Transcription
Okay, so I guess we should go ahead and get started, and the second part of the lecture. And so here I tried to think about what what it is that we're detecting and what it means for our understanding of planet formation, which has really evolved over the last 20 years. And specifically, I want to try and give you answers to the following questions. So think right now about whether or not you think you know the answers to these questions: What does the ensemble of hundreds of exoplanets tell us about planet formation? How do exoplanets compare with our solar system? And then a question: Do you think we know a to sub earth, the frequency of earth-like planets? Anyone want to volunteer question answers to any of these questions? Huh? Oh, ATIS of Earth is the frequency of earth-like planets around other stars. So it could be a number; it could be like a percentage, like 20% of stars have earth-like planets. And by earth-like planet, I actually do mean kind of an earth analogue. So I mean an earth-mass, an earth-sized, sort of in the habitable zone. That was the goal of the Kepler mission. So did Kepler achieve its goal? Do we know what a de sub earth is? All right, savvy group. How about um, we've got a model; we had this great model. Well, okay, so let me just pose these questions, and then I'll go through, and I just wanted to try and answer these three questions in my in my talk. Okay, so how is the discovery of so many exoplanets impacted our understanding of planet formation? So here's Sherlock again, and so I'd like you guys to tell me or describe the solar nebula model and in particular what features of planet architectures does this solar model explain? Does the solar nebula model explain? So probably had this in astronomy, your intro, if you've had intro astronomy classes, right? What is the solar nebula model? What does it basically say? Yeah, okay, good. And what what things is it successful at explaining in particular? Okay, how about what are some of the features of it? Yeah, cut pardon. Oh, right, the rocky planets are close in the inner regions, and that's because it's hot there, right? And so you expect the only refractory elements will survive in the inner part of the disk, and the gas giant plan is formed further out beyond the so-called ice line, right? So, and all the planets are rotating in the same sense, right? So this is a conservation of angular momentum that tells us that this the fossil these fossils of the protoplanetary disk, you know, came from something like that. So it was it's been pretty it's, you know, I would say it's so neat, it's so elegant, it works so well; you have to believe it, right?
Okay, so there are chapters and previous heliophysics series about how protists stars condense under the Rayleigh genes criteria from gas giant clouds, molecular clouds, and a giant molecular cloud can form, you know, hundreds of thousands of stars. You see here this beautiful picture of the Eagle Nebula, which has been sculpted by stellar evolution because the most massive stars have the shortest lives, and they die violently with supernova explosions, clearing out the the dust and leaving behind these sort of just little cocoons of stellar nurseries for the lower mass stars to form. Yes, sir. Yes. Oh, yeah, nice. And what? Okay, excellent. Yeah, burying stars being born right here. So there you go. Okay, so we had this idea and made sense to theorists back in the 80s, maybe. Oh, actually going back to Contin Laplace, right, that probably there was a proto that a protoplanetary disc, a flattened disk, and and that idea came about because they saw that the planets in our solar system were in it in a disk-like structure. And so we went along with this fairy tale for a long time that, you know, that protoplanetary disks form, but what's sort of amazing to me is that it wasn't until the mid-1990s that we actually saw them. There was data to suggest that there was some kind of dust around the stars that IRATH observations showed that there was excess dust, but who knew if it was like in just a cocoon in a shell shape or in a flattened disk? And so it was really in 1996 when Hubble had its glasses put on, but O'Dell and when had their great paper showing, yes, these are pancake-like structures that form around stars. And so we now had this nice picture, and I love this cartoon, which I took and credit in the book chapter from Dmitry seminoff, who gave a talk at that proto stars and planets six meeting, because it shows it just feels like everything we think we know about protoplanetary disks. There's turbulence in the disk; there's dust that settles down toward the mid-plane; there's a temperature profile in the disk where it's hottest closest to the star and also hottest on the upper layers of the star, the gas, the dusty couples from the gas and settles down into this cooler mid-plane region; there's an ice line which is further out from the star where, you know, you can get icy Mantles on grains, and those icy Mantles then electrostatically stick together and and planets. But actually, almost everything we know about disks is based on models and this very sketchy observation of flattened pancake structures from HST. The opacity of the dust is so high that you can't see into the disk to confirm a lot of the information about the