Transcription
So, um, Bob Anan said that, um, you know, I have different styles for different people. And, uh, I love Jupiter and hate Mars, which is true. Whereas he loves reconnection wherever it is. Um, I also looked at Mattius Röl's lectures from yesterday, and his Dynamo talk was like, equation, equation, equation, equation, equation, equation, equation, equation. Um, I love graphics and diagrams. My husband is a graphic artist, Steve Crusher Bartlett, and you will see a lot of these graphics that he has made. He did all these for me. She's very convenient.
So we're going to talk about planetary magnetospheres today. I'm going to set the scene, and then, uh, David Brain's going to talk about, um, planets, habitability of planets, and particularly thinking about, um, interactions of the solar wind with objects that maybe don't have magnetic fields. But first of all, I need a quick, I was not here when you did this, quick hands up. Soloposis in the room? Okay. Helio people? People? Solar wind? Okay. Earth ionosphere magnetosphere? Okay. Planetary space physics? Good. And then other, which is totally okay. Okay, right. Thanks.
Now, I love this quote. We're going to be talking about magnetic fields. It's kind of interesting to think of how people started using magnets and thinking about the Earth's magnetic field, um, way back when, thinking about navigation. See the boat at the bottom, um, and knowing where you are and so on. And working out, um, you know, latitudes, easy to work out by just, uh, looking at where the sun is in the sky. But to do longitude is difficult. And one way, before they started using, um, uh, clocks and so on, uh, they used magnetic fields and trying to work out using the magnetic field. But I love this quote: "May the gods damn all such sham pilfered distorted works which do but muddle the minds of students." So I hope I'm not going to muddle your mind today. I have no idea. I just love the quote.
Okay, so we're going to talk about the magnetic fields of planets and the magnetospheres. And you'll see the scale, the range of scales is huge between that of Mercury, that would fit within the Earth, the magnetosphere of the Earth, that would fit within Jupiter, the magnetosphere of Jupiter, that is tiny on the scale of the heliosphere. So this is something to think about. So we can talk about magnetic dynamos, and you've had a lecture on magnetic dynamos. Um, but my question to you is, what are the three main ingredients for a planetary dynamo? Somebody want to volunteer one thing? Yes, convection. Some kind of flow that's inside. That's convection. That is presumably driven by what? No, what drives the convection? Sorry. Heat. Yes, heat. Particularly, you need a temperature differential, temperature gradient. Okay, so you need both cooling at the top and heating from below. Okay, what else do you need? Conducting medium. But it's not, not just a piece of solid iron. It has to be liquid. A liquid conductor. There's a third ingredient. Sorry. You need a seed magnetic field. But that's pretty easy to find, right? There are fields everywhere. Rotation. Okay, good.
So these are the three, um, quantities you need. And planetary magnetic fields, contrary to what some people think, they all have enough rotation. The problem is really an issue of the electrically conducting fluid and convection, uh, to make a dynamo. Such as something like this. Okay, so let's look at the magnetic fields of the planets that have magnetic fields. We have Ganymede, Mercury, Earth, Jupiter, Saturn, Uranus, Neptune. And of course, for the Earth, you have liquid iron. And indeed, for Mercury and Ganymede as well. But for Jupiter and Saturn, you have liquid metallic hydrogen. So at about two and a half, um, million bars, you turn hydrogen into this metallic phase, uh, which is huge at Jupiter, not so much at, at Saturn. Jupiter is three times the mass of Saturn. Jupiter is 318 times the mass of the Earth. Saturn's about 100. And so the difference in mass, they're the same size. So that means that the density of Saturn is tiny. It would, in fact, float if you could get a bath that big. Um, and so the pressure, you have to go deeper to come to that sort of pressure at Saturn. Now, Uranus and Neptune, we'll talk about those magnetic fields later. Um, they have ionic water, so some kind of ocean which is conducting. It's got, um, electrical, it's got, uh, ions in it that will make it conducting. Uh, we'll talk about that later. But what's important here is to compare Earth and Jupiter in terms of strength, an absolute magnetic moment. Along the bottom, compared with that of the Earth, you can see Jupiter is 20,000 times bigger. That's a lot. Okay, so that's going to make a big difference in terms of the magnetospheres.
Now, normally we talk about the Earth's tilt, uh, of about 11 degrees of the dipole. Um, and for Saturn, it's nothing, which is a problem. Whose theorem does this violate? No tilt of the magnetic field symmetry. Didn't you hear that? It was not possible to have a symmetric magnetic field. Curing them, right? So somehow you have to symmetrize the magnetic field. Dynamo cannot be symmetric. That's a puzzle. Okay, we'll come back to that maybe. Um, Jupiter, just the same sort of tilt as Earth. And then Uranus and Neptune, huge tilt, both the tilt of the spin axis from the, um, orbital motion, but particularly the tilt of the magnetic field. Okay, but this, that's just a dipole. In reality, um, the fields are not dipoles. They're much more complex. And so what we do is we do this spherical, um, harmonic analysis and, and take a magnetic field of a planet and divide it up into components, uh, of increased complexity, starting off nice and simple and adding, um, a greater complexity at higher order. And, um, then you fit this to the observed magnetic field and derive what is appropriate for each planet. So when we look at the first three components, you see here that Jupiter, Earth, and Saturn are fairly similar, with the dipole being strong, the quadrupole being weak. You look at Uranus and Neptune, you go to higher complexity, they have higher power, the amount of power at that higher level. And so that's telling us Uranus and Neptune, you have a complex field, and somehow you have to have a dynamo, um, able to produce that. So when we look here, this is the same sort of thing, just looking at the ratio of the quadrupole to the dipole. You can see that Uranus and Neptune are highly irregular. And when you look at the surface field, you can see here that, um, there's much more structure in Uranus and Neptune. Now, we've got to be a little bit careful because we've only had one flyby, one set of measurements for Uranus and Neptune. And this is, um, only measured once, and it may be that it has changed next time we go. Uh, notice that the, uh, polarity for Earth and Jupiter versus Jupiter and Saturn is different. They had flipped. We'll come to that.
