Transcription
Okay, so we'll go ahead and get started. My name is Debra Fisher. I'm a professor at Yale University, and I thought I would put up—since actually somebody asked me yesterday where is Yale—so I was prescient enough to put up a little oops, damn, darn. Okay, maybe there's not—okay, good. So here we are in Connecticut, on the Long Island Sound, and Yale is a really beautiful campus, all built in neo-gothic style. And then here are the happy faces of my smiling team, and they contribute a lot to everything that I know and then try to distill for you in this talk.
So I was asked to talk about the characteristic of exoplanet systems, and what I decided to do is to break this into two parts. The first part is going to be a review of the techniques that are used to find exoplanets, but then emphasis on the observational biases, the incompleteness, and things like that. Because if you don't understand that, then we have this huge ensemble of a thousand exoplanets, and one can say, "Who needs more exoplanets?" Right? Is that when is enough enough? But I think you'll see and appreciate that we're not really sampling the entire parameter space, or perhaps the most interesting parameter space if you're interested in earth-like worlds. So okay, let's see, maybe here. Okay.
So the review is going to be, again, to help you understand the exoplanet statistics, to review the techniques that have been mostly applied to finding exoplanets. That includes the Doppler technique, which is the technique that I've been using since 1997; the transit technique, which Kail really started in 1999 with ground-based detection; direct imaging, which is just taking off now with the commissioning of GPI, but is also—we have some great results from the Hubble Space Telescope; microlensing, which is—you just have to admit—the coolest technique, either because it relies on the warping of space-time continuum; and then astrometry, which has tremendous potential, but only if we have an astrometric spacecraft above the Earth's atmosphere. The Europeans have recently launched Gaia, so I think there'll be some interesting stuff there. Okay, okay.
So I, I did sprinkle in some questions, trying to make this an interactive discussion, because it's no good for me to stand up here and just say stuff that I think you should know. I would like you to tell me, you know, what you know, what you don't know, what you have questions about. So feel free to raise your hand at any time. And then I put pictures of Sherlock in every so often, so when you see that, that's your cue to wake up and stop doing your email, and, and try and answer the question. And most of the questions are just conceptual as we go along.
So just as a make sure we're all on the same page: one slide. Gravity, of course, is a central force; it connects the star and the planet along a line that passes through the center of mass of the system. The planetary orbits obey Kepler's law; the stars at the center of the focus of an ellipse; the planet sweeps out equal angles and equal time intervals; and the orbital period is proportional to the semi-major axis to the three-halves power. There are other angles which I haven't shown here, but I have in my chapter, which is almost getting done, and there's, there's the orientation of the orbit, all right. So we're not looking at the orbit in this nice neat, you know, face-on configuration; the orbit has been randomly thrown into space and has some angle, little Omega, which defines if it's an elliptical—if it's a circular orbit, there's its—it doesn't matter—but if it's an elliptical orbit, little Omega defines this orientation, like that of the long axis to your line of sight. And then big Omega is an angle like this that twists it in the plane of the sky.
The Doppler technique—this slide was taken from Savvy Aid Musk when I was on his PhD thesis committee. I loved this, so I borrowed it from him—and you can see that you sit here with your mascara on, looking at the star. All right, we never see the planet that's orbiting out here, and we're measuring spectroscopically the motion of the star, the Doppler shift of the star. And so the atoms in the atmosphere of the star are red-shifted, or the spectral lines are red-shifted and then blue-shifted as the star comes toward us and away from us. And we map out—an incredibly high cadence—something very bad is happening here—in very high cadence this radial velocity curve, which shows over time how the velocity of the star is changing. Of course, the velocity of the star is constant, but we're only picking up the line-of-sight velocity, and so you know that component is changing. And we model these data; we get the orbital period right away from the amplitude of the signal; we get the mass of the planet times the sine of I; and it's also scaled to the mass of the star. Okay, so this fine I, generosity, is, is, is one of—there may be weaknesses of the Doppler technique. We don't observe the full mass of the planet.