temperature and pressure profile with millimetre observations. You can see the outer part of the disk where the opacity is lower, but I think it's gonna this part of this will change somewhat with Alma observations, which will give us more information about gas and velocity flows inside of the inside of the disks. So so the planet formation is really governed by this idea that the temperature, which the source for this temperature is the host star, is falling off as a function of distance from the star. Here's this nice little these little 1 micron sized grains out beyond the so-called ice line which develop these icy Mantles and begin to stick together. These are the first building blocks of planets and planetesimals. We had even in the night sort of 1980s and 1990s some interesting ideas about how to form gas giant planets. The solar nebula model also predicted or posited at least that planets formed from accretion; they form inside out. Most of you probably know that there's a competing model where the planets formed by gravitational instability, so outside in, and this was raised during the discussion section yesterday and is possible for some types of planets, I think, but here's a sketch, a cartoon sketch of the gas giant planet formation model put forward by Pollock et al. in 1996. There are three phases: In the first phase, you have mostly solid growth, okay, and the planet is experiencing some runaway accretion, which I'll talk about a little bit more in the next slides, until it's feeding zone is depleted, and then it sort of just sits there very quietly, very slowly trying to accrete gas and dust, but this phase two is a very long phase, and that's what sets the whole timescale for planet formation, and you'll see that this was a problem, a conundrum for a while. And then in Phase three, once the core reaches a mass of about ten Earth masses, its gravitational reaches extend it out, and runaway gas accretion begins. So the picture from Pollock et al. goes like this: Here's phase one, phase two, and phase three, and you can see the rapid growth of solids, the very slow growth of phase two, and then phase 3, one runaway growth for the gas giant planets. Yeah, for the gas nine planets. Okay. Now you can see the problem. So at the same time this came out in 1996, people were beginning to get measurements of infrared excesses and other measurements of spectroscopy which indicated the the the mass and amount of disks around young stars, young stellar objects. And so if you look at this, this tells you the fraction of stars in these various clusters that have that have disks, let's say that have infrared excesses as a function of time, the age of the stars, and here it is in millions of years. So here's two million years, four million years, six million years, and you can see that by 1 million year it's 1 million years, yeah, half of the stars, young stellar objects and a cluster have lost their disks. All right, so that's a problem to reconcile with this picture, which tells you that phase 2 takes 5 mm years, six million years, right, to grow to the ten earth masks or so that runaway gas secretion can take place. This tells you that in two million years, three million years, the discs are gone; they don't standard they don't sit around for this long. And so does that mean that this picture is wrong? Well, I was saying yesterday is someone that I think this is one of the triumphs of exoplanets is that there is a solution that's very quite neat and elegant. We now know that planets, most planets, undergo orbital migration, right? And so the first gas giant planets that were found are in close orbits. The planets are moving around in the disk in a way that the solar nebula model never predicted. When you add in the dynamical interactions of the planet with other planetesimals or embryos and with the disk, it changes the solar nebula model in some profound ways, and in particular, if your gas giant planet is not just sitting there, you know, going through a single lane in its orbit around it around the star, but is allowed to move in its feeding ground in terms of gathering up planetesimals increases, right? It doesn't just deplete planetesimals from region 1 region; it gets to move in, and it can also they can also move out. And so that means that the planet growth can be is much more rapid; it shortens phase two in this picture. Yeah, yeah, yeah. So we still can't see inside the disks, but you're right; there are lots of models; there are vortices that trap these one-meter size particles so that they can rapidly grow. I would say that, you know, there are some interesting suggestions, and whether or not this is a completely solved problem is unknown, but obviously, whether we've solved it or not, nature has solved it. So yeah, but that's true that that is a good point; the the picture goes kind of like this: In phase one, you have a planetary embryo that's going through a sea of planetesimals, and it's accreting matter; there's a kind of convergent growth here because if you have two of these little guys smashed together, they double their size, and they grow pretty quickly for the larger one, and it's it's fractional growth is actually slower, and so there's the planetesimals growth is kind of a just-so story with convergence to larger particle sizes until