So the Earth's magnetic field, when you look closer, there's more complexity. And indeed, if we could run the movie, this is the radial component. I couldn't run it on my, um, PowerPoint, but we've got the movie which they're going to run, at least I think he's going to run. You able to run it? Yeah, maybe. There we go. Kind of cool to watch. There we go. You can see one polarity, yellow on top, blue below. It gets more complicated, equatorial blobs, and so on and so forth. Highly dipolar, and then eventually it's switched to the other side. Okay, so this is a, a movie of the field through the Earth's flip, of the Earth's, uh, dynamo. So we go, sorry, how long did it last that time series? Um, you know, I don't remember. I, I got this from a previous heliophysics summer school presentation. I think it was Dana Lopez who gave it to me, and I don't remember. Well, okay. So we go to this. Thank you. Um, you see here that if you look at the flips, how do we know? How do we measure the Earth's reversals? Why do we, how do we do this? How do we know millions of years ago what the Earth's magnetic field was like? Where do we go to do this? Where did you say ice cores? Nope. Ice does not have remnant magnetization. Rock? Volcanic rock? Yes. I rock. Yes. And so you go, say, to the Earth's, the mid, um, Atlantic Ridge, and you go away from the Mid-Atlantic Ridge, and you see the field flipping as you move away. So this is earlier, this is newer, and you see versus time, flips in the field. And, of course, you could go to other places. The Mid-Atlantic region was where they first started discovering this, but of course, you could go to other places and map out the magnetic field as a function of time. But what you'll see is there are times where it's flipping like crazy, and then other times when it stays static for a long time. And so the rate seems to vary with time. So you've got to come up with a dipole that sometimes stays in one polarity for a long time, and then other times flips. This is not so easy, of course.
Now, we know that the Earth's magnetic field is, um, changing. If you look, the North, you'll see that the magnetic pole has gone from, um, across the North, uh, the North Atlantic, not North Atlantic, across the Arctic Ocean, and then the South, a little bit wandering around, out of Antarctica. So there's two things. One is the geomagnetic pole, and the other is the magnetic pole. What is the difference between them? Which is the magnetic pole, and which is the geomagnetic pole? What's the, what's the geomagnetic pole? Any idea? Doesn't seem to be varying as much, does it? The magnetic pole? Okay, like average. It's like a straight up and down line, sort of, kind of. You're getting there. You're getting there. Okay. One is the dipole approximation. The dipole approximation. So you take all of the magnetic field and you do a, this harmonic analysis, and you say, what is happening to the dipole, the strongest component? And that is the geomagnetic one, and it isn't varying a whole lot. But if you look at where the field is radial, going in and going out, okay, is it the South Pole? Where does it go into the Earth? Is it the North Pole or the South Pole? It goes into the North and out of the South for the Earth, right? Now, but it will change. Okay, good. So what we have here, yeah, sorry. Yes. Yeah, yeah. So when you saw that movie and you saw that complexity, there ain't no magnetic pole, right? Because it's all over the place and it changes with time. So, yeah, you can always probably do some, um, uh, dipolar approximation, but when it's highly complex in the middle of a flip, it's not really dipolar. Okay. Okay. Interesting complexities.
Let's flip to Jupiter, yes, and talk a bit about Juno. This is the Juno spacecraft, built at Lockheed Martin, South Denver, near here. And you can see a human for scale. This is huge solar panels, a whole bunch of instruments, including a magnetometer out here on the end. Oh, hitting the wrong button. No wonder it wasn't working. There we go. Uh, at on the end of the, the, um, boom, and we measure the magnetic field orbit by orbit. We've now done 63 orbits. Uh, these are the first few, and you can see as we fly over the poles, close to Jupiter, actually, um, underneath radiation belts, just, uh, less than half a radius from, from Jupiter, um, we see these variations of the magnetic field orbit by orbit. And this is a movie showing you the complexity derived after about, uh, 35 orbits. And you can see stronger in the North Pole, in the South, um, there seems to be some irregularities. Um, it's pretty much dipolar, but once you get in close, you can see particularly this blue region where you have a very weak field, um, region, and so on. So, uh, in, in many ways, this is similar to the Earth's asymmetries. Um, but, but North is stronger, South is more regular. Um, there's this magnetic anomaly, which is similar to the South, um, American anomaly that we have at Earth, um, where there's a weak field region, high radiation precipitating in that region, impacting the atmosphere and ionosphere. And that's where they turn off Hubble and can't take pictures when they're flying through this South Atlantic anomaly because of the high radiation dosage on the, um, spacecraft. Oops.