The detection of exoplanets has not been easy; it requires extremely high-precision measurements. And I put up a couple of familiar examples here. If you consider Jupiter, Jupiter induces a reflex velocity in the Sun of 12 meters per second, and the orbital period is 12 years. So you have to look for 12 years very carefully and maintain control of all the errors in your system so that you can pick up this, you know, sine—so more or less sinusoidal variation—due to Jupiter. The Earth is even harder; the Earth tugs on the Sun with a velocity—induces a velocity—of 10 centimeters per second, and of course the period is one year. So the Doppler method only measures this line-of-sight velocity. This is the radial velocity. Circular orbits produce a sinusoidal variation; if the orbits inclined, then the radial velocity amplitude is attenuated by the sine of the inclination; and we have to model at least one full orbit. If it's an eccentric orbit, you can see it right away because instead of having a sine wave, you have a sawtooth pattern.
So here's the collection of planets that have been detected with the Doppler technique, and you can go to exoplanets.org or exoplanets.eu and quickly map this up yourself, plot this up yourself. So this shows the mass of the planets and Earth masses on a logarithmic scale; here's one Earth mass; and this is orbital period in days. And then these, um, the green bar and the blue bar are meant to capture something, you know, about what we think about habitable worlds; so planets that are too massive, okay, are not going to be rocky, Earth-like planets. I'll have substantial atmosphere; it's not that we think life couldn't form on these planets, it's just that, you know, think about it: if there were a really weird life, silicon-based life or something like that, and we're sitting right on the bench of a biochemist, would they detect it? You know, if you ask them that question, it gives them great pause. All right, so if we want to find something that we think we have any hope of recognizing, I think we want to look on worlds that are similar to our own. I can talk about this in more detail, but I think that biochemistry is beginning to show that life is a natural outcome of system equilibrium chemistry. So you have the right pressure, and you have the right temperature, and the system goes along—okay, not in every case—but these will be life-enriched worlds. I think the, the planets that sit in this little box right here, like our Earth. Okay. So you can see how many planets have been detected that are in the habitable zone by the Doppler technique, and the answer is zero. The closest we've come is this little guy here; this is the planet around Alpha Centauri B; it's about one Earth mass, that's in Sinai, but it's probably close, but it's in a three-day orbit, so it's a roaster planet.
The Doppler technique uses shallow spectroscopy; that's because we get so much information. And what we're doing here is we're zooming in—this is a 2D spectrum that we take—and we zoom in, and here's the one-dimensional extraction of flux versus wavelength that we extract. If we zoom in on a Doppler line and think about what we're trying to do, well, here is the red line sort of indicates a normal spectral line, and I've tried to lay down the pixels behind it, and then the shadow just shows what the intensity profile would look like in the 2D image. And what you can see is that one pixel is about 15 microns; the typical dispersion way is about 0.05 angstroms per pixel; and this means that if the, the spectral line shifts by one pixel, we're measuring a velocity change of 2,000 meters per second. Okay, so that means if you want to work backwards—that define things like Jupiter—we need to measure the shift of this line with a precision of about a thousandth of a pixel. All right, and so that's what makes this tough. And if we want to find Earth on this kind of a detector, in this kind of a spectrometer, it would be one ten-thousandth of a pixel shift. So that is a tricky measurement to make. Yeah, definitely. So I'll tell you more towards the end of the second lecture about a project that we're working on—so an innovative instrumentation to try and overcome this. Yeah, we think we can get there.
So now, question is: how do you measure wavelengths? Shows well, the first, you know, wavelength Doppler shift measurements were made using these two lyric features. So if you do a nice expect extraction of your spectrum, one of the tests that you can do to see, "Have I really extracted the spectrum properly," is look at these two lyric lines, which are completely opaque, and they should go to zero. If they don't go to zero, then there's something wrong with your extraction. Okay, so but that's just a little technique. So all of these lines—this band head here—comes from the atmosphere of the Earth, and here are some stellar lines. So people would say, "Okay, I've got this, these Earth lines imprinted in my spectrograph; the Earth is fixed with respect to my, my instrument," all right, but the stellar lines will shift back and forth. And this kind of a measurement let people get down to precisions that were Doppler shifts of about 1/2 of a pixel. Okay, so now, given what I told you here, Sherlock, what are the precision would a half of a pixel shift imply or yield, and how does this compare to the precision needed for exoplanet detection? Well, this is so obvious, I'm embarrassed to actually ask you because we just talked about it, right? But it's a—okay, I'll ask anyway. Okay, a kilometer a second, and, and why is that not good? In this because Jupiter is—is over the period is 12 m/s amplitude, but you're right, we need one meter per second velocity precision to be able to measure that. Yeah. Um, well, I think about that when I build the instrument and how I want to sample the instrument, but I'm not sure exactly what you mean. Yeah, yeah, well, right. So Nyquist sampling would mean—when we build instruments, we design them so that we have some spectral resolution, which is set by the optics, and then the question is how many pixels do you want to put across that resolution element. So that's when I think about Nyquist sampling, and right now we—all the spectrometers are built at—to sample just a little bit more than the Nyquist frequency. So the, the instruments are designed to sample, you know, three—you want at least two, two and a half pixels—they're designed three or four pixels per resolution element. Yeah. Okay.
