Transcription
All right, so I've talked about the plasma. Now I want to talk a little bit about how the properties of the obstacle matter. The first thing, and probably most critical, is the issue of conductivity.
And so what I have here is a solar wind, or other plasma, flowing from upstream from the left onto the obstacle. The width of the solar wind that could, in principle, encounter the obstacle is twice the moon's radius. You'll notice there's a big difference in these two diagrams between what actually happens as the flow reaches the obstacle. So, and we're assuming now a sub-magnetosonic flow, so I don't have to worry about shocks.
The electric field of the flowing plasma imposes a potential drop in the solar wind. I mean, if there's an E, I can write it as minus grad Phi in the steady state. And so there's a potential drop across, and for a poor conductor like the moon, that potential drop imposes itself across the body. The surface charge accumulates and shorts out the imposed field, and plasma flows unhindered to the surface. And so I'm showing it flowing into the surface on one side, and I'm showing an empty region. Now, that empty region is empty of flow; it's not empty of magnetic field. These lines are meant to be flow streamlines, so don't think that there's no magnetic field there, but all the plasma, to zeroth-order, has been blocked from reaching the region behind the obstacle.
Now, for a good conductor, and Io is a good example, the electric field drives current through the body. Because once you impose the electric field on the body, the body can conduct, can conduct, and just work. And so I start driving current through the body. That current has to close; it closes through the upstream plasma, and it produces a J cross B force that diverts the plasma upstream of the body. And now we get a fraction of the flow that is actually running into the surface. And you can see that I've tried to show here a length across the upstream solar wind that corresponds to plasma that actually is on flow lines that will run into the body, and the rest gets diverted enough to go around the body.
Now there's very nice mathematics that relates the conductivity to the electric field and tells you what fraction will actually, of the upstream flow, will actually close across the body. Let me just say that if it's a perfect conductor, all of the plasma will go around; if it's a perfect insulator, all of the plasma will flow on. And for realistic conductivity, some fraction will actually encounter the surface, and there will be a finite, a finite potential drop across the body. So the electrical conductivity that I'm talking about may be that of the body itself, but in most cases it's actually an ionized envelope that surrounds the body.
There are examples that are really kind of dramatic. I have an Enceladus plume movie which showed last time; it doesn't want to show now. Okay, well, believe it or not, these are plumes that are moving back and forth. This is a movie that maybe will work that shows me the volcanoes at Io, taken from New Horizons images. There aren't many of them, so I'm just looping; it's going back and forth, but you can see that the plume is time-varying. That's a volcano off the surface of Io. And so we have some very major sources of neutrals, like the volcanoes of Io and the plumes of Enceladus. There are also the possibility of neutral particles sputtered off the surface and vapor trails from comets.
Here's an example of sputtering by particles of different energy. The left panel is showing what happens if sulfur plus ions are sputtering from the surface of Europa. This is a cut north-south and in the radial direction toward Jupiter. And so you get sputtering by sulfur ions. In the middle panel, it's by oxygen ions, and in the right-hand panel, it's by protons. And so you can see that Europa is surrounded by a cloud of neutrals, and there's always a possibility of ionizing those neutrals. And indeed, though it's extremely, there's good evidence that we get ionization of these neutrals to form what we call pickup ions. So, I am neutral collisions or other mechanisms of ionizing these neutrals then allow currents to flow, not through Europa, but through Europa's environment. So, though that's the source of the material that carries the closure currents I was discussing as necessary when I showed you the Alfvén wing currents in the canonical planetary environment, of planetary moon environment, the interaction region can be highly extended.
So here's an image of a comet, and this is the direction toward the Sun, and this tail is a dust tail. It lags the comet in its orbit. The comet's orbit is probably in this direction, and it's lagging the comet, and it's—oh, I don't think you can see when I point with my pointer—the comet is moving in this direction, the Sun is in this direction, and this is the dust tail, and it's lagging the comet in its orbit because neutral material moving farther and farther out is going with a slower and slower angular velocity. But you notice there's a second tail that's lined up with the direction to the Sun, and that's the plasma tail, and it is formed of material that's come off the comet and someplace along the way has been ionized, either by photoionization, by impact ionization, or by charge exchange. It's now picked up by the solar wind, and it's flowing away from the moon at the solar wind velocity, which is very, very large, so it looks almost perfectly aligned with the Sun. If you got far enough away, it would begin to lag.