you end up with in this picture, you know, a few planetary embryos that are left behind. Once these planetary embryos reach a certain size, they begin to gravitationally focus the planetesimals, and so they extend their reach, and they can grow a little bit faster. Then once the the embryos are formed inside of the disk, there are a couple of possibilities; there's a type one migration that can take place; planets embedded inside the disk; it's too small to clear a gap; and resonances between the capillary and velocities and the patterns feed in the disk set up Lindblad resonances that excite spiral wakes in the disk, and you can see these wakes shown here, and then the next slide I have a picture showing the evolution to PI type 2. Okay, so so in Phase two now the embryos gravitational has gravitationally focused and collected planetesimals; it's cleared out a gap, something like this, until until it's the gravitationally focusing part, this sort of zone of influence that it has reaches the hill rate spill hill sphere radius, and at that point, anything outside the hill sphere radius is not going to be collected by this guy, by this embryo. And so you'll hear a condition for accretion that's used as a by theorists in in body simulations as if two things come within a hill sphere radius, then they in their code they just make them one, make them magically one; that's how they handle the collisions there. Here is a model from beginning sort of to end; discs evolved from type 1 into type 2 migration. So you start out with these spiral waves being set up in the disk; you can see that as the planet is growing, the spiral waves actually serve to dump more material on to the growing planetesimal; it clears a gap in the disk, right? And when it's in this sort of earliest phase, the type 1 phase, it feels this huge headwind, right, as it's orbiting and wants to orbit in a capillary in orbit but feels this headwind from the gas and dust that's left behind in the disk, and and here that's no longer the case, but now that the gap has been cleared, now a material comes in, and it tends to pile up on the inner edges of the disk; it can also pile up here, and if the pileup of material on the inner edge here of this cleared annulus becomes comparable to the mass of the planetesimals, it will exert a torque on the planetesimals and cause it to move in the disk. All right, so so do migrating planets then? One question is, do they sweep up most of the inner planets? No, we found all these hot Jupiters; you clearly see that they migrate in. Are these going to be places where earth-like planets won't survive because they've been disrupted? And another interesting question that has a lot of interesting ideas but I think hasn't been stalled solved completely is what stops migration? Yes, yeah. And what? So there seems to be a pileup of planets sort of in three-day orbits, and and so, you know, why don't they just as they're migrating in just, you know, what would halt them? So magnetic fields have been proposed; there's a lucky timing where the disk clears just in time as the planets coming in, and so there's no longer any inward spiral motion that that slows down, but for whatever reason, we find that these gas giant planets that form initially out beyond the ice line can migrate in and very close in orbits. Yes, yep. Absolutely. [Music] Like a Bode's law kind of thing? Yeah, that is a good question for a dynamicist, and I would think in this sort of a picture that there would be in the within the residences they'd be kind of resonant orbits, but I pretty sure that what we know now is that planets form in great abundance; there are lots of planetesimals that are competing. Yes, yeah. You mean where are they located and what speed are they going? Their orbital periods will be slower than Keplerian because they're in the disk, but they want to be right; they're trying to approach a Keplerian orbit because they're less random motions like the gas and dust would experience. So there these are basically, you know, when these one-meter size balls, the problem is that they do feel this headwind of ploughing through gas and dust that causes them to lose energy and spiral inward, and so the the question has always been, wait for the theorists who models this, wait, as soon as they get to be about a meter size and they're traveling faster than the gas and dust around them, that creates a pressure that causes them to spiral inward, and I lose them all the time in my simulations. And so other that this requires, you know, more sophisticated explanations, like maybe there are vortices that trap these things or you get, you know, over-dense pressure regions or maybe these things grow incredibly quickly or yeah, but we still I think we still don't know how you get over that meter size barrier. Yeah, friend. Oh, yeah, the breakfast. Oh, well, the radiation pressure from the star is important in the inner part of the disk, right? And so the disk is going to become less more tenuous, have lower density as you as the planet moves closer in, and so there's less pressure to continue Excel, you know, having the planet lose energy. Yeah. Oh. Oh, yeah, I'm not sure I think of it as a more gradual process, but something that happens over a million years that, you know, the dust is being steadily eroded by