ASTR 160: Frontiers and Controversies in Astrophysics

Lecture 5

 - Planetary Transits


Professor Bailyn talks about student responses for a paper assignment on the controversy over Pluto. The central question is whether the popular debate is indeed a “scientific controversy.” A number of scientific “fables” are discussed and a moral is associated with each: the demotion of Pluto (moral: science can be affected by culture); the discovery of 51 Peg b (morals: expect the unexpected, and look at your data); the disproof of pulsation as explanation for the Velocity Curves (moral: sometimes science works like science).

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Frontiers and Controversies in Astrophysics

ASTR 160 - Lecture 5 - Planetary Transits

Chapter 1. A Case for Pluto? Interactions between Culture and Science [00:00:00]

Professor Charles Bailyn: I have spent a very enjoyable weekend reading your Pluto comments. No, that was fun. It is a surprisingly–it’s a surprisingly deep topic. There are technical issues about how orbits of planets work. There are these interesting cultural and political currents that underlie the whole thing. And also some sort of deep philosophy, or what the literary professors like to call “theory,” about what it means–what it means to name something, and what the consequences of particular names are. And so I thought I would make a couple comments on the Pluto thing first, before we get back to the Hot Jupiters.

Let’s see. The first thing I would say–let me encourage you all, when you get this kind of a question–answer the question that’s asked. The biggest problem in the answers that I saw was that sometimes you just didn’t address the specific question that was asked. What I asked was, “To what extent is the Pluto controversy a scientific controversy?” You don’t answer that by a narrative describing what happens. If you say, “Well, they discovered Eris, and then that threw the scientific world into confusion, and then they had this big meeting and there was all this fuss, and then people started to get involved who weren’t scientists,” and so forth–that doesn’t answer the question. Because the question was, “To what extent is this a scientific controversy?”

There are two possible categories of answer to that question. One is, “Yes, it is primarily a scientific controversy.” And the other category is, “No. It was primarily not a scientific controversy.” And if you didn’t say one of those things, or something somewhere in between, then that’s not kind of responsive to the question. I would say that you could answer that particular question in this case, in both directions, perfectly well. If you want to make a case that it’s a scientific issue, you say, “Look, classification is very important to science.” I made that point in class on–a week ago, and that, you know–you’ve got to have your classifications right in order to understand what’s going on. And what has happened? Here is–new data has come in, which has thrown the old classifications into question. Although, it should be noted that there wasn’t officially a definition of “planet” that goes back to antiquity. And one of the things they were trying to do was to create one. But that–as new data came in from the outer parts of the Solar System, we had to revise our classifications. And this is a key point of science, and therefore the whole thing is, at root, a scientific issue.

But you could also argue the opposite, in that, you know, the scientific issue was not really in doubt. Nobody was questioning whether Pluto and Eris and all those things ought to be in the same category as Jupiter. Clearly they’re not. That wasn’t the issue. The reason this became so controversial is because there were a lot of people who –scientists and non-scientists ‒ who thought that it would be nice if Pluto could remain a planet. And therefore, they came up with these rather convoluted definitions, in order to maintain the idea that Pluto should remain a planet. And then, they got into trouble, because fifty other things would, therefore, also have to be planets. But it’s rooted in a non-scientific desire for Pluto to remain a planet, and for very few other things to be admitted to this pantheon. And that is fundamentally not a scientific thing, and you could argue that that’s the whole root of the entire issue.

Now, one of the interesting things is that these non-scientific things affect the scientists too. A lot of you quoted this guy, Alan Stern, who’s a planetary–a famous planetary scientist, who objected to the way it all ended up by saying, look, one of the definitions that they’ve put down is that you have to clear out your orbit. And Pluto doesn’t make it in that–in that context, because it crosses the orbit of Neptune, which is a much bigger thing. But, Stern goes on to say, Neptune also crosses the orbit of Pluto. And so, obviously, there’s some hidden assumption here about, you know, the thing that’s much more massive counts, and the thing that’s less massive doesn’t count. But that hasn’t actually been stated, and so this is a lousy definition. And so he objected on scientific grounds to this definition.