So how do metals carry, conduct current? Anybody want to tell me how a metal carries current? Oh, come on, with electrons. Okay. So if the ions are fixed and the electrons are mobile, and they move through the ions readily, but there's no metal near the surface of—so we—where can the current flow, and why, and and what carries it? Any thoughts? Well, you could carry it with ions, or you could carry it with electrons. On the other hand, to a very good approximation, the ions and the electrons are moving together at the V cross B velocity. So we need to do something to separate the ions in the—yes, it has to be something charged, and we have two types of charged; that's true. So this recurrent requires electrons and ions to move differently. Nobody—what you—you were hearing about the ionosphere. What, what makes the ionosphere conducting? Why isn't the ionosphere like the magnetosphere, with the ions and electrons moving together? What's different in the ionosphere? I see somebody in the back of the room smiling. Okay, anybody ever thought about collisions? Don't we—didn't we have a discussion about the difference between the F layer and—they remember what happens in the A flare? What it—what happened in the F layer? Anybody remember what—what was responsible for the collisions? I mean, what was experiencing—was it the electrons? Okay, so it was the ions with the larger gyro radii, and the question was how frequent were collisions compared with the ion gyro period or frequency? If it's near the ion gyro period, you begin to be able to separate the motion of the ions and the electrons, and that allows current to flow. So that's a—so as I said just now, the in the low-energy collisionless plasma science, ions and electrons move together, and that doesn't make current, but we could either have a fluid layer beneath the surface—I said there are no surface metallic layers, but there is the possibility of a fluid layer—or the high neutral gas density, partly ionized, and where there are collisions. So you could have an ionosphere if the density is high enough to make an ionosphere that's collisionally bound, in some way gravitationally bound, then you can carry the closure current in the ionosphere, but you can actually carry the closure current with pickup ions, and that's something we're going to talk about. So that's what I call discussion material.
So here is how you carry current with pickup ions. So first I'm showing you—you can see my pointer—that's so much easier. So I have a field out of the board, of an electric field up. I have a neutral with a bound ion and electron, and the whole thing is flowing. So the E is consistent with V cross B, I hope. And now we ionize the neutral, and all of a sudden the neutral comes—it's at rest; it's at rest. I—was the plus charge going to move? So if somebody other than David tell me—well, the ion move right, left, up, or down? You can be right one-fourth of the time by answering any of them. Okay, you tell me which way will the ion move? Why? It—what's—what's exerting a force on an ion, a positive charge at rest? Does a magnetic field exert a force on a charge at rest? No. Okay, Nathan, it—what does the electric field—so which direction? Lovely, by n mu. Good. And which direction will the electron move? Down. Okay. So here they go. Why are they twisting around? Because there's a magnetic field, and as soon as they start moving—at rest, the magnetic field doesn't do anything to them, but as soon as they start moving, they start twisting. And if I got it right, one is twisting one way, and the other is twisting the other way, but they are moving at the E cross B velocity. So at the end they've both reached the same point—no current. Okay, both drift at the E cross B, on average. I mean, of course they're—they're always moving at different velocities, but on average, both moving in the E cross B direction at a pro speed velocity.
Now the effect of pickup then is just to make an ion-electron pair, and so there's a momentary current along the out direction of the electric field. You notice that at the end of the—when we've got a constant situation established—the gyro center, the mean position of the ion has shifted up by one ion gyro radius; the mean position of the electron has shifted down by one electron gyro radius, but that's effectively zero. So there—the whole—the bottom line is that a plus charge has moved one ion gyro radius on average. Well, that's enough to make a current of the charge times the ion gyro radius in the direction of E, and since we have many of these ionizations per second, we get a current density that's in the direction of V, but it's Q times the gyro radius times the time derivative of the pickup rate—I mean, the pickup rate, excuse me. Okay.
Now collisions between ions and neutrals also provide a mechanism for having—yes, Junior, that lect is neglecting what? Gravity. Gravity is neglected in all of this discussion. It tends to—it—gravity balances the centrifugal force at Jupiter, for example. At two Jovian radii inside of that, or even near that, you better start thinking about gravity, but out where the moons are, gravity is down by so much that we can ignore its contributions. Thank you for pointing that out. Okay. So this is—that was a strange current that—let me just go back to—that's a peculiar current; it's a current in the direction of a—it's very transient, so you really have to have a rather large pickup rate to make this be a current that is significant, but I believe it gives you a pretty good idea, despite the fact that some of my colleagues question—I think it gives you a pretty good idea of how you make a current in the direction of the electric field.