So, um, when we analyze these and look at power, which is vertical versus, um, harmonic degree, and you make more measurements, you can begin to sort out. So for the Earth's dynamo, it's interesting. We can go to more complexity, but at some point, you hit the crustal field. You can't analyze the Earth's dynamo to higher complexity because it's masked by the remnant magnetization of the rock on the crust. At Jupiter, on the other hand, there is no crust. You can keep going to higher and higher order and go to higher complexity. And the picture on the left, the diagram shows what if you were to have the core or the dynamo region go to 85% of the radius, or 75%. So the two lines are different, where you would put the edge of the dynamo. And so on the right is the actual analysis of the real data. And what is derived is a dynamo boundary at about 0.81, so 81% of the radius is where we think the dynamo boundary is from analyzing this higher order moments of the magnetic field.
So when we look inside, we use the gravity to measure the distribution of material. And what we found is, yes, we think the dynamo region is this outer layer, um, of metallic hydrogen, highly conductive. But what we find is instead of a small core of heavy elements, the elements seem to be mixed in with the metallic hydrogen out to about 40% of the radius. And the big question is whether or not the dynamo can continue in that region, or whether, in fact, it's more stably stratified deeper down. So if you think about the dynamo, um, for the Earth, you have this diagram from Glatz from 2002, showing, you know, you generate this dynamo inside the liquid metallic, sorry, liquid iron outer core of the Earth. The energy driving it coming from the settling of pure iron into the solid inner core, and the mixture of slightly, um, mixed up iron, liquid iron on the outside with a bit of sulfur, a bit of silicon, a few other heavy elements. This differential of settling down of heavy iron into the center is that, that gravitational potential energy is what actually drives the dynamo, with the cooling on the outside due to plate tectonics producing that big temperature gradient to drive the Earth's dynamo.
Now, when we go to Saturn, this is a model showing that you generate a dynamo inside. But it looks like the argument is that we have at Saturn, the outermost layer. So if you look here, a weakly conducting layer. The argument of how you might make Saturn more symmetric would be to have that outer layer a little bit conducting, so that it wraps up. It's not that you're generating the, the, the magnetic field there, but above the dynamo, you have a little bit of a conducting region that's rotating around that smears out. So this is the way in which you, one way that you could deal with this calling theorem. It's not that the dynamo is symmetric. No, it's that the field becomes symmetrized by this, um, material flowing around outside, partially conducting. That's the current theory. It's up to you guys to perhaps build a dynamo model and prove there's some other way of doing it.
Okay, now getting back to Jupiter. We indeed think there are dynamos dominated by a lot of rotation at, at, at Jupiter. So the flow is thought to be largely in cylinders, and you can see these, um, these models here showing these, um, cylindrical, um, flows inside. But the question I have is, since we have with Juno discovered that this big region of heavy elements dissolved in this region, what happens if you have the dynamo around the outside? What happens above and below? And could you have a difference in the dynamo above and below that maybe leads to this big asymmetry between the North and the South? So this is just a conjecture of how you might, um, have to adapt your dynamo to explain, uh, what's going on North versus South, as well as having this inner region that is not, um, purely metallic hydrogen.
Okay, so let's get to the terrestrial planets. Let's go through these. Yes, no. Which has a magnetic field? Mercury, yes. Venus, no. Earth, Moon, Mars. It did. It did a long, long time ago. Okay. But this is the big question. Why? Why, oh why, oh why? Okay. You say, "Poor little Mars, it cooled off and it just solidified. Bye-bye." Okay. I'm happy to say bye-bye to Mars anyway. Um, but Venus. Now, I don't have any stickiness. This, you know, I'm not going to gain anything if we go to Venus because I work on magnetic fields and country magnetics. But why is our sister planet so different from us? Why, oh why, oh why? We've got to go there. You know, damn JPL, they're just lazy. They just go to Mars because Mars is easy. Venus is really, really difficult. But that's where we should be going. And what we should be doing is to do some geophysics experiments that actually find out what the heck it's like inside. Right? Why is it so different on, on Venus than it is on Earth? Okay, so we need some geophysical measurements to solve this problem. But I will point out again this issue that when you have a crustal magnetic field, it seems it has this complexity. So a higher order, you maintain this power at higher order. And then here is the Earth, the dynamo, um, field of the Earth here. So, you know, looking at a planet's magnetic field as a degree of complexity gives us some sense of, uh, what is caused by the crust versus what is caused by a dynamo inside.
Dave Brain did his PhD thesis on Mars, and, to my great frustration and irritation, but there was nothing I could do about it, he was destined to go that way, and he'll be talking about it later today. And indeed, what's interesting is when you look at all of these planets that don't have internal magnetic fields, what you find is they tend to be escaping atmosphere, escaping at a pretty similar rate, which is very interesting. Why do these different planets have atmospheric escape rates? And he's going to talk about that later.