And some of you noted that Stern is the principal investigator of the New Horizons Mission, but I don’t think you noted the implications of that. The New Horizons Mission is a planetary probe that is on its way now to Pluto. And the reason that it was launched–Al Gore was actually very enthusiastic about this when he was Vice President. The reason that this was launched was because Pluto was the only one of the planets that Voyager didn’t go to. And so, we have these fabulous pictures of, you know, Saturn and Uranus and Neptune. We have no fabulous pictures of Pluto because nothing had gone there. And in the late 1990s people thought, well, this is dumb. There is a planet out there that hasn’t been explored. We’ve got to have a mission to go to this planet. So now, it’s seven years later–the mission just went past Jupiter actually. So it’s on its way out, and all of a sudden, the thing that it’s going to has been demoted. This is awkward. [Laughter.] You know, we’re spending 100 million dollars of your money to go see the last of the planets, and now it’s not a planet anymore. And here’s the guy who’s in charge of that mission. And so, of course, he objects to the change in definition that demotes his object–which he’s spending fifteen years of his life and 100 million dollars of your money to study–has now been kicked out of the realm of the planets. So, not surprising that he would take that particular point of view.

Mike Brown’s another example. That’s the guy who discovered Eris. And he has a lovely thing on his web site about how “planet” ought to be a cultural definition. And he kind of advocates for a thing where, because it’s cultural, you’ve got to keep Pluto in. And because you’ve got to keep Pluto in, you’ve got to allow anything bigger than Pluto. So you just have an arbitrary, culturally enforced cutoff at the mass of Pluto. And then–and things that are more massive get to count also, because otherwise it would be unfair. Look what this does though. It means Eris is a planet and none of these other things are, which means Mike Brown is one of the four people in the history of humanity who has discovered a planet. [Laughter.] And so that’s a very convenient definition. And so, you know–and then he actually very graciously goes on to say, well, I’ll settle for being the discoverer of the largest dwarf planet until a bigger one gets discovered. But you can see, he’s not really happy about it. He’d much rather the thing be decreed the tenth planet, and perhaps reasonably so. So, the scientists are also affected by these kinds of things in ways that you have to think a little bit about before–as you interpret what their take on the scientific parts of the controversy really are.

So let me summarize all of this–this is going to be–I mentioned in the first class that I was going to tell fables about science with morals attached to them, and that you could then explore these further in your optional paper, if you choose to write one. So here’s a fable, which is “The Demotion of Pluto.” And one could ascribe a variety of morals to this, but let me write down one version that happens to appeal to me, which is just the fact that I think science can be affected by culture. And you need to keep your eye on that kind of thing when you interpret things that scientists say; particularly if they’re saying it to journalists. They’re often much more circumspect in the things that actually get published in the journals. Okay.

There was one kind of argument that rubbed me the wrong way a little bit when some of you said it, which was–people had a little bit of a tendency to say, you know, all this definition and classification stuff, that’s–the word ‘trivial’ or ‘silly’ is sometimes used. That’s kind of unimportant, and it detracts from the science. And, I have to say, I don’t agree with that. I think it’s important for the science to get these classifications right, because otherwise you don’t know how to describe what you’re looking at. You don’t know how to interpret it.

Chapter 2. Velocity and Center of Mass [00:08:53]

Oh–I should mention something about grading, I guess. It was six points on that problem. The way I did it was, I started out–everybody sort of started out with five of those six points, and if you said things that were incomplete or incoherent or dumb in some way, you got points taken off. But there was also an extra point you could get for being especially coherent or especially original or interesting, or just generally waking me up after I’d read forty others of them. I bring this up just to point out that if you get five out of six on that particular problem, that doesn’t mean you’ve done anything wrong. It wasn’t that we started with a perfect score of six and started subtracting things off. It just meant that I felt that there were others in the pile who were somehow more coherent. We’ll hand these things back at the end of the class, by the way. And I’ll make some remarks about grading of the overall problem set at the end. Okay.