Now I want to talk about ions and neutrals. And so let's imagine we have a bunch of neutrals around—same setup—B out of the paper, slide wall, and E going up. And now I have some particles moving in—the ion bumps into a neutral, and that displaces it; it also slows it down. And so the effect is that at the end of a certain amount of time, the electrons have—they've been not affected by this collision at all; they're just moving along at the E cross B velocity, and the ions have been slightly displaced—that—that's a—it does depend on just where in the gyro motion the collision comes, so that's not really important—but they've also been slowed down, and so—mathavan displaced—it depends, but it—they've been displaced in the direction of E. So the fact that the ions have been displaced and in the direction of E gives you a component of current along E; that's a Pedersen current. The fact that the electrons have been undisturbed means that there is a net current not in the E cross B direction, because the current, of course, is number times velocity times charge, including the sign of the charge. So since these electrons are carrying charge fast in the E cross B direction, there's a net current in the minus E cross B direction. That's the whole—yeah, but they wouldn't—like—I—they—I said—think how far they get displaced depends on just where they get—they hit—no, if there aren't—I mean, the—the—the net displacement will be in the—in—think I think the net displacement has to be in the direction of E—it stops, it starts again in the Eider—yeah, yeah, I—thank you very—regardless of where you stop it, it starts in the E direction, so there's a favor—it favors the—thank you, good. So there's a net movement of positive charge in the E direction, net flow as negative charge in the across B direction. That's what happens in an ionosphere, and it requires that the collisions be at the rate of the border the ion gyro frequency. If it—if the rate goes way above the ion gyro frequency, these poor ions that have gotten collided with never—never get away because they—they keep getting hit, so they never get accelerated. And if the ion gyro frequency is—is very different—is very much—anyhow, you've worked it out; I'm getting myself twisted it up with bigger and lesser.
So let's start looking at specific cases, and the first one I want to look at is Earth's moon. I just have to see if there's something coming up—no—was that one? Okay. So these are real data. I think I'm going to show you very little real data, but I am quite taken with the data being provided by the Artemis—I said famous, but I should call it Arnhem—Astana—fall of you know about the Artemis mission—with Artemis mission put five equivalently instrumented spacecraft into orbit around Earth to study substorms, and after solving the substorm problem, they—they decided to send the two outer spacecraft to the moon and launch a new mission called Artemis. Now, the beauty of Artemis is that, for the first time ever, we have one spacecraft in the so unperturbed solar wind, while we have a second spacecraft very near the moon. And by comparing the data from these two spacecraft, we can see what the moon did to the solar wind. The changes are very, very small, so you have to have really good knowledge of what the solar wind is doing in order to see the changes. And Jean had all have done a study in which they've used hundreds of orbits—maybe thousands, I think, I can't remember—and here is the distribution of the magnetic field—uh, I don't understand—I should have had density—why is there—it seems to have lost my density plot—I didn't understand, but there should be a density plot. The density plot is showing a very significantly depleted wake. The scale on this starts from two moon radii upstream to twelve moon radii downstream; they're all in the solar wind. And what you can see is that in the region that we call the wake, that is depleted of plasma, the magnetic field strength goes up. And that's—so that you will have pressure balance. You have, in the solar wind, you have magnetic pressure plus thermal pressure; in the wake, you have just magnetic pressure. If you want them to balance, you have to squeeze the wake in and raise the field strength of the magnetic field. So the magnetic field is a little bit stronger—this is the top of the scale is 1.3 nanoTesla increase—that's the change between the solar wind and the—the field in the wake. And then there's a region in which it's lightly deeply did relative to the solar wind, and that region is bounded by wings that we can understand in terms of the relevant waves—the sound magnetosonic waves that are present. So it's—it's really very beautiful set of data that tell us just how the moon interacts. Basically, what you see is nothing happening upstream, and that's true in the density too, and that supports this picture I was showing you where a non-conducting body really does not affect the plasma that's upstream. The—everything here can be understood in terms of removing the—the solid material—the plasma of the solar wind and just seeing how it refills with time and how the magnetic field compensates for the loss of plasma pressure.