So let's talk about magnetic, um, magnetospheres. And let's talk a bit about, first of all, they have a bow shock. Why? Why do planetary magnetospheres have shocks? Very basic question, right? Why does the solar wind? What is the property of the solar wind that leads to a shock? It's supersonic. Yeah, it's supersonic. And, um, I actually wrote a paper back in the mid-80s about the flyby of Uranus, and at the time, it had a Mach number of 17, and that was just like the highest Mach number. And I made this diagram and had this big, up here is Uranus with the highest Mach. Of course, they've since been to, there's a bunch of planets, particularly Saturn has a high Mach number shock, but high Mach number. Okay. So then what happens when the solar wind goes through the bow shock? What happens then? Slows down. Yeah. So you're losing kinetic energy. What happens to that kinetic energy? Turns into thermal energy. Yes. Okay. So we have, um, a magnetosphere here. And this theory goes back to the 30s when they knew the Earth has a magnetic field. They don't really know about the solar wind, but they're beginning to think about the solar wind. So you have an obstacle, you have a supersonic solar wind, you make a bow shock, and, uh, it turns out that that's about 1.3 times the magnetopause, which is the, the boundary that is the obstacle, to the solar wind. So you're converting kinetic to thermal, and the flow is diverted around, and the pressure actually is a bit less because of this diversion of the flow around at the magnetopause. The upstream.
Now, to calculate the, uh, location of the magnetopause, you want to follow Chapman-Ferraro theory, going back to the 40s, yeah, know, long time ago. Took the solar wind pressure coming in, took the, uh, magnetic field pressure of a dipole, just assumed a simple, straightforward dipole, balanced those two pressures to derive that distance. Now, you're going to be distorting and changing the magnetic field, so you'll end up with a current on that magnetopause boundary. So that increases, um, your, uh, obstacle. So you have to put in your dipole, you put in the ram pressure, you double because of the currents, you, it's equivalent pretty much to, uh, doubling the dipole field. And so you end up with this relationship that leads to where is the magnetopause, the location of the boundary, the obstacle boundary to the solar wind. And you end up with a formula, which is this Chapman-Ferraro formula, that tells you that you got a stronger field, you're going to have a bigger magnetosphere. If you have a stronger solar wind, you'll have a smaller magnetosphere. All of this is intuitively pretty obvious. Okay. So this is the Chapman-Ferraro distance that relates these two. And in practice, um, this number 2 to the 1/3 is effectively, in reality, about 1.2. Which I think is pretty close to what 2 to the 1/3. I haven't done that calculation recently.
Okay, so now I've got an exercise for you to do. Let's take the Earth and what we're going to do is move it out to 8 AU. And I want you to, by answering questions one, two, three, four, address what happens to the Earth's magnetosphere using this Chapman-Ferraro calculation. So in your table, let's go through and do questions one to four. And, um, if you don't have a calculator, you, you can probably just do it on a piece of paper or any your head. I picked easy numbers for you so you can do this. This gives me a chance to have some coffee. Okay, I'll just, let's just do the first one. How, how does the, um, density, the mass density, so that's density times atomic mass of the solar wind, how does that, um, vary with distance from the sun? Does it vary with distance in the sun? R squared, right? You think about the fact that you've got a sphere, it's going out through a sphere, that area there, this radius squared. Okay, that's good. Um, okay, how does the solar wind vary with distance? More or less. Somebody over here. How does the solar wind vary with distance from the sun? More or less. It goes like this, yes. But on average, it's pretty constant, right? Okay. Now, so then how does this vary with distance? Notice that sixth root. Oops. There. Okay, you got, you got, you getting it? You getting it? You getting it? Getting it? Getting it? Getting it? One-third, right? So the row solar wind is is, uh, D squared. So you have to take the sixth root, you get a third. Okay. Now, move the Earth from 1 AU to 8 AU. Does it get bigger or smaller? The Earth's magnetosphere. If you moved Earth out to 8 AU, would the magnetosphere get bigger or smaller? It get bigger, right? How much? I chose eight for a reason. It would double, right? Cube root of eight is two. Good.
So this is a useful exercise to think about the effect of this solar wind. So now, if you think about Uranus and Neptune, you know, out at Neptune is at 30 AU, right? So that means that 30 squared is a thousand times weaker, um, pressure out the 30 squared, right? Okay. Okay. Um, now, if we compare this Chapman-Ferraro distance for the magnetospheres that we have with what we observe, is if you look at the calculated distance, which is the middle row, with the observed distance, that's pretty good for Mercury, pretty good for the Earth. Ooh, not so good for Jupiter. Pretty good for Saturn, pretty good for Uranus, and pretty good for Neptune. We'll come back to Uranus, it's kind of an interesting case. But look at particularly Jupiter, and to some extent Saturn, these magnetospheres are much larger than you would get for a dipole, right? And so there's, there's something else going on. And what's going on is source of plasma. In particular, at Jupiter, we have Io venting out large amounts of material. There's a movie of its gas coming out of a volcano. It has hundreds of volcanoes, the most volcanic object in our solar system, venting out sulfur dioxide that condenses onto the surface. Uh, so you have an atmosphere of SO2, and a lot of that stuff is escaping. It becomes ionized, trapped in the magnetic field of Jupiter. Orbits around, not orbits, it rotates around with the magnetic field at the 10-hour orbital period. I mean, not orbit, it's not orbiting, it's being carried by the magnetic field, which is going with the spin of the planet because it's coupled to the ionosphere, and the ionosphere spins at the same rate as the atmosphere, and the whole planet spins at 10 hours. Okay, not 24 like the Earth, but 10 hours. And so you have this donut or torus of plasma that surrounds Io that fills up the magnetosphere. Ton a second, and you have million amp currents that flow from Io to the planet. So this is a very different situation to what we have at Earth. And the Earth's, um, magnetosphere, we'll come back to this.