So the telluric lines were great, right? But they're in the infrared, and after all, the two lyric lines are blowing around with speeds of about ten meters per second. And so we actually take that idea of the telluric line atmosphere and we put it in a controlled cell, right? We, we build our own spectrum—reference spectrum—and we use iodine to do this. So here's—it's about the size of a beer can, right here—and the iodine is—I've built several of these cells—and we fill them with iodine at high temperatures so that it goes in as a gas, and then we have to keep these cells warm through the night. And then imprinted—you can see the difference flipping back and forth—there's a stellar spectrum, and all of else that's on here—all of that other scratch is—yes, yeah, no, of course, thank you. I'd rather do that. Okay, good. Right, and everything else here is our iodine lines—thousands of lines, right—that create—their edged into the spectrum, and they create this nice grid, and then we can measure the Doppler shift of the stellar lines with respect to these very stable iodine lines. Okay, so I could give a talk on, on how to measure toplicians, but that's not what I'm gonna do today. Instead, I'm gonna tell you—and I'm happy to talk to you about this later—that we think we've solved a whole bunch of problems in terms of getting higher precision. State-of-the-art precision right now is one meter per second; there are lots of RV machines that have been built; they all get one meter per second, okay, or worse. Lick is much worse; Tech is about a meter and a half per second; Harkes is about a meter per second; sometimes it's, you know, they've been—and they get point eight meters per second. Okay, so we need to control the instrumental stability; so we gotta keep the temperature and pressure stable; we have to work with the detector manufacturers to build—to have detectors which are dependable and repeatable and understandable; we need uniform illumination of the optics; that means we will never use a slit to couple light into the spectrograph; we will always use optical fibers and double scrambling. We know from our simulations that there's enough information content in the spectrum to be able to pull out five-centimeter-per-second precision over a band of from 400 to 700 nanometers. So the information is there, but then we come down to our analysis errors, which I've been working on for the last 10 years. The point spread function modeling has been a big pain; the data analysis—when we use the iodine technique—we've just demonstrated—we'll have a paper that'll come out in the next few months showing that the iodine technique is degenerate, and we will never get better than a meter per second precision with the iodine technique. So, so we want to get rid of iodine for a couple of reasons, and so my, my group—my instrumentation lab at Yale—has built a fabric—nobble Fabry-Perot frequency comb. It works; it's not the laser frequency combs which use pulsed high-soft lasers, but it works from 400 to 700 nanometers, and we're expecting to get wavelength stability that's good to a centimeter-per-second precision.
Okay, so that leaves us with everything that you guys know about, and one of the reasons that I was excited to come here, which is the Astrophysical noise. And so from my entire career, I've been told that we can't do better with a Doppler technique because we're hitting the floor of the stellar noise. And I was told that as a postdoc when our precision was 3 meters per second, and then when we got to 1 meter per second, I was told that, "No, the floor of the stellar noise is 2 meters per second," and now we're at 1 meter per second precision, and that is apparently the floor of the stellar noise. Okay, stellar noise might be offensive to people who study stellar astrophysics because they think of it as a signal, right? These are things like pulsations—5-minute pulsation signals in the star—granulation. Okay, I don't care about granulation, but what I do care is if the magnetic field strength varies, then this—the strength of the granulation changes—and so the signal—the spectral line profile—will change. Spots that rotate on the surface of the stars and long-term activity cycles—all of those things. But let me just put forward this idea that measuring the Doppler shift of a line, right, every single line is moves in a predictable way; it's just Delta lambda over lambda equals V over C, the non-relativistic Doppler equation, period. Okay, but all of these things affect the line differently; they're not moving the line centroid. So, so I believe that if we build the right instrument, we should be able to distinguish between these two distinct signals; we just have to try harder. So how we address the Astrophysical signals is now the hot topic in this field. So the Astrophysical noise is, as I said, these are spots, flares, meridian, all flows—these have—we heard yesterday—I have velocities of, you know, perhaps a kilometer per second—subsonic, supersonic outflow velocities when they come out, right? What goes up is not exactly what goes down because the intensity of the hot outflow and gas is different from the intensity of the cooler gas that falls back down, and so you end up with convective blue shifts in the spectral line profiles. These come from this—again, the, the stellar photosphere—and they'll be different for lines of form at different depths in the stellar atmosphere. So can we distinguish the photosphere, okay, from the Doppler signals? I should probably have a little Sherlock standing here, except I don't know the answer to that question. I hope so.