Another general point that showed up in other parts of the problem set was a kind of issue about velocities and the center of mass. Let me–here’s the center of mass of some orbit, and, of course, that’s not a physical object. That’s just a point in space. And the key thing to understand about the center of mass is, the center of mass doesn’t move. It doesn’t move in space. That’s a fixed point in space. So, this doesn’t move–actually I should be more precise. Its motion doesn’t change. So, if it’s stationary in some coordinate system, it sits there. If it’s moving at some velocity, it continues to move at precisely that velocity. So the–it’s–and then, you can redefine the coordinate system so it doesn’t move in some other coordinate system. But it doesn’t go around in circles or ellipses or anything. What does go around are the things going around it, one of which is the planet, which is over here–the other of which is the star, which is over here. And the way these two things move, they have to stay one on each side in a straight line that–woops, I’m going to miss–in a straight line that goes through the center of mass. I drew that wrong, so let me redraw it here. There we go. Yeah. And so it balances, right? That’s what the center of mass is. It’s the balance point. And so the star has to stay exactly opposite to the planet.

How big are each of these things? Well, that depends on the ratio of the masses in an equation we wrote down before. The consequence is that as these things go around they stay on opposite sides of the center of mass. So the amount of time it takes the planet to go around the center of mass–that’s the orbital period–has to be the same as the amount of time it takes the star to go around the center of mass, also the orbital period. So the orbital periods, P, are required to be the same because it has to take them the same amount of time to go around this center of mass. Because they have to stay on opposite sides of it the whole time. The P is–So the orbital period, P, is the same for the planet and for the star, whereas the velocity and the semi-major axis are different. Because, while it takes the same amount of time to go around, the star is going for much less distance. So the distance is shorter, and therefore the velocity has to be less for the star. So we can talk about the Vstar versus Vplanet and a star versus a planet. And we can add these things up to makeV total and a total. But you don’t do that with the period. The period is the same. Okay. So that’s an important concept. Questions?

Let me point out that this concept of the center of mass gets more complicated when there’s more than one planet. Because again, the center of mass is still a fixed point, even when you’ve got two planets ‒ and so one of the things–so the star is going around the center of mass because of this planet, but it’s taking other extra little wiggles as a result–if there’s a second planet, as a result of that planet. The center of mass has to stay exactly in the same place. And the consequence of this is that the motion of one planet is actually a little bit affected by the gravity of the other planet. So it, too, is executing extra little wiggles due to the presence of the second planet. Those wiggles are very small compared to the motion that’s induced by the Sun, because the other planet’s much less massive. But they really are there, and, in fact, the planet Neptune was discovered because the orbit of Uranus had extra wiggles in it that couldn’t be accounted for by the known planets.

And so, in the nineteenth century, a couple of clever mathematicians figured out from the motion of Uranus where Neptune had to turn out to be, in order to explain these extra, unexplained motions. And then some astronomers looked, and there it was. It was a huge triumph for Newtonian physics and a damned hard math problem, too. And so, this concept becomes a little more complicated in the case where there are more than one planet. But in fact, the way we’re going to deal with that is just to separate it into one planet at a time.

Let me give you an example of that. Let’s see, I don’t think we need to change the lighting. Woops! Backwards. Here we go. All right. So, this is a radial velocity curve of some star, and it–you can see these points. Here are the observed radial velocities at a variety of times over a course of three or four years. And then they’ve drawn in a sine curve–or it’s actually not quite a sine curve. It’s close to a sine curve. And you can see that the sine curve more or less goes through these points, which is nice because that indicates the presence of a planet. And you have velocity over here, but I should mention something about velocity.