this by the radiation. I'm not sure that there's anything. Yeah, I don't know. Does anyone else have a comment on that? Yeah, it's a great really great question. Ah, that means that means ah, okay, right. So leads to um there's a lot of debate about whether or not it's the disk that's driving the planets in or whether it's planet planets scattering that's driving them in, and Erik Ford has done some interesting work that suggests that what's happening is that the disk is clearing, and if you if you started out, here's gonna be my cartoon sketch, okay, and it's not it's not this is not hard not backed up with hard observations, but if you start out with a disk that has high density either because it's around a massive star or because it's high metallicity, then I suspect that you have many sites where the planetesimals are growing pretty quickly, pretty rapidly, and you reach this, you know, 10 earth mass core threshold quickly, but now because the density was so high, you have these things stacked up in close proximity to one another, the disk is gradually clearing, and while type 1 and type 2 migration can be invoked, you also now have the problem of planet planets scattering as you're going around, you know, these things are pumping each other's orbit eccentricity as they come at by close approach. So what happened in our solar system, you know, there was theory in the 1980s which said that suggested that Jupiter might have been closer in in the solar system and that maybe Neptune and Uranus had actually formed in between and were, you know, in a gas-starved region because Jupiter and Saturn were gobbling up all of the gas and were kicked out. But, you know, what could you do? You could say maybe that's true, but it was really the observation of exoplanets which showed that orbital migration and these dynamic emotions were so important that actually breathed new life into that whole theory, and now as I think we said yesterday, observations of the Kuiper belt would show this, you know, resonant edges in the distribution really suggest that that that's what happened, that Uranus and Neptune were in between and they got kicked out; that's about the only way that people can explain this capture of the Kuiper belt objects into these resonant orbits. So they're there like them, the dust bunnies, you know, under your bed, and when you roll the ball through and you look through and you can see this distribution, you know, it tells you sort of what happened, and and that's that smoking gun in our solar system that there was actually evolution. So it's not just that our our solar system probably also experienced quite a bit of migration. How oh my gosh, come on, somebody help me. How dynamicists, somebody help me. Oh my god, I can totally see him; I'm blanking on his last name; I can't believe this. Um, okay, the grand tack theory, does that ring any bells? Jeff, you must know him; he's that Southwest Peter. Yes, how love is him. God, please never tell him I did that. Okay, so yeah, so however, son has this green. Oh, great, Mom. Exactly. And morbid Ellie have these theory of a grand tack where the Jupiter probably came in, you know, almost as close as Mars and then ended up migrating back outwards again. So, you know, that would have been an interesting fairy tale, but I think it now has a lot more support. Yeah, yep. Our young star. Oh, or cars like the sign and back. Yeah. Oh, right, right. All right, great. Yeah. Oh, sure. Um, well, the the gas and dust, right, feel more turbulence, and their motion is not Keplerian. I mean, yeah, and but the but as the particle accumulates some mass, it's its motion will be Keplerian, and so the velocities of those things are different; the velocities of those two components ones like more like a fluid, right, that and other is a solid body plowing through it. Yes, they a year there's nothing on score that we it's better to look wise and have. Yeah, I'm gonna say that planet formation is a chaotic process, and that it's it set the initial conditions are important in terms of how strong the gravitational interactions will be and and then the whole system like goes depending on those what those initial conditions allow, and you end up with a complete, you know, it's completely chaotic. And so in some cases, the initial conditions will probably generate fewer gas giant planets, and it might be related to the metallist ER surface density at the mid-plane of the protoplanetary disc. Yeah, and in other cases, it's higher, right? We see this planet metallicity correlation for the hot Jupiters; it's very strong. So increase the metals, increase the surface density of the mid-plane of the disc, you inc, you know, you have more gas giant planets sort of migrated inward, and and and I think that's because there were more of them to interact is my guess, but yeah. Okay, so what exoplanets have brought to our understanding of the solar
Nebula model: Is this fact right? There's observation that planets migrate, and they seem to end up in impact configurations. That is, if you're playing a sim planet game—in you're a theorist, right—and you have a planetary system that's been discovered, and you try and drop planets in, the whole planetary system will fall apart because there aren't empty places where you can put planets in and have them survive.