Okay, we know a lot more now because NASA launched the Kepler mission, and in fact, what we hear is that most stars—or many stars—are more active than the Sun. We cannot rely on finding the handful of stars that have low activity, right? We're gonna have to address this issue head-on. So here you see the flux of a star that's varying over time; this to me looks very much like spot noise; this is a, a 30-day window photometric measurements from Kepler; here's another star; another star; another star. So this is going on, and what would be really great is to simultaneously monitor the photometry of stars while we're taking our Doppler measurements, and you'll see why I think this is important again when I get to the second half of my talk. Okay, the, of all of the things that can go wrong on the surface of the star in terms of noise, star spots are the one that worried me the most. These have orbital periods that are similar to the planets that we want to—sorry—these have rotation periods—periodicity z'—that are similar to the orbital periods that we'd like to extract, right? And they happen for reasons that you probably know already: a stellar line is rotationally broadened; when the spot blocks out fluxes from the approaching limb of the star, you lose a little bit of flux from that part of the spectral line contribution, and when it's on the other side, you lose some of the red-shifted flux. So this—my code is not very clever right now—and does not really have the resolution to know what's going on—that doesn't have the instrument—doesn't have the resolution—so my code says, "I look—the, the whole center of mass of the line just shifted red-word," and here it just shifted blue-word, right? And so I interpret that as a Doppler shift, and it has a periodicity of the rotation period of the star. Okay, so that's, that's a problem. So my undergrads are actually working with one of my grad students; they developed a spherical grid, and on this spherical grid they allow a dark spot to go around, okay, and so—and, and then they take an intensity-weighted velocity—a calculated intensity-weighted velocity at each—for each moment here—this is no JD—so this is time on the x-axis—and you can see just from the spot alone, you pick up a radial velocity signal, okay, just from, from that alone. So that's superimposed now on our spectrum; it's not this clean though because the spots going over granulation, and when it crosses granulation cells, very strange things are happening, right, in terms of masking the hot upwelling. And so my grad student, Matt Shigera, is working with Minister Bonnie Basu, student Joel Tanner, to look at 3D models of granulation and to figure out what kind of sampling we really need to be able to see this effect in the spectral line, and then we can solve for it and go on to finding planets.
So here's some Doppler data for Tau Ceti. Tau Ceti is—it's an old star—older than the Sun—its chromosphere is and active; it's a G8 star. We always hold this up as our poster child for, "Look how good our velocity precision is," okay, and to you guys, this is a scale of plus or minus 100 meters per second over time. This may not look very good, but this was really pushing the state-of-the-art back in the day, right? So this is on the old Hamilton spectrograph at Lick Observatory where I tried and tried to improve the precision, and now I realized that it was, it was always going to be a lost cause because the instrument wasn't stable enough. So I was the PI for—
Chiron, which is a spectrometer that we built at CTIO, and on the same scale, you can see that we've improved things quite a bit. But you see this interesting variability right here that looks very systematic, and this still isn't good enough. This is now one meter per second precision, and where we have to go to be able to pluck out the earth is this kind of a signal, long term, with long-term stability. So this is for an instrument that we're now designing, expressed with the D for the Discovery Channel telescope.
Okay, on a scale of minus 100 to 100, the Chiron data looked pretty good. But now I'm going to be totally brutally honest with you, and I'm going to zoom in here on a scale of plus and minus 4 meters per second. It's the same data that I showed you on the previous slide in the bottom left corner, but now I've put in this picket fence here, which is a picket at every, at the periodicity of the rotation period of the star. So this star rotates with a period of 33 days, and every 33 days I've dropped down a blue line. And so what you can see is that where we're measuring right, this looks highly structured. These are not random velocities. So I, I don't, I can't say unambiguously what it is, but so here's what Sherlock says, and I would like to hear what you guys think. Does this look like a signal from photospheric from the star process? Does it look like exoplanets? Does it look like instrumental noise?