What they mean is not actually velocity. What they mean here is radial velocity. And this is an important point. It’s not that the speed changes. What changes is–between here and here on this plot ‒ is not the speed of the thing, but its direction. Because at plus 200, that means it’s going away from you at 200 meters per second. At minus 200, it means it’s coming toward you at 200 meters per second. That’s why you can have a minus velocity. At zero, it does not mean that the thing has stopped. It’s going at the same speed as it was up here and the same speed as it goes down here, but in a different direction. So, it’s going still at 200-plus meters per second, only it’s going sideways. And so it’s neither coming toward you nor going away from you. Therefore, its radial velocity is zero, and you measure no Doppler shift. Remember these plots are created by measuring the Doppler shift, and the Doppler shift tells you how fast something is either coming toward you or going away from you. So, that’s an important point. You can have dramatic changes from positive to negative in the radial velocity without changing the speed of the object at all. All you have to do is change its direction. So first, it comes toward you, then it goes sideways, then it goes away from you, then it comes sideways again.

So that’s what this plot represents. And you can see that these points go up and down, as they should if something is in orbit around the center of mass. And these little points down at the bottom are–represent the difference; actually, they’ve put it down here, this should be zero on the scale. This is the difference between the observed points and this sinusoidal model that they’ve put up there. So, they’ve just calculated the differences, and there’s some scatter. But it basically follows pretty well, the scatter is a whole lot less than the changes in the velocity.

But it turns out, you can do better than this. And here is an example. Now, what the line is now is not one, but two sine curves added together, one of which was the one we saw before. So they fit for two planets now. And the other is another sine curve with a different amplitude, because that planet induces a smaller motion in the star and also a different period. And so, at certain points, the periods line up and you get big deviations. Then at other points, you get wiggles on top of wiggles, and these things kind of beat against each other. So this complicated pattern of this line here is just two sine waves added together. And now, the points line up much better. If you recall, these deviations between the points in the lines before were, you know, of up to, say 50 meters a second. And now they’re much smaller. The things fit much better. I’ll show you a blowup now of this region of the plot where a lot of these points are, and you’ll see what I mean.

Here are the points. Here is the line, and you can see that this complicated line really fits these points quite well. That’s evidence that there are two planets in this system. But, in fact, it gets even better than that because what they then did was they said, all right. Here’s what we’re going to do. We’re going to take these so-called residuals. We’re going to subtract off our two-planet model. And we’re going to see whether we can see anything interesting going on in what’s left over after those two planets have been taken away. And when they did that, they saw this.

This is–they sort of grouped them all together, and they found something with a period of 1.9 days that now has what looks like a sinusoidal wiggle of about a few meters per second. Remember, where we started, the deviations were 200 meters a second, but you now subtract off this–these two planets ‒ and you’re left with a third. And so this system is now known–this particular star that they were observing is now known to have three different planets around it, of which this one is the one that has the shortest orbit, 1.9 days. So there are now several examples of things in which we know that there’s actually more than one planet in one of these systems. And this is how we find that out that the motion of the star is not just one sine curve, but the superposition of two ‒ or, in this case, even three of these things.

Now, one of the interesting things about this is it’s quite a short orbit, 1.9 days. That’s one of the shortest orbits known. It also has a relatively low amplitude. The velocity–the radial velocity changes are quite small. So, the induced speed in the star is quite small. Those two things put together give you a relatively low mass of the planet for reasons I’ll make specific in just a second. This is one of the lowest mass planets that’s been discovered in this way. It’s only about ten times the Earth’s mass. That’s kind of comparable to–a little less than Neptune and Uranus. And so, in this case, it isn’t actually clear whether you should think about this thing as a kind of low-mass outer planet or a big Earth-like rock. And so, that isn’t clear in this particular case.