Other moons of interest are the Galilean moons of Jupiter. And even though this is sort of out of focus and D and fuzzy, they think it shows you that Mercury is smaller than Ganymede, and it shows you the order of the Jovian moons—Io, Europa, Ganymede, Callisto—and all of these are really interesting in their interactions, but I'm just going to focus on Europa. And the problem that we face in outer planet science is even more acute than the problems that are faced in magnetospheric—Earth magnetosphere—or even solar physics. We rarely have enough measurements. We have flybys; we have—never had—other than for Earth's moon, we haven't had a scientific spacecraft in orbit around these moons. We're hoping that will change, and that's where theory and simulations are helpful. And so I'm showing you a simulation of the interaction with Europa. In this picture, the upstream flow is hitting the surface, interacting with the—the quote surface of Europa, but again, I think that's largely the—the ion population that's—that's been formed around Europa that provides the obstacle. You get what we call these Alfvén wings that show you where the kinks in the field develop, carried by Alfvén waves. You can see compression upstream where the flow is slowed, and that—that propagates—that's a compressional wave that propagates upstream. So we do have nice simulations of Europa that seem to reflect quite well the kinds of things that are observed in flybys of Europa. It also shows a second kink back here where the field magnitude begins to decrease, and the second compressional wave begins to contribute. So aside—with apologies—apologies to my friends who are experts in simulation—simulations are extremely useful, and I see one of my simulator friends smiling—use them to educate your intuition, but don't believe them. You've heard about problems—I think earlier this week—what—last week—with grid sizes and roundoff errors, but that's only one type of issue. And to me, the most serious is boundary conditions. When we simulate the Earth's magnetosphere, we have a little problem; we have supersonic, super-magnetosonic solar wind coming in on one side; nothing can go back outside, at least in the MHD limit. So to say that we can prescribe the inflow, it's fine because we know that no—none of the waves can go back upstream and do anything to them. I mean, of course, I understand there are things on other scales than MHD, but even in the MHD limit, we don't have to worry about that upstream boundary. On the downstream boundaries and the side boundaries, we usually set open boundary conditions—say anything that gets there keeps on going out—but—Navier—try to simulate Ganymede. Ganymede's in a sub-magnetosonic flow; as soon as Ganymede feels the wind hit it, it starts sending waves back upstream, and it modifies the inflow, and you don't get that right. So what you do is you damp out the waves because they couldn't be very important, and that's bad enough, but the internal boundary, which affects overwhelmingly most of the simulation box, we don't even know what the boundary conditions are at the surface of Ganymede. So that we have all kinds of problems that arise, and I've—I asked ideas, but I've sort of given you the kind of problems that arise. There are other problems—see, when you simulate a moon, it's much—you capture the physics much better if you use a spherical grid because the whole system is dominated by this spherical obstacle, but the boundaries of the box are usually rectilinear, and when a spherical grid hits a flat surface, it doesn't know quite what to do. There are—there problems there. So the final statement is that most people do not remember that when you write down differential equations, coupled or non-coupled, simple or complex, the solution is not known until you specify the boundary conditions. Just think about the equation for an exponential—until I tell you where I'm interested in it, whether I want it to go to zero at infinity or whether I'd be perfectly happy to have it go to infinity—an infinity—you don't know what the solution to the equation is. So the boundary conditions are part of the question, and you have to have them right.
You want to get the right answer, and we never have them fully right. So you can really get very, very badly misled by having the wrong boundary condition. So use the simulations; look at what they tell you, and then go to the data and try to see if they—if you can understand them better by using the simulations. Okay, so now I—I’ve been talking about conducting moons, but of course my favorite moon is Ganymede, which has an internal magnetic field. But I also kind of like Europa; it has a different kind of internal field.
So there are permanent magnetic fields, and those are like Earth’s magnetic field and Jupiter’s magnetic field. They are generated by the kinds of dynamos that Sabina Stanley told—talked about. And the only moon with a significant permanent, large-scale magnetic field of internal origin is Ganymede. There are a lot of adjectives there; that’s because, for example, the moon—our moon—has very highly concentrated magnetic regions on the surface, but they’re local; they’re not global.