And I will tell you that there was a paper by Thome et al. which looked at HARPS data and Keck data, and maybe I can't remember a couple other observatories, and what they announced were five planets in the data. Okay, I think that that was probably—well, I don't agree with this analysis that they did—but one of the planets had a period of 35 days, and I can see exactly why they would think that that's a planet. Does that look like a planet to you? So we'll start with that question. Then if not, why not? Yeah. Okay, you don't see any—what? Okay, well, I, I see that right, exactly. Okay, I guess what I mean, right, this is what we, what we have when we sit down and look at our data, and now we're in this, like, you know, era of where we have to say, "What the hell is that?" you know, and why isn't it flat? We tried; we went back; we put the, you know, we did so much to stabilize the instrument, and this is what we get for all of our work. You know? Pardon? Yep. Well, when I, when I take, when I take a Fourier analysis, then outcomes 33 days. Yeah, it's very strong. Now if, yeah, in almost every window. Yep. Okay, that's what I, I think as well. Alright. And so, so now what does this mean for us as we go forward? Right? It means this is what my velocity, this is all my velocity code can do; my Doppler analysis code can do is pull out this signal, and I can say, "Oh, yeah, it's a spot. I'm gonna model it." I can come up with not just one spot, but I'll put in a few spots, and they'll be at different phases, and I'll put in an attenuation, and I guarantee you will be able to beautifully track this velocity curve, and then the residuals will be nice and flat. Okay, but will that be the right explanation? How will we really know if we don't have other evidence? And other evidence that I would like to have are two things: I would like to have precision photometry from space to go along with the simultaneous measurements of these velocities, and I would like to have a spectrum which has enough sampling so that I can look for line bisector, right, line profile variations, which would look like spots and not like Doppler shifts. But I can't do either one of these. I have right now my instrument. Yeah. Yep. For a G8 star, it's just, it's an old G8 star. Right. Okay. Right, right. Yeah. Okay. So now if I were to plot down the Keck data on top of this, there would—which of course I did—there were four data points; they jumped all over the place, but not enough to see any structure. So who knows what we were seeing? Right? And also the error bars were large; they're a couple of minutes. So again, you have to realize the scale is small. So if you say, "Go back to that picture I made where my students have this rotating spherical grid," you can say how big the spot is, and it's less than 1% of the star that induces this kind of an effect, and so it would be hard to see without very precise photometry in the back. Exactly. Oh, that's a great point. So I'm not sure about a couple of weeks. I think that the timescale for spots is probably a few rotation periods. Um, this again is a G8 star; has a huge convective envelope. Right? But I think I do see some attenuation in here of the spot signal. Right? And you know, and it's probably multiple spots and some out of phase. Yes, that's a great point. Okay. And now study our beautiful stable star has an inclination of 30 degrees, and so that means if you put a spot at a latitude of 60 degrees, you see it the whole damn time. It's unbelievable how nature is like against us. Yeah. Right, because there's no radial velocity. Oh, right, right. That's, that's a great suggestion. For our little telescope, this on a 1.5-meter telescope, we need bright stars. We sort of chose Tau Ceti because we knew that the inclination is low, so we thought that would suppress any spot noise, and it has, and still with a tiny spot we can, we can pick up this in our—when we model it. So yeah, any spectral—what? Oh, no, I haven't—that's an interesting idea. Great, great suggestion, then. Yeah, that would be awesome. Good, good suggestions. Then I would like to talk to you guys more about that spectrophotometry—polarimetry, sorry—looking for polarization. It'd be horrible. Yeah, might not be a very strong magnetic signal on the star, and you know, things like Zeeman splitting, I think you'd never see. Yeah. So that's what we're gonna have to, we're gonna have to like push on all these fronts because we have to distinguish these two things. What? Uh, right, right, right. Yeah. Okay. So, so anyway, I think the solution is we need new instruments and we need new techniques, and they have to be simultaneously. We have to pull the community together to solve this problem and not just, you know, throw up our hands and say we can't do it. Okay. So, so that's what we're gonna do. We're building our—as our instrument will have very high resolution and high spectral line sampling, so we'll be able to measure line bisectors more precisely and use other techniques. So I'll be talking to as many of you as possible.