This was what we saw with the first multiple-planet system, Upsilon Andromedae. There were three coherent signals, right? The planet that was 3/4 the mass of Jupiter was parked in a 4.6-day orbit. And then there was a planet in a Venus-like orbit, 242 days, that was 2 times the mass of Jupiter. And then one out at, you know, almost a Mars-like orbit that was 4 times the mass of Jupiter.
And so Jack Lissauer and Eugenio Rivera did this experiment where they tried to put in moon-sized particles into the system, and they found that there weren't any stable places. So when you look at—because of this, right—because these systems are packed, the planets can see—they feel the gravitational perturbations as they go around in their orbits—and they exchange eccentricity and inclination; they exchanged, yeah, angular momentum as they're as they're going around in their orbits. So the numerical integrations show that the planets are stable, but the eccentricity is oscillating, or the planets—okay. So now there's more pictures of oscillations. So now Sherlock is here, so let me ask you: Do our solar system planets show changes in eccentricity? Are we in a packed planetary configuration? Okay, other planets—do you think he said the Earth will show some changes? There are Milankovitch cycles and other cycles, so there will be some change in the eccentricity of the Earth. What about the other planets?
So this is for the class that I had last in the spring. I had my students run numerical simulations, and they started out with our solar system, and they couldn't believe it. They came back and said, "Something is wrong; these planets are—their eccentricities are all, you know, being exchanged." And so our our solar system is actually—okay, how Levison will get mad if I say it's packed—saturated, but it—there are, you know, because um—he'll raise his hand and he'll say, "I found a little window in between Mars and Jupiter or something where I could put a moon-sized particle and it survived," and then I would say, "But how—you ran a million simulations before you found that little tiny window." So we are pretty full. Okay, if we're not packed, and simulations by Jacques Laskar and Jack Wisdom independently have run our solar system forward in time and show that, over time, the planets are—there—our gravitational perturbations—and eventually a planet will be lost from our solar system. Our solar system will continue to boil down. So right now it's in—this is on a timescale of billions—few billion years—so nothing to worry about now. And I think it's Pluto anyway, and so we already demoted it.
Packed means that if you're running a simulation and you watch these planets go around—okay, like clockwork—two things are happening: First of all, it's not exactly clockwork; there's actually some exchange of eccentricity between neighboring planets. But packed means that, let's say I have this huge space in between Jupiter and Saturn and I want to sneak a planet in there. Packed means that there's no place I can drop a planet or a moon-sized particle in and have it survive without perturbing the other orbits. So it—so that tells us that these systems evolved into this state, right? They start out over full with planetesimals, and they boil down. It's the gravitational game of musical chairs. They boil down into systems where all the gravitationally stable niches may be filled—may be filled. Okay, and this has been postulated by several people. Rory Barnes and Sean Raymond have done simulations where they say, "Let me take some of the systems that have been—where Doppler planets have been found—HD 189733b, 55 Cancri, Upsilon Andromedae—and let me just do this: I'll throw in thousands of moon-sized particles and let the system evolve and see where they're—where they survive," right? And then wherever they survive—so this is basically—it must be time, although I can't read the axis here—you know, then this is the place where they say, "Okay, if I put a fake planet here, it survives," so you should be looking here with your Doppler technique or other techniques to try and find planets. This is an empty region, okay, where you haven't found a planet yet.