Oh, now then there’s also the issue of induced magnetic fields. And for—just to remind you—if you change a magnetic field, to remember what Faraday’s law says: dB/dT is equal to minus curly. So as soon as you change a magnetic field, you produce an electric field. If you have an electric field and a conducting medium, it drives the current. Currents drive magnetic fields; you’ve got a loop. A changing magnetic field produces a changing current, and the current produces a perturbation magnetic field. And at the Galilean moons, the external field varies as Jupiter rotates because of the 10-degree tilt of its dipole from its spin axis. So the dipole is always wobbling around the spin axis, and you can see that in some of these images of sulfur ions taken from Earth and published by Schneider and Trogir. So the—this line across is the emission from a torus of ions at Io’s orbit. Io’s orbit is—is at Jupiter’s equator, but the ions are closer to the Jupiter’s magnetic equator. And what you can see is the orientation goes up and down. So this is one side of Jupiter; this is the other. You see it’s tilted up here; it’s tilted down here; it’s tilted down here. Those are different phases of the magnetic rotation.
So at the—at the position of the Galilean moons, you’re going from above the magnetic equator where the radial component of the field is outward from Jupiter to below the magnetic equator where the radial component of the field is inward. And so this is what happens when Jupiter’s dipole moment rotates around: first it points one way, then it points the other, then it points back and—points down as it rotates back and forth. The equator goes up and down, and you get an inductive response at—if you have a conductor embedded in this time-varying magnetic field. The amplitude of the inductive response is determined by the time-varying component of the external field. On average, at the orbits of the moons, Jupiter’s magnetic field points southward. That average field changes very little; the north-south field changes very little; it’s the radial component that changes. And the magnitude of the inductive response is determined by the amplitude of the time-varying field and the conductivity and thickness of the conducting layer. So then you get the—a—you get an induced field that is oscillating in its orientation. So all the Galilean moons seem to develop inductive fields in response to the time-varying field of Jupiter.
And so here I’ve just put in—in equations—what I said in words: time-varying magnetic field produces an electric field that requires that there’s a current provided that there is—is a finite conductivity or even a very large one. And then the current that you—the perturbation current you’re driving—now produces a perturbation magnetic field, and that’s the induced field. And let me just tell you that we saw evidence for induced fields at the Galilean moons, most compellingly at Europa. So here’s Europa. We have a time-varying primary magnetic field that is going in the radial direction toward Jupiter; it changes direction; that drives a current that is flowing around Europa someplace near the surface because the signal is very large. And remember, dipole field falls off from the distance with distance from the region where it’s generating like the ratio of your distance to the generation radius cubed. So it falls off very rapidly. We know that the inductive field is close to the maximum that we can imagine for the size of the primary field. So the current has to flow very close to the surface. So those are what we call the eddy currents. They produce a perturbation field that has a dipolar shape outside the body; it’s actually uniform inside the body, and it is this perturbation field that the Galileo spacecraft was able to observe.
Now you’ll recognize that if it’s varying in direction in time, sometimes when you’re on this side—whatever this side is—of the moon, you should see the field pointing up, and then when you get into a phase where the field is reversed, you should see the perturbation field pointing down. The effect of a—of the maximum inductive field you can make is to cause the external field lines to be expelled from the body. So that’s what the total field would look like. I think all of the—at Europa we found the induced field pointing in opposite directions on two different Galileo flybys, which couldn’t have happened with a permanent field. For the other moons, let me just first say that if you have an inductive response, you have to have a conducting layer within the moon. If you have an inductive response that’s near its maximum size for a sphere of the size of the moon, the layer in which the currents are flowing has to be very near the surface. Now the three moons that have icy shells—Europa, Ganymede, and Callisto—have a region that we know is made mostly of H2O. What we don’t know is what is the state of H2O. When we look at the surface, we can see it’s solid, but the equation of state of water is very complicated. There are heat sources in the center; the pressures going up; the temperatures going up as you go in. It is not implausible that there is a liquid layer between the outer surface and the rocky interior. And the evidence that these three moons—Europa, Ganymede, and Callisto—have inductive fields is the most—to me—the most compelling evidence that there must be a melted layer in the H2O ice that covers the surface. You need some electrolytes dissolved in that layer in order to account for the conductivity, but salty water—seawater—would be a good enough conductor to account for the observation of the inductive field.
Now Io has no icy layer. Furthermore, we did not have direct measurements of the inductive field at Io. However, we find that the data that were acquired during flybys of Io can be far better fit if we assume that there is a conducting magma layer very near the surface and that there’s an inductive response at Io as well as the icy moons. It requires a global magma layer. So all—all of these moons seem to have—have some sort of conducting layer very near the surface. You—if you tried to ask what the inductive response of the metallic cores would be, it would be so small we couldn’t detect it above the surface.