So let's just first of all, though, look at the small magnetospheres we have. Uh, Mercury, which is very much like the Earth but small, much more dynamic. There's no atmosphere, very, um, dynamic little magnetosphere in close to the sun. So very strong magnetic field. So, sorry, strong solar wind interacting with the magnetic field. Out at Ganymede, it's the only moon in our solar system that has a magnetic field. It's about the same size as Mercury, similar magnetic field as Mercury, but it's embedded in the magnetosphere of Jupiter. And the flow inside, even though going around every 10 hours, is pretty fast, it's still subsonic. So there's no upstream bow shock. Um, but you do have aurora and a dynamic magnetosphere. There are two missions that are on their way. BepiColombo is on its way to explore Mercury, and the JUICE mission, which is an ESA mission from Europe, going into orbit eventually around Ganymede in the, uh, 2030s. So, uh, Mercury has, uh, very little atmosphere, so very little ionosphere, uh, conductance. But there's a rapid Dungey cycle that, um, uh, convects material around Mercury. And there are times when the solar wind pressure is so strong that actually the solar wind hits the surface, you know, completely pushes the magnetic field to the side. Um, okay.
So let's talk about dynamics of the magnetospheres. And there are three components here: the ionosphere, the magnetosphere, and the solar wind. Okay. And depending which you're going to couple to which, you get different dynamical systems. So first of all, if we couple the ions in the solar wind, you get the Dungey cycle. Okay. If you couple the ionosphere and the magnetosphere, and the ionosphere is rotating with the planet, you will get a rotating plasmasphere. If you couple the solar wind and the magnetosphere on the boundaries, you will get a viscous interaction, was the way it was described back in the 60s, but we'll talk about the specifics of how that actually works, um, uh, later. So let's first of all, we all know about the Dungey cycle. I've done the dance. Um, and so this is reconnection driven with dayside reconnection, nightside reconnection. You explored with your lab yesterday what happens when you change the field and so on. Um, in this case, so you go from a situation where you have parallel magnetic fields upstream and inside, and you have much less, you have a closed magnetosphere. You flip to a southward component magnetic field, and then you end up with this open magnetosphere. You will know about this now, and you know about the Dungey cycle and how it varies with the orientation of magnetic field. Um, but inside that, there is also the rotating plasmasphere. Okay, so that's the boundary between where stuff corotates with the planet, and the convection is associated with the Dungey cycle.
So let's think about, um, this convection that we get. And I'm not going to go into this, but there was a debate back in the late 90s, early 2000s, about whether to take an approach of a BV approach versus an EJ approach. And there was a battle between Jean Parker and V. Vasyliunas. Two senior people of the field. Both of whom have actually given lectures in the Heliophysics Summer School. Right, Nick? I think I know. But Vasyliunas? Did Parker ever come to the Heliophysics Summer School? No. Okay. Anyway, I'm just going to go through the standard derivation, which says if you've got V solar wind and B solar wind, you end up with a convection, with some level of efficiency. And so that is the efficiency at which the solar wind kinetic energy is converted into convection. And empirically, it's on the order of 10 to 20%, probably closer to 10 than 20%. Um, and that it's pretty much constant. This is a crude approximation, across. So this is the dawn-dusk electric field that we were talking about. Um, and this then leads to a convection, uh, that you can scale because it depends on, using your, your, um, scaling factors, you can end up deriving how it varies, um, with size. So you can have, um, you, you have your polar view here of the, the Dungey cycle with a closed magnetic field versus open. And then you, you have the, I should have actually continued. Well, you have the actual, um, convection, uh, electric field here. Okay.
So then, yes, oh, um, so the, the one, the, the Dungey cycle one's obvious, right? That's the, the magnetic field is black and the, the, oh, previous one. Okay, yes. So that is the flow that is driven by. This is, okay. So if you've got, I should have to do it the other way, right? To be, no, it's consistent. You, if you open up the magnetic fields and it goes back like this, but it's the return flow, right? That is going in the equator. So this is looking in the equator at the return convection flow that is coming back towards the planet, around the planet, to the dayside to start off reconnection again, right? Okay. And it's distorted because you've got this electric field, and you've got, in near the planet, you have, um, corotation. Okay. So then what happens if you couple the ionosphere and the magnetosphere in a rotating plasmasphere? You have electrical currents that couple this ionosphere to the equator, and then you end up with, uh, driving the flow in the magnetosphere to co-rotate with the planet. So then comes the question: which is bigger, Dungey convection versus corotation? And you can, depending on how fast the planet is spinning and how strong the field is, or how strong the solar wind is, you're going to get a different situation. And in fact, if you put the numbers in for a, um, making the assumption of perfectly coupling planet to the magnetosphere, and that you have large-scale Dungey reconnection, then you can make a crude approximation that this, uh, balance between corotation and convection. At Earth, this happens around six to seven RE, which is consistent with the size of the plasmasphere, the plasmasphere inside rotating with the planet slowly every 24 hours, and then the stuff outside convecting around with a Dungey cycle. You do the same math at Jupiter, you end up with this huge number that the, the size of the, the plasmasphere should be out at 350 times the radius of Jupiter, which is way outside the magnetosphere. The problem with that is that in fact, the corotation begins to break down as you move further out. This assumption of perfectly coupling is not, is no longer, is not valid.