So this this leads to the hypothesis, okay, that planet formation is an efficient process. It leads—if not to packed planetary systems—to full planetary systems. And you know, this is a new idea. It was true of our solar system, but we weren't sure how broadly true this was going to be. There's also a second insight that's come from the discovery of gas giant planets—are many exoplanets—is this planet-metallicity correlation. So this is some work that I did with—why does it say Fang and Margot? That's my plot with Geoff Linton. I actually generated this plot back in the year—at least—is—right—2005, showing that the fraction—we analyzed thousands of stars, figured out their metallicity the best that we could, and then in each metallicity band we said what fraction of those stars has planets. So I would—I would posit that this is an unbiased way of determining planet-metallicity correlation, and we found that for metal-poor stars, right, that the—it certainly—it flat—at least flattened out—but when you go to stars that have a super-solar metallicity, there's a rapid rise in the fraction of those stars that have Jupiters, and these more Jupiters detected with the Doppler technique. So these are Jupiters that have probably migrated inward. So I think yes, we see it, and we see this in some solar—some multi-planet systems. People are testing this with the Kepler data as well. The problem is that there is no technique that gives you the entire parameter space—right—at all of the semi-major axes. And so I would say we see hints of it—that it exists in some parts of parameter space—but we—it's an extrapolation to say that it—that's true everywhere. Yeah. Okay. So I should say that there's new work that shows that this correlation does not hold for rocky planets. Okay, so that's quite interesting.
And the timescales for forming Jupiter—remember that that plot that showed that the disks are disappearing after a million years—there has to be something to make those cores grow fast, and I think it's metallicity—all right—fast enough so that they reach that threshold mass while the gas disk is still around and they can go through the runaway growth. But the smaller planets can grow on timescales—slow accretion timescales—of 50 million years. So paradoxically, the bigger planets grow in a couple million years to their full-grown size, and the smaller planets can take, you know, up to 50 million years, people think, to grow—to accrete. And if you look at the—at the weather—there's a correlation with metallicity in the star—it doesn't exist—all right—so yeah—so it's not—so again, I think metallicity is causal in this sense, and I don't think it's metallicity—I think it's surface density. Okay, so what does the ensemble of exoplanets tell us about planet formation? And now I'm running out of time. The most important thing is that it tells us that planets move around in the disk—that extends the feeding ground for planets—so that there can be more rapid core growth. The packed architectures that we see suggest an initial state where there are hundreds of thousands of planetesimals all competing and accreting, and the planet-metallicity correlation exists for gas giant planets, telling us that it helps boost the efficiency of core formation early on, but doesn't hold for small rocky planets.
How do exoplanets compare with the solar system? Well, we have models now that allow us to determine the interior structure of these planets that we can't even see; they're orbiting stars hundreds of light years away. And as I said before, the combination of mass and radius gives this unique two-layer model. We can also, in some cases, observe the atmospheres of stars with transmission spectroscopy. So as the transiting planet passes in front of the star, its atmosphere is lit up. Okay? If we can use the transmission spectroscopy to measure a scale height for the atmosphere of the planet, we can get out some pretty interesting information from this one simple little equation: The scale height is equal to kT—temperature—you can assume from the temperature falling off from the star—divided by mu times g—little g—the gravitational constant—or the grad—the gravitational field at that point. So mu is just the mean molecular mass or atomic mass, and in the case of hydrogen, mu would be two, and in the case of something like carbon or heavier elements, you know, mu could be as high as 40. So distinguishing between these two cases, you know, these give you scale heights that vary by a factor of 20. All right. So a transmission spectroscopy means that you can tell something about the atmospheric composition of the planet if you're lucky enough to be able to do transmission spectroscopy. If you're unlucky, there are clouds that form high up in the atmosphere and sort of block the radiation from the star from getting through.