Okay, then we get to Ganymede; that’s the one with the permanently magnetized body. I’ve already shown you simulations after having told you that you shouldn’t worry about them. I’ve shown you simulations of what the Ganymede magnetosphere looks like. One of the interesting things is that a magnetic field presents a barrier to the oncoming flow that is very closely linked to this idea that I was talking about of flux tubes—actual flux tubes—flowing toward each other because I’ve got a magnetic flux tube connected to Ganymede; I’ve got a magnetic flux tube flowing toward it in the magnetosphere of plasma. They flow to each other, and now it says that the plasma in one has to stay on the one, and the plasma in the other has to stay on the other. So we got a problem here unless the flow goes around. The magnetosphere—actually, you’ve heard about reconnection—some fraction of the interaction actually does involve reconnection. The dominant interaction is simply for the external plasma to flow around. Ganymede’s internal fields are an obstacle to the upstream flow except in the places where ideal MHD breaks down and you get occasional reconnection. The scale is about five times the radius of Ganymede. So—so it really stands off Jupiter’s magnetosphere—magnetospheric plasma—to a very large distance interaction region, much larger than the size of the obstacle. So Ganymede also has an inductive magnetic field; it’s hard to separate external sources and dynamo sources. So here’s somebody trying to simulate what the external field would look like if we just had an inductive response; what it would look like if we just had the permanent dipole; and this is a more complete image that shows the magnetosphere as it would appear when the moon is near Jupiter’s magnetic equator. But the effect of induction here is to change the tilt of the dipole by a few degrees. The—there’s some uncertainty about the argument.
Okay, there are many more moons; I’m not going to talk about them all. This is just a selection of the big ones, and I kind of like the image. So non-conducting bodies—others that would be similar to our moon—Rhea, a moon of Saturn; it’s non-conducting; upstream plasma flows right onto it. Conducting bodies—will—I talked a bit about Io and Enceladus, which injects neutrals and is a source of tens of kilograms per second for Saturn’s magnetosphere; has conductivity through pickup, the way Io does. Europa, Titan. We don’t know a great deal about—about Neptune’s moon Triton, but there’s evidence that it may have geysers, and they could—could get vapors from the surface and modify its magnetospheric surroundings. Small bodies—so asteroids and Pluto. Asteroids vary in size from kilometers to 500 kilometers; they’re widely distributed in the inner solar system, mainly between the orbits of Mars and Jupiter. They’re too small to be plausible sources of dynamo fields, but some are made of—you know, a lot of these asteroids arise when larger bodies that have already differentiated collide. And so you get asteroids that are like the stony mantles, and you get asteroids that are pure hunks of iron—that far from a differentiated core. And my favorite ones come from the core-mantle boundary and have little bits of olivine crystal embedded in—in iron. And when you shine—make a thin section and shine them up—they’re absolutely beautiful. So we have many different kinds of asteroids, and some of them have very high iron content, and it’s not impossible that they are magnetized. So we really know very little about their interaction with the solar wind. There’s a limited number of spacecraft with magnetometers that have gone by asteroids. Galileo flew by Gaspra, which was 12 kilometers in length, and Ida, 60 kilometers, and observed magnetic fluctuations that lasted a few minutes near closest approach to both bodies. Now the problem is that there are fluctuations in the solar wind all the time. Were those fluctuations produced by the presence of the nearby asteroid? We interpreted the fluctuations as if they were, but it may have been fortuitous. However, if we interpreted them as produced by the asteroid, we found that Gaspra had to be magnetized in order to make a signal—was because it was—Ida—a conducting body was adequate. I’m showing this funny picture here because it turns out that once you get to the scale of these asteroids, you cannot use MHD—time—five minutes. Okay, good; I’m almost there. You can’t use MHD because you’re violating the condition that the length scales have to be large compared with gyro radii. So to use different physics, you will have to worry about waves that are capable of carrying perturbations for these smaller-scale objects, and those are things like whistler waves, and you get strange shapes to magnetospheres. I’m not going into it, but it’s just a warning: don’t think that what we’ve been talking about applies without worrying very much about length scales when you’re talking about the small bodies. So there’s no upstream shock; the interaction regions differ from what develops in the MHD limit.