So when we think for the Earth, we have this idea of tail reconnection. This is the beautiful Dungey view that he drew on a napkin in 1961 in Paris. Data published and made him famous. Um, but in reality, it's a very messy situation, with three-dimensional structures, which is a lot harder to, to model.
Okay, now let's think a bit about the Dungey cycle at, and the timing of this for the Earth versus Jupiter. And we started a bit of this discussion, um, last week, but I want you to do the math. And we have, I want you guys to do the Earth, and you three, and then because Jupiter's bigger, we'll do four. These four tables will do Jupiter. Okay. So I want you to do that calculation assuming the solar wind is for 400 km a second, which is a bit fast, but it's an easy number. Then taking for the Earth, 10 times the magnetosphere, 10 times the radius of the Earth. Jupiter, 100 times the radius of Jupiter. There's the size of the planets. Do the math. How long does it take this Dungey cycle to go from opening up to being vertical? So that's at the, um, terminator, right, the day-night boundary of the Earth, or the day-night boundary of Jupiter. How long does this take? Okay, so you do, you do the math. I think you can guess which is going to be longer, but the question is, how much longer? Yeah, we're assuming that the magnetic field that is reaching out into the interplanetary medium is moving constantly at the top and the bottom at at 400. Give me a wave if you, I know these guys have got it because I can hear them. You guys got it more or less? Got a number? You guys got a number more or less? Got a number? Got a number? Got a number? Okay, good.
Okay, so if you put the numbers in, you get about three minutes worth, right? Do you get a number like that? About three minutes. And you guys got about five hours for Jupiter. So that would be fine if the interplanetary medium remained constant. You say, okay, well, for five hours, you've got reconnection at Jupiter and then drives the return. But the probability, according to Bob McFar at UCLA, who knows about these things, the probability of the IMF saying either Bz down or Bz up, or having a strong component down and strong component up, I know it's never perfectly that way, is about a chance of 0.1% or one part in 10 to the three. So it, it doesn't stay constant at Jupiter for five hours. Now, three minutes is pretty easy for if you want to drive the magnetospheric cycle. If it's three minutes to here, and then it's got to go all the way down here, and then return back, you know, maybe it's like 10, 20 minutes for the full cycle, or even 30 minutes for a full cycle. That's, that's pretty good to have a driver that stays constant for that time. But at Jupiter, you got a problem driving the Dungey cycle because it's constantly changing upstream. And so the scale of the magnetosphere is so big that you have to allow for perturbations outside, and you can't have a constant drive of the Dungey cycle at Jupiter, or indeed at other planets, large planets. Yep. Well, you're not, yes, it's sort of like if you, if you, if you turn off the drive, well before it's even gone halfway through a cycle, you're not going to make, you're not going to make a drive the flow, right, at all. It's just, it's just varying upstream, and the stuff inside doesn't really care. It isn't affected by the fact that it's changing outside. Yeah. Okay. Similarly, what once you've got, you know, it takes a while to do this part, but then you've also got to go down to the tail, have an X-line, you've got to, but you've got to bring the flow, the interplanetary magnetic field to the X-line to bring it back in again to the planet. And for the Earth, with a 10% of efficiency, that means that the magnetic field goes down at about 40 kilometers a second, and it takes on the order of 40 minutes to do this. So you've got, you, you've got a, it takes a while to drive a Dungey cycle on the Earth, but it's possible. But at Jupiter, it becomes tens of hours to do this. The scale is just too big, and you can't drive, um, the Dungey cycle. Yeah. Well, empirically, what we find is that if you, you're, you're, you're tapping the solar wind kinetic energy, and it's at, at the level of roughly 10% to for the Earth, driving the Earth's Dungey cycle. Okay, that's empirical. Yeah. Yes. Yes. So you think of it, it's connected straight up above, and then as it goes, gets carried down, gets carried down, and then reconnects. Okay. Okay.
So then what, what do we mean by viscous interaction? Well, we know that there's more complexity when you look at the boundaries. Um, there are waves, and you saw this in your simulations, right? Didn't you see waves on the edge of the boundaries of the magnetopause in your simulations? Those can be either magnetic waves moving along the boundary, or they can be Kelvin-Helmholtz, where you've got, um, the shear flow drives eddies on the boundary. And so there are many ways, and it's been observed, and it's clearly a factor where you couple the solar wind into the magnetosphere, you have this viscous. It's not well, viscous is a sort of implies collisions, whereas in fact, it's, it could be a still a collisionless plasma, but you can still have vortices associated with, um, uh, interaction, electromagnetic interaction between the solar wind and the magnetosphere across that boundary. Um, also at Jupiter, you end up with a great IMF. The picture on the right, you can see that you have here, um, the magnetic field gets draped over the top, uh, of the magnetosphere. Okay. So there are, um, it, there probably are considerable amounts of this viscous interaction, shear instabilities, small-scale intermittent reconnection, not global Dungey cycle reconnection, but smaller scale happening on the boundary. It's not that there's no reconnection, it's just that it, it doesn't drive a full dynamical system. Um, okay.