Let me make this a little more specific here. What are the inputs that you need to know to figure out how big–what the amplitude of that sine curve is–how big the wiggles are? You need to know a couple of things. You need to know the velocity of the planet, which isn’t what you observe. Remember, you’re observing the velocity of the star. So, velocity of the planet, which is approximately equal to the total velocity. As one of the exercises on your problem set, you can demonstrate that that is equal to GM / a, the square root of GM over a. So that means–Yeah?

[Unintelligible student voice.]

Oh, yes. Good. Thank you. [Adjusts overhead projector.] How about that? Yeah. Okay. So, this means short orbits give you small a, large velocities of the planet. This makes sense. If you’re in close to the star, you have to move faster to keep yourself in orbit.

But, of course, you don’t observe the velocity of the planet–you observe the velocity of the star. The velocity of the star is equal to the velocity of the planet, times the mass of the planet over the mass of the star. And so, large planet masses generate large star velocities. So the two things you need to know is: how short is the orbit and how massive is the planet. And so if you have a short orbit, that’ll give you high V planet. And if you observe–so you observe the short orbit. And the other thing–if the other thing you observe is a low, relatively speaking, V star, then it must be true that you have a low planet mass. Because if this is big and this is small, you’ve got to compensate for it by having a small value out here. And we’ll come back to this kind of reasoning in a minute.

Does that make sense? So in fact, that particular planet with its very short orbital period but its low induced velocity in the star–so short period, short semi-major axis, but also small V star, is the lowest mass planet, I think, at this point, that has been observed by this particular method. Okay.

Chapter 3. Observations of Hot Jupiters and the Selection Effect [00:24:23]

But as it turns out, most of the ones–the short-period planets–that have been observed are more massive than that. And we’ve got these Hot Jupiters. And so the argument here, using the same kind of reasoning, is that you have short periods, moderate values, moderate to high values as these things go for V star, and that tells you it’s a massive planet. And as I pointed out last time, this is deeply disturbing in terms of what we know or what we think we know about planetary formation. So, short period plus massive is, to put it mildly, unexpected–so unexpected that they almost weren’t discovered at all.

What happened, this–the discovery of the planet around 51 Pegasus happened in 1995. And the way this worked out was, there was a team of astronomers, Geoff Marcy and Paul Butler, chief among them, in California, who had the best equipment for doing these kinds of very high-precision radial velocity measurements. And they had embarked on a campaign to find Jupiter-like planets, which they thought they could do. And they were piling up data on many stars. They were looking at many Sun-like stars. And then one day in 1995, they woke up and a bunch of people in Switzerland announced the discovery of the first planet, which disturbed them mightily, because they had been scooped. And, it disturbed them even more when they discovered that the particular star that this planet was around–this 51 Pegasus thing that I was talking about last time ‒ was one of the stars that they themselves had been observing.

But the thing was, the period, you remember, was four days. And Marcy and Butler and Co. were expecting the periods to turn out to be ten years. So they hadn’t checked to see whether there were four-day variations. And as soon as this paper by these other astronomers, these Swiss astronomers who discovered the thing, was published, they said, damn! We’ve got a big pile of data on this particular object in our desk drawer. We ought to take a look and see whether these other guys are right. So they looked at it and within a week of re-analyzing their data, they were able to confirm the fact that this really was a planet in a four-day orbit. And, annoyingly to them, they already had the data that they could’ve announced it first, if they’d looked at it and asked the question, “Does this thing actually have a four-day orbit?” But it didn’t occur to them because it’s well known, you can’t have a Jupiter in a four-day orbit. So, they kind of didn’t check.

So here’s another fable for you, “The Discovery of 51-Peg b.” That’s how you label these planets. A is the star, B is the planet. And the moral–I guess you could say this in a couple of ways. One would be to say, “Expect the unexpected.” And the other would just be to say, “Look at your data.” But look at your data so that you could see things that aren’t the thing that you expect to see in your data. And that’s kind of an important lesson, I think.

