density as of early 2013. These plots change almost daily, so it's hard to keep up to date. And let's let's look where they all come from. There are some that are masses from TTVs that's Transit Timing Variations, you can see these orange in through here, masses from RVs, that's Radial Velocity. These are the black points. And you can see that there are a lot of things that have these radial velocity measurements. You can also see the solar system ones, these are in diamonds. I will let you guess which planets they are. What planet do you think is at one earth radius right there? Well, it's the Earth. There's the earth, and actually Venus right next to it and it sits right on the dashed red line and also on the green line which is what the density and your radius would be if you were an Earth like a composition. You'd continue to go up in density as you get bigger because there's more and more compression from that gravity there. So they should have kept this line going up like this so you can see what really happens for larger planets, and then look what happens. Here's the density again, here these individual measurements the blue points are sort of an average over a region and there aren't a ton of measurements in here at the one earth radius size, but they're all big. They're all high density. And what you don't get to see is the uncertainties in these, and these uncertainties can be quite big, but these are all quite large densities like you would have if you were a rocky planet. What happens. Well there's a peak right around here 1.5 maybe where then the densities start to go down. What does this look like? Well, it certainly looks like this somewhere around 1.5 Earth radii, there is a change, that 1.5 is something like the largest you can have an Earth like Rocky planet. Although you do have some appear that are measured to be high density that are up through here. And 1.5 is maybe the smallest you can have a Neptune like, although, again you have some of these low density things in through here that could, well, be Neptune. There it doesn't have to be a strict divide between these things. And it's interesting of course, that this divide right around 1.5 is that spot where you have the largest number of planets. One and a half Earth radii is that most common size of planets in the regions that have been surveyed by Kepler. Why is it because you get some rocky ones and you get some ghastly ones in those two populations overlap so you have a lot of objects that are that size? Maybe, maybe it's telling us something else about how planets form. Maybe it's telling us about an entirely new type of planet that we don't know anything about, that we've never seen in our own solar system, maybe it's not just either Rocky or Neptune like, maybe there's something else in the middle. These results from Kepler are I think someone most profound results we've gotten on planets in the last decade. We now know so much more about what a planetary system might look like. We used to have an example of one, our own, and now we have hundreds and thousands of planets and planetary systems and we know that the variety is huge, and it looks a lot like we're kind of strange. These data from Kepler are continuing to be analyzed. There'll be new results coming, I suspect, for many years to come. So you should pay attention to announcements from the Kepler team for many years, but I think it's already clear that the impact is quite huge. In the next lecture we're going to talk a lot more in detail about what these planets right here in the middle might be like.