Okay. So in summary, I've taken a lot of time talking about the Doppler technique, but it's what I know the best and what I love and care about and working on. So, so we can summarize the biases in the Doppler detections in this way: The Doppler observations favor the detections of more massive planets. Right? They induce the larger reflex velocities, and really we haven't detected that many planets that are less massive than Neptune, which is 17 times the mass of the earth. And it also favors the detection of planets in closer orbits. The radial velocity amplitudes are reduced by the, or by the inclination of the orbit, but this constraint is actually not as strong as you might think. Even if you get down to an inclination of 13 degrees, or at 13 degrees, M sin i is a factor of two less than the total mass. All right. And if you calculate the probability, there's an 86% probability that the inclination is actually higher. So again, this is also in, in the chapter that I have for how you calculate the probability of inclination. You have to have at least one full orbit for detection. So you don't go to the telescope and find the planet, and you're done. You have to, you know, you have to stick with it for a while. Our current precision, a meter per second, is not sufficient to detect Earth analogs. The stellar noise is limiting the precision with our current instruments, but it's been a successful technique that's detected more than 500 planets in the last 20 years. And in this nice plot, which was first made up by my friend Greg Laughlin many years ago—he's a theorist—and so he would plot this, that detection x, the number of detections as a function of the year of discovery. And for Greg, there was a really clear trend here, and if we just waited till 2015, we'd be finding lots of Earths. Right? But we, to actually make that leap, we have to continue to improve our measurement precision.
Okay. So now the transit technique has been incredibly powerful. Here we're looking at the stars, and we're measuring the brightness of the star. This is a technique called photometry over time, and it has to be measured differentially. So you have to have good comparison stars. And in this nice plot—picture that was figure—that was put together by Josh Winn in the exoplanets book, he shows what the flux looks like over time, and you can see that it's a, it's a kind of funny shape. So when the planet is here in front of the star, you have a minimum in during transit as the, as the planet blocks out light from the star. As the planet goes around, just before the secondary eclipse, you have a combination of the star plus the illuminated planet, and so it actually brightens a bit, and then it, as the planet goes behind the star, dims down. So you have the star alone. So this is great because when you have this configuration, because you have a way of getting a spectrum or any information about the star alone, just look when the planet is hidden behind the star, and then you can look at any other time, and you can divide out that signal from the star and get information about the planet. The transit depth is dependent on the ratio of the planet to the star radius. Transits only reveal the radius of the planet, not the mass. And the radius of the planet therefore depends on knowing the stellar radius accurately. So that's been tricky with all of the Kepler data. Of course, the transit detection is more favorable for close-in orbits. That's because you can see a slightly larger range of orbital inclinations when you're, when the planet is close to the star. Here's an expression for the probability of a transit, and you can see that as the semi-major axis increases, the probability of the chance it decreases a bit. There's also an eccentricity term that comes in here, and I think my next slide—I can't see—no. Okay, let's—slide after that. So I'll wait to come back to that point. Here's some nice data, I think taken by Tim Brown with the Hubble Space Telescope. This shows two stars, TrES-1 and HD 209458. Is the bottom line; that's the first detected transiting exoplanet, and you can see this little blip here in TrES-1, which is a K2 star, I believe, and that happened because the planet was crossing a spot on the star, and so you got this, you know, you had less flux that was being lost than in the integrated disk. So with these data, you can determine four quantities: You can determine the mass of the star, you can determine the radius of the star—wait—yeah, well, let's see, I think you have to know the radius of the star, and I have to go back and read that paper again. So there is a paper here, Seager and Mallén—or not Arnett, or Nellis, in 2003, where they list in a very clever way how you can pull out all these parameters more than you might think, but at the end of the day, stellar variability also limits the photometric precision for transits. Okay, here it looks like it's not much of a limitation, but you can imagine that if this were a very shallow transit and there were more spots that it would be a problem. So for smaller planets that are comparable to the photometric, you know, depths of this, of the spot signals, this is a real limitation. In this nice paper