Anyway, it turned out, it was relatively easy to find these Hot Jupiters, and within a few years they–Marcy, and Butler, and the Swiss, and some other teams as well ‒ had found literally dozens of these things. So within a few years, there was dozens of Hot Jupiters known around many stars. And so they hadn’t yet, of course, found anything like our own Solar System. Because they hadn’t been looking for ten years yet. The orbit of Jupiter, you will remember, is ten years long. So, they found all these Hot Jupiters, and this might have suggested that ordinary Solar Systems are rare–Solar Systems like our own. Planetary systems are rare. But I’ll put a question mark after that, because it isn’t really at all clear that that’s true. And the reason is that Hot Jupiters are easier to find than ordinary Solar Systems, for exactly the reasons that I wrote down just a minute ago. The fact that they have short periods and massive planets generates larger values ofVstar. Both of those factors make for large values of the thing that you’re actually trying to observe, which is the velocity of the star.

So, of course, if you go out and you have some new technology and you’re trying to observe something, the first ones you’ll observe are the ones that have the largest signal of the kind you’re trying to observe. So if you’re observing radial velocities, you’re trying to measure V star, the first ones that are going to pop out at you are the ones with large values of that.

It’s also true that it’s easier to observe these shorter periods. If you’ve got a four-day period and you observe the thing for a month, you’ve watched it go back and forth, you know, eight times or something. If you want to wait for eight orbital periods of Jupiter, that’s 80 years–and it’s just going to take you longer. There’s a general rule in science that no project can take longer than it takes one graduate student to get a Ph.D. Because, of course, it’s the graduate students who do all the work, and it’s just hard to recruit a graduate student to work on a project that won’t be completed until they’re 70. And so these shorter periods are easier to observe, just because they’re short, in addition to the fact that the thing you’re observing is much easier to see.

This is called a “selection effect.” So you’re just more likely to see certain kinds of objects than others for the straight-forward reason that they’re easier to see. And those will be the ones you find first. And if you don’t take this into account in thinking about the statistics of these things, you’re going to screw up because, of course, you see the easy ones first. Of course, you see lots of them before you see the others. Nevertheless, the existence of even one Hot Jupiter was a crisis for planetary formation theories. Because there’s no way any such thing ought to exist. But even one Hot Jupiter messes up our theory; so, I’ll just write that down, “messes up theory.”

Chapter 4. Hot Jupiters - Double or Pulsating Stars? [00:31:55]

And so, as soon as even the first of these was discovered, people started to think about what the alternatives might be. And there are two kinds of alternatives, ways to explain the data without having a Hot Jupiter. So, alternative number one was that a so-called “low inclination double star” ‒ so, I’ll explain that in a second. The second object in this is supposed to be a star, not a planet, and there are known double stars with short periods. They’re formed in a very different way. Double stars don’t form–the second star doesn’t necessarily form out of a disk around the first star. It’s formed–I don’t know ‒ by splitting the star in half at some early part of its evolution. And so you get a very different expectation for what kinds of periods you have, and there are many double stars known with short periods of this kind. But so, then, how do you explain–if it was a double star, you would expect that the induced velocity would be much, much bigger because the star is much more massive. And so, what you do is, you explain it by saying, well, here is your–here is you observing it and the orbit, the orbital plane is like this. It goes up and down. So the stars are orbiting each other this way. So they neither come toward you very much, nor go away from you. And therefore, the velocity is high, but the radial velocity, which is the thing you observe, is low. So, high velocity, but low radial velocity because the system is going sideways–orbits are, the technical term here is “face-on,” not “edge-on.” Okay.

So, that was one hypothesis. This didn’t work out for two reasons. Problem number one, no evidence for light from more than one star. Stars are much brighter than planets, right? So, if you’re looking at a star-planet system, all you expect to see is the light from one star. And that’s what is observed. If you’ve got a second star in that system, the second star shines like a star. And so, you would expect to see some evidence of light from a second star in that system, and none of those was observed.