Oh, Pluto. Once again, I have to appeal to simulation. We don’t know anything about whether—what the magnetic or conducting properties of—of Pluto are. This is a simulation that goes beyond ideal MHD, and I think you probably will see a shock and changes of density and composition, but it’s—it’s really exciting to know that we’re going to have some data. The thing that I have to say is, as a magnetometer person, it’s a scandal that they have no magnetometer.
Okay, comets. So I figure that we should at least have the fun of looking at some of these SOHO images of Comet ISON going by the Sun. I don’t know if you saw it coming in from the right. I think there’s another round in which you will see it coming in over here, and there are two tails. I think you can see the two tails, and then it goes out on the other side; it’s broken up, and then I think we—it goes on—I’m going to play the whole thing because I’d like it—I don’t know if you’d like it, but I like it. There’s some of that—those were several images, and I think we may have some from another spacecraft. This isn’t just a different instrument. So that went a lot faster, but it’ll keep coming in from the side somehow. In this wavelength, it doesn’t show the two tails, but—so the important things for the interaction issue are that—I don’t know what this is—STEREO. Okay, this is STEREO Ahead, so it is seeing it coming in from the other side. I don’t know if you caught it coming in from the side—from the lower—here it comes. So what you can see is that the region of interaction at a comet goes on forever; it’s very, very extended. I have no idea what’s happening on the outbound path. They seem to say that the comet broke up. And anyhow, the important thing is that the—that there’s a lot of detail. We don’t even know if there’s an upstream shock. And because I’m getting near at the end, I’m gonna ask you a question and answer it myself: would there be an upstream shock? Well, we don’t really know because the pickup—the ions—the neutrals extend so far from the comet that pickup ions lead to slowing of the solar wind, and in—in the limited data we have, we saw this solar wind become denser and slowed way before we saw a shock, and the shock was a little bit ambiguous. It is possible that you can slow and increase the density of the solar wind by so much that it—it doesn’t have an upstream shock. And so that’s something that’s quite interesting.
Though other planetary systems—here we’re on our own—and I decided that this was a good question to ask the class instead of trying to come up with an answer. So that’s—I think—that’s my last slide. Yeah. [Applause] Mary sir. Okay, the question was if you can tell that there’s an inductive field at Europa and it’s coming from close to the surface, what can you say about the thickness? And I’m not quite sure what Mary meant because there are two length scales that are important: one is how far beneath the surface it’s buried, and the—and the second is how thick the—the liquid layer is. And the answer to both is no, but the—I just want to say the—the—the entire ice layer is rather small; it’s only like a hundred kilometers. It’s probably not buried by a hundred kilometers, but the kind of thing most people want to know is: is it buried by something between one and ten kilometers, or is it deeper than that? And we can’t tell. The second thing is that with the limited data we have, we cannot tell how conducting the shell is. We can tell that it has to have a conductivity in excess of some number, and—but you may remember that the skin depth depends on the conductivity, but you get the same—if you have enough material to be beyond deeper than one skin depth, you can’t tell the difference in the signal whether it’s ten times the skin depth or one—just exactly equal to the skin depth. So we can’t even tell the thickness of the—the fluid layer. While we send a commission that way, right? More. I think your last question is really interesting—like you—inaudible—clarified a bit—same late—what if you take Jupiter and its four Galilean satellites, make it 100 times closer, and Jupiter is in the Sun. That’s not unrealistic; hot Jupiters are seen around stars that are very, very close in, right? Right. Yeah. Well, but I don’t think I have to repeat it; just knows how to communicate so loudly. So what would I expect? You know, the problem is first—the first question really will be: what’s—what are the properties of the stellar wind? I mean, I’m not an expert on that, so—say it’s the same as the Sun, then the main difference, of course, would be that you’d have a lot more ionization going on in Jupiter’s upper atmosphere—probably much higher—much larger conducting regions around the moons; that’s—that’s my guess. Yes. So in other words, the flow might not be coming from the Sun. Oh, you know that at Earth the aberration is four degrees because of Earth’s motion around the Sun; the symmetry axis is not in the strictly in the radial direction from the Sun but is rotated by four degrees. So if you were in a much stronger solar wind, the symmetry axis would be highly rotated, and that’s a very interesting idea; I like it. Yeah, I like that.