I like to highlight two planets because I know that, without the combination of transits and Doppler observations—if you just had one or the other—for both of these planets, you would think that these are almost identical planets. GJ 1214b was detected with the transit technique. The planet is in a 1.6-day orbit; it has a mass of about 6.5 Earth masses. Because it's transiting, we get a mean density of about 1.8 grams per cubic centimeter. This implies a water-dominated composition, right? This is a low density, or there's a core that has a massive envelope of hydrogen. Let's contrast this with 55 Cancri, okay, where the period is 0.7 days and the mass is 8.6 times the mass of the Earth. The mean density here, though, is 10.9 grams per cubic centimeter. So these are dramatically different planets compositionally, and if we just had transit observations or just Doppler observations, we would never actually know. So this is pretty impressive—a combination of techniques to understand the characteristics of exoplanets. Theoretically, we can make up a mass-radius curve that shows these models for different compositions. Pure iron composition would give you—here's Earth masses on the x-axis and the radius in Earth radii—so as a function of mass would give you this radius of planet. If you go to 100% water, right, which is pretty hard to do, then you end up with something that's much larger as the mass increases. So now we can plot down on the theoretical curves the detected planets and and see where they fit and and begin to understand them in terms of their composition.
I can tell that I'm running very short on time. I'll just say that there's a nice paper that came out by—yeah—okay—by Marcy et al., which shows that there's a crossover point in the composition of planets. They looked with Caltech data to try and—at least statistically determine the mass—they couldn't actually measure the amplitudes because the precision isn't high enough—but they—they developed some understanding—some limits on the density of planets—and yeah—and showed that the mean density of planets—here's the radii distribution—the mass distributions—there—as sort of in the about 2 to 4 grams per cubic centimeter. There's some weird things like some planets with negative densities because of the way that the Bayesian analysis was done, but you know, we can reject those as outliers and say that, in a statistical sense, we're learning something about the density.
So one of the things that my student has done—a Jack Moriarty—is trying to understand the composition of terrestrial planets, working with Niko Madhusudhan. And I'll go through this quickly, but we start with a model for the protoplanetary disk that gives a temperature-pressure profile, and these come from just literature, and we assume a certain chemical composition—let's say Solar—and this work was done—Jade Bond did some beautiful work on on this—showing what happens as the planetesimals evolved. So we know that the refractory elements are survived at high temperatures and that only the volatile elements—you can only get at cooler temperatures—these correspond to being close into the star or further out from the star. And what Jade Bond did was show that if she tagged the planetesimals with the equilibrium chemistry that you'd expect and then let the system interact gravitationally with a mercury code that she could track the chemical composition as the planets—embryos—accreted material. So my student Jack took this—I'm a little—one step further and said, "Okay, couldn't you have actually carbon-rich planets?" So something that we don't have in our solar system, and there have been a couple of papers that have been hotly debated—if the planet has a carbon-dominated interior instead of a silicon-dominated interior, it means very different things in terms of the thermal transport inside of the planet. So it'll mean different plate tectonics; it'll mean different things for habitability. And what Jack showed—looking at sequential condensation—that is, taking temperature-pressure profiles at different times as the disk evolves—is that the carbon-to-oxygen ratio that was needed to form carbon-rich planets was lower than we ever assumed. So here his models—going along with time—you see the inward motion of material in the disk; the equilibrium chemistry is evolving in the disk of stuff accretes, and it's the temperature and pressure change. And then the takeaway line is right here: If you don't assume the sequential condensation—you just take one snapshot of the of the disk with a certain temperature and pressure—you see that you need very high carbon-to-oxygen ratios to be able to form any carbon-rich planets, and they can only form out here and sort of a 1 AU. But the—if you include sequential condensation, then you can get carbon-rich interiors over a much broader range of semi-major axes and down to slightly lower C/O ratios. Okay. So one problem with that is that when we look at white dwarfs—white dwarfs have presumably accreted—they're planets—and so their surfaces should be polluted with whatever was in the interior of the planets. And so the white dwarf populations don't support this idea that there are carbon-rich planets. They only see pollution of white dwarfs for with oxygen, iron, silicon, and magnesium—the four dominant elements of the interior of our Earth. I think that these two ideas can still be consistent with one another because another one of my students is analyzing a chemical abundances of stars and especially C/O ratios and finds that C/O ratios greater than 0.8 are actually quite rare. So I think that's probably that—yeah—so during the evolution process as they go through the giant phase, then they presumably—okay, maybe that's another—no—but they actually—they do see—um—you wouldn't expect to see—would you expect to see oxygen?—right?—this really looks like Earth mantle pollution on the white dwarfs—that's the claim—near there—such a place—yeah—yeah—I'm not sure—it's a good point—okay—okay.