by Heather Knutson, HST multiband observations were taken for HD 209458. The depth of the transits doesn't change so much as the shape of the transits as you go from red to blue. And so these show the different wavelengths that were measured. Here's the bluest, and here's the reddest, and here's Sherlock. And so, why do these HST transit curves of 209458 have a different shape at different wavelengths? Atmosphere of the planet? Okay. Different optical depth of the star? Yeah. The limb darkening of the star, because in the red, the star looks very much like a disk. Right? I mean, the, the effect from limb darkening is almost nil. So as you were sort of alluding to, when you go to the blue, the limb darkening becomes more important; it softens the edge of the star, and so you end up with a shape of the transit curve that's more rounded. So limb darkening—when you look at limb darkening, you're looking through the edge of the star; you're always looking to an optical depth of one, but you're looking at higher levels in the star, which are cooler, right, then when you look right on the center of the disk. You're looking deeper to hotter regions in the star. So here you're looking always at redder wavelengths of light, and so the star in red wavelengths appears almost like a more—it has a more solid edge, but at blue wavelengths, right, it's diminishing because of the, the reddening from the limb darkening. Does that make sense? Okay. Right. Okay. Yes. Oh, shoot. Okay. So I just want to say that the combination of a planet radius and planet mass, right, which you get from Doppler and transit measurements together, are really powerful because they tell you the mean density of the planet. If you just assume a two-layer model for your planet, you have a completely constrained model for the interior of the planet, and this is incredible. So you measure some size for the planet and some mass, and you can say, "Well, this was the right mass," but to build this two-layer, right, this is presumably the inner solid layer, and this is maybe a mantle layer that's a little lower density. I could get the right mass this way, but I would have the wrong radius, and I could reapportion then my allocation of solids—interior and mantle material—here, and I could get the right mass and there—oh, and the right radius—oh, and here the wrong mass because I have too much, too little in the solids. So anyway, this two-layer—that the combination of transits and Doppler measurements constrains the simple cartoon model of a planet interior perfectly. Well, if you want to assume a gas layer, then it's more difficult.
Okay. So Sherlock again, how would orbital eccentricity and the orbit orientation affect the transit duration and the probability of detecting a transit? Okay. Right. So if you're looking, and the star is here, and right, and so, and periastron passage is here, and apastron is here, right, then the planet is traveling slowly. But what's the probability of detecting this because now the distance between the planet and the star is quite large? Right? And remember that probability expression that I gave you—the farther away you are, the harder it is. But now if I flip the eccentric orbit like this, then all of a sudden a planet that has a large semi-major axis has a still a small distance from the star at periastron passage, and so the transit probability goes up as long as omega—little omega—the orientation of the orbit is right. Okay. And so it means that we can, we, and we have found planets in 200-day orbits that are transiting because that we had this lucky orientation. Okay. Here's a question: Do you think that the atmospheric circulation in the planet could affect the transit light curve in any way? Okay. And so, how could it affect it? Was a white person? All you—okay, but you're looking at the night side of the planet, right, during transit. You're looking at the night side. So how does the—I'm not sure if it's the albedo, right? Okay. Okay, exactly. So you're thinking of, yeah, how big the atmosphere looks, and also, but also whether the circulation of the atmosphere is efficient. Right? If it's very efficient and you have winds that are bringing the heat around the backside of the planet, it brightens the backside of the planet, right? And now your transit depth isn't as big, and you misinterpret this as a smaller planet than it would have been. Right? Absolutely. It does definitely affect the second occultation. I totally agree. Okay. We talked about how star spots affect the curve and limb darkening, and I'm going to be completely out of time, and but let's see, here's the total count of—don't wanna break the—transits that have been detected, and you can see how the bias in, in this detection technique. So the transits are clearly favoring the detection of short-period orbits. It's not—we don't know if this is actually a flat distribution, but we do know that they're missing them here, and we do know that we can correct for the geometry of the detection efficiency, and that probably this is just an observational incompleteness. So you—I think you all have my slides that show the transit detections. I want to just quickly flip through a few other techniques.