The other problem is a kind of statistical one. There are many Hot Jupiters. Now, if you’re going to explain all these things by having face-on orbits with respect to us, imagine what some observer somewhere else in the galaxy–with all these things–here’s us in the middle of our galaxy, or somewhere in our galaxy. And all these objects happen to be lined up exactly face-on toward us. Some other astronomers would have to see them edge-on and so forth. So why is it–what cosmic conspiracy has caused all these things to be lined up face-on toward us? It’s as if someone had carefully set up all these double star systems to fool us into thinking that Hot Jupiters existed.

This is the kind of argument that people tend to reject because it requires that we are in a very special place, or that some very special coincidence has taken place. And that isn’t–and as you keep finding more and more of these things, you wonder, well, how come–aren’t some of them lined up edge-on? And in fact, it has to be very close to face-on, and so the odds that all of these things are face-on to within plus or minus one degree starts to become really small as you pile up more and more of these objects. Many Hot Jupiters–they can’t all be face-on. And so, as more and more of these things were discovered you could explain any one or perhaps two of them as being face-on star systems. But it starts to get more and more difficult to believe that all of them are in that category. Okay. Let me see–what do I want to do here? Okay.

Alternative number two is pulsating stars. Now, this is interesting. Stars do pulsate. The Sun pulsates just a little bit, not enough so that you could see it in this way, but there are other stars known that pulsate by large amounts. They go out, they go in. Think about what happens if you observe a pulsating star. Here it is when it’s small but getting bigger. So, all of the star is expanding. But if you look at that star, you only see the half of the star that’s on your side of the star. So you only see this part over here. And all of the surface of that star is coming toward you. Right? Because this part–it’s expanding–so this part’s coming toward you; this part’s going half-sideways, half-toward you. This part’s going half-sideways, half-toward you. So if you add up the light from all this, it has a net bulk motion coming toward you.

Now, supposing you look at it when it’s at a different part of its pulsation cycle. So now it’s big, but going–but falling in. Now, you’ll see the opposite. All of the parts of this star are moving away from you. Some are moving sort of sideways, but others are moving away from you. And so you expect that if you observe a pulsating star you’ll see first positive radial velocity, then negative radial velocity, then–as it pulses back out again–positive radial velocity. And that starts to sound very familiar. Right? That’s pretty much what we observe. It goes up, it goes down. And so the suggestion was that these things might actually be some kind of pulsating star. Okay.

So, problems with the pulsating star explanation. Basically, solar-type stars, which these were–stars aren’t supposed to pulsate like this–aren’t supposed to have large pulsations. And it’s also true that pulsations, in general, don’t lead to sinusoidal variations in radial velocity. An orbit naturally gives rise to a sine wave if the orbit’s close to circular. Pulsations–there’s no particular reason to have that pattern. You could have sudden rises and then gradual decays and then things of that nature. You don’t expect it to be sinusoidal.

Chapter 5. Measuring Doppler Shifts to Understand Hot Jupiters [00:39:49]

But both of these things–you know, what’s weirder? That there a lot of Hot Jupiters in the world, or that you have some kind of pulsation mechanism that you haven’t experienced before. Both of them are sort of equally in violation of current theory, and so you might as well assume that you have weird pulsations as well as having weird planets. However, it turns out that the pulsation theory makes a testable prediction. And to explain this prediction I have to take a little digression and talk a little bit about how Doppler shifts are actually measured.

So, measuring Doppler shifts. What you do is you look at what’s called a spectrum. Those of you who–no, gosh, I’ve spelled that wrong. “Spectrum.” Spectrum is just a plot of intensity, how much light there is, against wavelength. And if you work out–if you measure the spectrum of any particular astronomical object, you’ll see that at certain wavelengths there is much less intensity or much more intensity than at many other wavelengths. So, you’ll get a plot that looks kind of like this. There’ll be certain specific wavelengths that have abnormally large or abnormally small amounts of light coming from them. These are referred to as spectral features, or sometimes, lines. And when you have too little, these are called absorption lines. These are called emission lines because you have extra emission or absorption of radiation at those particular wavelengths.