So how does exoplanets compare with the solar system? Multi-planet systems are common—same as the solar system. There are new categories of planets like super-Earths that we don't have here. There's a wide diversity in density and in chemical compositions that we don't see here. Okay, last question: Do we know a terrestrial Earth? And I can go through this quickly—that was the motivation for launching the Kepler mission. And you know, it's almost—if you believed in a conspiracy theory by aliens, then you would think that, you know, that second reaction wheel going just as we were about to get out to the habitable zone around the stars in the Kepler field is suspicious. But in any case, you know, we've tried to analyze the frequency of Earth-like planets. So we can do this for short-period planets, right, both with radial velocities and with Kepler. And what you see—this is low planet mass—this is high planet—this is 1 to 100 planet minimum mass—and this is planet period—no—planet radius—thank you—planet radius—because you don't get the mass—okay. So in both cases, you see—you can make one sweeping statement: Small planets are way more common than gas giant planets. Yes, three minutes. Okay. So this idea—the habitable zone—which someone else is going to be addressing, I believe, and has been talked about in previous presentations and the previous trilogy of books—shows that, you know, we unfortunately didn't really get down to the habitable zone with the Kepler data. There was some really lovely analysis by Eric Petigura, Geoff Marcy, and Andrew Howard where they tried to extrapolate. So here's what they defined the habitable zone as, and it was a very generous definition—luminosity—that was anywhere from a quarter to four times luminosity intercepted by the Earth—okay—that, you know, Ravi Kopparapu and Jim Kasting—we know—we would say that that's, you know, that's pretty broad—but you can see there really aren't any points in there. So with their extrapolations, they concluded that perhaps 20% of sun-like stars had Earth-like planets in the habitable zone. We did this as an exercise, and we think that the answer is somewhere between 10 and 40 percent, depending on the extrapolation assumptions and using the beautiful data that Eric Petigura actually had. And now, instead of looking at the Petigura habitable zone, which is the red zone, we looked at the habitable zone defined by Kasting and Kopparapu—it's much narrower—and there just aren't enough planets. So do we know a terrestrial Earth? Probably not. Well, we do know is that almost every star has planets. We know that small planets are more common than gas giant planets, and we know that most systems are multi-planet systems. So there's been a paradigm shift in the last years, and I'll just conclude by saying that we're starting something called the 100 Earths Project. We just got NSF funding for our MRI proposal to build a new spectrometer. If we keep using the same instruments we've used in the same—in the past, we're going to get the same results; we're going to get 1 meter per second precision. So we're trying to design instruments that are fundamentally different and to design an instrument that can distinguish stellar noise from the Doppler shifts. So this will be located at the Discovery Channel Telescope, and our delivery date—which is quite aggressive and ambitious—is 2016. So thank you. [Applause] It's um—at the Lowell Observatory—yeah—Flagstaff—okay—400 billion—all right—very good—okay—exactly—okay—thanks very much—yeah—okay—yes—[Music]—with the planets—oh my god—that is—yes—did you say you saw with the IA—you just did—right—yeah—well, I have—I've named three of them—Dinky, Jupiter, and ForPeter—those are the planets around Epsilon Andromeda—but yeah—yeah—all right.