Direct imaging. Direct imaging basically takes the star and shrinks it, okay, with adaptive optics correcting for scintillation in the Earth's atmosphere. And so when you go to the observatory, they'll say you're measuring a strong ratio of what, a fraction—it'll be zero to one, right? In high strong ratios mean that you have a higher concentration of starlight in the core here, but you always have a halo intensity out here, and since the planet is separated spatially from the center of the star, you know the planet intensity will be like this, and when you add this to here on this logarithmic scale, you see nothing. Okay. But the detection techniques—GPI is a new instrument that's much better; has much higher-order corrections, and you can compare these observations. Here's Keck AO of the two same two stars, HD 18799. This is a simulation of GPI. However, I've seen the data, and the data look like the simulation; it is actually stunning, a stunning clean image. So what matters here is angular separation, and you need fairly bright gas giant planets for them to be able to show up here, either through reflected light or through their own light. The key is—the other thing is that you're biased to seeing younger stars. So this is the luminous—circular planets—the luminosity of the planet as it ages will decrease, no matter what the mass of the planet is. And so for a given sensitivity in AO, you know, here's the current sensitivity, you can only get very, very young Jupiters, and they tend to be in young star-forming regions far away. But with GPI, we're able to reach some cooler, older Jupiters, which is going to be, I think, extremely important. If you do simulations, you see that you're still only dipping into a small fraction of exoplanets in this modeling. So here's a summary of the biases of the direct detection technique. And then microlensing is amazing because what you're doing is you're at the observatory; you're looking at a distant star. In between you and this distant source comes an interloping star; we're gonna call that the lens star, right? And the lens star is warping the space-time continuum, right, so that the, that you used to be able to see one ray—one ray coming from the source star—now all of those rays that were diverging are bent towards you, and while the lens star passes in front—between your line of sight—you get a temporary brightening. Okay. So here's the cartoon: You're at the observatory; you're watching the source star. Down comes the lens star with the planet, but here's what you observe: You see a brightening first from the star, and then you see a second brightening from the planet. Okay. So the key—the key is this—the key is what I'm gonna ask you: Microlensing was developed as a technique to find dark matter. The time of the microlensing event scales with the mass of the lens. Let me ask you what parameter do you think affects the amplitude of the brightening? So that's exactly what I would think as well, but no, it's not. It has the mass is as a very low-order term. What matters is the impact parameter—so how close you come either to the center of your line of sight with the source or along some caustic—and that's a stunning result. It means that microlensing is sensitive to little planets, to moons, to all—
Sorts of things that we can't find with other systems. So here's a result: it was announced on July 3rd from Michael lensing team. Andy Gould was the first author. This is the lens, this whole picture, a binary star system, and around one of the stars is a planet. Okay, so there were in fact three lensing objects: star A, star B, and then a two earth-mass planet. Okay, that lens this background source, and the those these stars are thought to be something like three kiloparsecs away, so incredibly far away. And here are the data, and you can see that binary stars causing these two dips here. The planet actually causes a sort of negative dip in the in the photometric curve because it's crossing a caustic in some strange way.
And what you see here is this beautiful also coordination. So this is one of the great things in astronomy that you, for you young people, I want to encourage you: we're team together. Look what you can do if you team together around the whole world, right at longitudes around the world observatories, we're picking up this star as it was setting from another one, and they were able to reconstruct this only with that team effort. So that's incredible. W first will be launched soon. Here's HST with pic field. Here's JWST, and W first is going to dwarf these instruments in terms of its field of view of the sky for detecting microlensing and other things. You guys should be watching this instrument very closely. And David Spergel has a nice article on Astro pH: what every astronomer needs to know about dub first. So here the microlensing biases summarized here.
And then astrometric is a little bit easy because we haven't really detected any planets with the astrometric technique. It relies on, you know, the center of mass being far away, so it means that you're favoring long-period orbits unless this is done from this from space, though the sensitivity won't be high enough. I was on the SIM team long ago, the space interferometry mission, which unfortunately was cancelled, but you know, I think Gaia is launched; it's the new game in town, and it's going to be incredibly exciting. So it will measure, you know, 10 to the 8 stars and obtain 70 measurements over a five-year period for some really quite exciting work.
Ok, I think that's our break, and take 10 minutes, and then all yeah, take 10 minutes, we'll be good. Yes, yeah, and we can take a few questions. Yes, I didn't yeah, it might be in the second half of my it's definitely in my book chapter, and I can't remember know what is exactly in the second lecture, but yes. So this is an amazing technique, so as it's just like a star spot, the planet will block the approaching and then the receding to the side of the star, right? But instead of traveling on the surface of the star, so having a rotation period of 33 days, the planet crossing is a few hours, and you can measure this with the radial velocity technique. And so the combination of that that technique is amazing because it tells you whether or not the planet is coplanar with the equatorial spin of the star, and so it's a very powerful yeah technique that's added a lot of information. Thank you.
Yeah, they're bright. Yeah, they're more luminous when they're young. That's right. Yep. Oh, well, wait, the first 10 or 20 million years. Well, okay. Yes, so you're right; there's still some debris disks, and the zodiacal light from the debris disks definitely impacts the contrast that you can measure, so that's that's exactly a problem. Yeah, so I think it's why it's important to be able to look at the older planets which may still have there may still be some debris disks, but they're probably more tenuous. Yeah. Good. Alright, ten minutes.