So then let's go through the plasma sources. This is a big factor. We've talked about Io at Jupiter producing a lot of sulfur and oxygen. Uh, Earth, we have oxygen coming out of the pole. At Saturn, we have water molecules coming from Enceladus. Uranus and Neptune, it's a very, very small source. Now, there was a very interesting paper at the magnetospheres of the outer planets conference last month where Jamie Shinsky from JPL looked at the solar wind data around the Uranus flyby. And what he found, as observed by Voyager, there was actually before it was fairly uniform pressure, very high pressure pulse just before Voyager arrived, and then it dropped down to normal afterwards. And he conjectured that maybe at the time of the Uranus flyby, it happened to be a highly compressed, emptied flux, emptied magnetosphere. All of the material that could have been coming from the moons inside, Uranus, making a magnetosphere in some way similar to Saturn, or maybe even Jupiter with material coming from the moons, had flushed all the material down the tail because of this high pressure event, which is very surprising. So this paper is not yet published. I'm dying to see it when it is published. But it could be that we happened to fly by at a time when the magnetosphere was emptied. Yes, the density was really low. We were looking at the density with the instrument that I was involved in analyzing those data. It's not much there, mostly protons coming either from the planet or the solar wind. And so, but if we go back again, maybe there'll be a whole bunch more stuff. So big mystery as to what's going on with Uranus. Sorry, this was January of '85. Yeah, they did. That's what Jimmy Shinsky did. So, yeah, yeah. Which is very intriguing. And I was like, why the heck didn't we realize this back then? We should have looked at the data. Anyway, cool. Um, okay.
So with the Earth, we, what? Yes. Um, um, yeah, well, I think we'll do it. I think we'll do it. I think we'll do it. Um, so for the, for the Earth, there's a lot of people think the cartoon is the solar wind comes in through the CUSP, right, right? And it fills the magnetosphere. That's the cartoon that people think of, right? The reality is, yes, material does come in through the cusp, but most of the material in the magnetosphere comes out of the ionosphere and then circulates. And some of it comes out of the ionosphere into the plasmasphere, and some of it comes out of the ionosphere and circulates into the magnetosphere. And maybe, um, Bob Mitchell will talk a bit about this tomorrow. So the Earth, about 5 kilograms a second, compared with Jupiter's, a second, a thousand kilograms a second, big difference, fills up the magnetosphere. Here's a different way of, um, drawing it, showing the energy where you have low energy solar wind coming out, low energy in the plasmasphere, but material that's gone through the cycle gets heated up, so you end up with this warmer material around the outside of the plasmasphere. As again, we have for Jupiter, this, um, Io torus, which is about, um, total mass of about two megatons, source of a ton a second, replaced in about 50 days. So it's a very slow process. It stays there, rotates around and around, and more material is added. Some material is is spread out, but it's around for a long time. It's a long time frame, big scales. We know about this because if you look at this torus glowing plasma in the UV, you see a whole bunch of lines associated with the different ionization states of sulfur and oxygen. Now, this is messy stuff that most space physicists don't really want to think about about spectra, and, you know, chemistry and charge exchange and ionization and all that messy, messy chemistry stuff, right? Not to mention the quantum mechanics of calculating what the efficiency of the, you can look, the tools for doing all that, you can look it up, you don't have to do the quantum mechanics yourself, but it is messy in terms of all of this process. And you have to think about the source of mass and how it comes in, it becomes ionized, some of it becomes neutralized, transports out, and then you have to think about the energy. The energy coming from ionization, you get pickup energy, you get energetic electrons. Electrons are so easy, any wiggle of a, a wave heats electrons really easily, right? So my idea, I, you know, wave-particle interaction, like I don't need to do the math, you just know electrons are so easy to heat, you end up with hot electrons wherever you look in the solar system, right, pretty much. And they do a lot of powering of stuff. And in this case, they power the emissions, and that then radiate. You radiate about two terawatts of UV emission, and that cools it off, and then it slowly moves out. Here we have the source at Io. You have the strong electromagnetic interaction driving Alfven waves that propagate out to Jupiter. They bounce back and forth, they generate aurora. Um, and this interaction produces the interaction at Io is mostly producing neutrals that become ionized by electron impact ionization further out, away from the moon, not directly at the moon. Energy comes from pickup. So if the plasma is moving, moving faster than the neutrals, once the neutral becomes ionized, it gets accelerated up to the corotation speed. It derives a large gyro motion, and that is basically heating the plasma. So ion pickup, similar to the ion pickup that in the solar wind, interplanetary medium. The radial transport, this is something that we're working on. We don't really understand how it works. There is this idea that flux tubes connected to the planet interchange. If you're producing it closer in with flux tube A, it will interchange and move out. This is centrifugally driven flux tube interchange because if you think about it, if it's rotating around fast, the centrifugal forces are going to want to push it out. But you have to interchange the whole flux tube, and the ends of the flux tube are in the ionosphere, anchored in the ionosphere, and they don't want to move around because they're connected. The ionosphere is coupled collisionally to the neutrals of the neutral atmosphere. Now, you can drive, you can describe this flux tube interchange as a diffusive process. But just like diffusive processes with the radiation belts of the Earth, it's somewhat of an empirical description. It's not a physical description. It happens to work mathematically, it matches the data, but be warned, we don't really understand a lot of the transport in magnetospheres. So it's coupled to the solar to the ionosphere. Um, you really, what the plasma in the magnetosphere is tapping this flywheel of a rotating magnetosphere. And, um, as it moves out, you end up producing, uh, auroral currents that, um, um, enforce the corotation. Um, and you also have radial currents that lead to a current sheet in the equator. Now we have.