There’s a good explanation of why this happens from atomic physics. I won’t go into it in detail, but let me just say that there are specific wavelengths with much less or much more emission–or more emission–and each one of those wavelengths is caused by atomic transitions, which emit more or absorb particular wavelengths of light. So, it’s caused by atomic transitions. I won’t explain what those are in detail, but each comes from a specific chemical element. So, hydrogen has particular wavelengths associated with it. Helium has particular wavelengths associated with it, and so on and so forth.

And this, by the way, is how you can determine what stars are made out of–determine composition of stars. But for the present purpose, the point is that you can go in with a bunch of hydrogen in the laboratory, and measure what the wavelengths of these spectral features are if nothing is moving. So–can measure these wavelengths at rest in a lab. And so you know in advance what the rest wavelengths of these things are. You go out and measure them in stars, and it turns out they’re not quite where they’re supposed to be. And that’s how you determine what the Doppler shift of any particular object is, by comparing these spectral features to where they are in the lab.

Now, here’s–so if we go back to talking about pulsations, so here is–this is kind of a blow-up of an absorption line this case. So here’s intensity, and here’s wavelength, and it looks something like this. And so there’s a particular set of wavelengths that are absorbed. Now, if the whole star moves, if the star is moving because there’s a planet around it–what happens when it gets redshifted? Well, this whole thing moves to the right to longer wavelengths, and you get something that looks, you know, sort of like this. So this is–whole star moves away from you. And so, the whole thing shifts back and forth.

But pulsations are a little bit different. When you get a redshift due to pulsation, it’s because, you know, you’re looking at something that does this. Part of the star moves away from you, but part of the star moves sideways. And so, only part of the emission is redshifted, but other parts of the emission are not. And so what you do is, you sort of–it’s not like the whole thing moves sideways. It’s that it sort of gets smushed out. Because part of the star moves sideways, but–part of the absorption line moves sideways, but part of the absorption line doesn’t move because it’s coming; you know, it’s, like, coming from this part of the star, which is going sideways to you. And so what you do is you get something that looks more like this.

So this is–part of the star moves away. So the center of this line has moved. Here’s the center here. It’s gotten even more redshifted than in the case I drew there. But part of it has been left behind. And so the prediction is that for pulsations the shape of these spectral features changes–shape of “lines” change–whereas for orbital motion, only the position of the lines change.

So this can be observed. You can go out and observe, and you can see whether the shape of the lines change or not. And they did that, and it’s not pulsation, but is consistent with orbits.

I think this is kind of a cool experiment. Because, you know, this looks a lot like science. Right? There’s two hypotheses, each of which makes a different prediction. Prediction one–hypothesis one, it’s got to change its shape. Hypothesis two, it does not change its shape. You go out, you measure the thing, and you find out which hypothesis is right. This is just what they told you in eighth grade and, therefore, just what I told you a couple of days ago never happens in astronomy. But sometimes it does. And so this is yet another fable, “The Disproof of Pulsation as Explanation for the Velocity Curves.” And the moral here is, “sometimes science works like science.”

So there were, for several years, all of these attempts to try and explain the Hot Jupiter, the radial velocity curves, without actually having to bite the bullet and believe that Hot Jupiters exist. None of them were very convincing. This double star hypothesis didn’t seem to work out. The pulsation hypothesis didn’t seem to work out. But nevertheless, people kept trying to come up with alternative explanations, until something happened that pretty much nailed down the idea that these things really, honest-to-goodness, are planets. But I don’t have time to tell you about that now, so we’ll talk about it on Thursday. Okay.

[end of transcript]

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