to think about what happens as this plasma moves out and um fills up this large magnetosphere. How do, how do magnet, how do plasmas communicate along magnetic fields from one place to another? What is the usual way? What carries the information from here to here? How does this bit know what's going on there and this bit know what's happening there along the field line? Waves, yeah. Which waves? Alfvén waves, right? Hannes Alfvén got the Nobel Prize, the only space physicist to get a Nobel Prize, for Alfvén waves. So this is important. And indeed, what we know is that when we look at this coupling between the ionosphere and the magnetosphere, the rotating magnetosphere at some point – and I have no idea where all those question marks came from; oh, that was a sigma somehow got, didn't translate from one to the other – that is um Pedersen conductance in the ionosphere. At some point, the coupling breaks down and there could be a variety of mechanisms. You may end up developing potential drops, E parallel. So at the Earth's ionosphere, we have potential drops, double layers, that are developed at high latitudes. Uh, or it could be there's a limitation in the Pedersen conductance in the ionosphere. That is, at some point, the stresses in the magnetosphere cannot be enforced into corotation because of the coupling; there's limited coupling between the ionosphere and the neutrals in the ionosphere. Or it could be that the stuff just starts transporting out faster than the Alfvén waves can communicate to the planet.
And so in practice, what we find is that the communication between the the the plasma disc, the material moving out from Io, and the planet begins to break down at about 20 R_J, and that communication basically stops around 60 R_J. And so you end up with um breaking down the coupling; so you end up with a configuration where you end up um distorting the magnetic field in the uh outer magnetosphere, producing these electrical currents that distort the magnetic field, and then you end up with the aurora happening where this decoupling starts to happen. And so what's happening is you're driving electrical currents; you have electrical currents um that are, if you have an upward current, um then you're having electrons going down and this produces the aurora, and that's equatorward. And then further out you have a downward current with upward going electrons, um and so these current systems have been observed. Uh, there the idea of that that that you're coupling between this magnetosphere and the rotating planet, but at some point it begins to break down and these electrical currents cannot keep the whole thing corotating. So we think of the aurora is where the corotation begins to break down. And if you look at this Hubble movie, you can see the main aurora; it's a fairly uniform, steady, thin aurora. You can see very dramatic polar activity. It so somehow maybe that is connected to the outer magnetosphere, connected to the viscous interaction on the boundary. And then you can see a couple of things: you see this very bright thing here – this is Io, and the Io aurora associated with that million, million amp current. And then you have actually there's um Ganymede and Europa also have aurora associated with their electromagnetic interactions. So we have three types of aurora: the variable polar stuff, the steady main auroral oval which is the breakdown of corotation, and then the satellite aurora.
And um I'm actually going to skip this and move on. Um, you know, there's cool movies and so on showing all of this. Um, I want to mention a couple of things. One is we see in the magnetosphere a lot of hot plasma, and the question is how does the plasma heat up? And there was big debates about how that would happen. What is the role of electrostatic voltages? If you look at the Earth, everybody says oh it has to be double layers, double layers at high latitude region. But in fact it's probably waves, Alfvén waves, that heat both the electrons and the ions in the plasma sheet, and you end up with a um hot plasma sheet associated mostly with wave heating. Um um that heats the the ions and the electrons. Okay, I want to skip on. So the consequence of this is as the plasma moves out, instead of as it expands cooling, which you would expect from a just general ideal gas law, it in fact heats up because there are these waves that are heating the material further out. As it comes in, it also adiabatically heats and you have injection, dipolarizations, and so on. Um, but the important point is you end up with a plasma beta – that is the ratio of the kinetic, the thermal energy, to the magnetic field energy density – is greater than 100, a very high beta plasma. This is very unusual in a magnetosphere, have such a high beta plasma. And that's basically saying that the magnet, the plasma takes over and pushes the magnetic field around, not the other way around. Okay.
And so here you have um what happens is the the the transport uh becomes kinetic. You you may have cross field line um motions of the plasma; it's no longer strictly confined by the magnetic field. Or you have ballooning mode or other kinds of instabilities that drive the radial transport further out. But the net result is that if you think about plasma pressure between the inside and the outside, you have to add, when you do your um your Chapman-Ferraro calculations, you have to add the kinetic energy of the sorry the thermal energy of the plasma that's inside. So when you take the Earth and you have a dipole and you change the solar wind, um compare it with what happens at Jupiter. So at if you increase the solar wind pressure by a factor of 10, the Earth's magnetosphere only shrinks by 70%, but at Jupiter it's a factor of two, because the gas pressure is much more compressible than the magnetic field. So if you have a dipole, the dipole is very rigid; it doesn't it's not easy to compress because of the um the R cubed of the uh magnetic field strength is a function of distance. Um whereas if you have gas pressure, it's it's more more compressible. So finally at Jupiter, I want to mention that um at some point the centrifugal forces lead to ejecting blobs down the tail, plasmoids down the tail, and you end up indeed with tail reconnection, but it's not Dungey cycle because the time scales are too long; this is centrifugally driven. So if you take plasma and it goes down the tail, at some point it gets lost, right? It goes you reconnect and you send blobs of plasma down the tail. And that's this has been observed. Um with an next line that's on the dawn side, yeah. The radial transport is a ballooning mode? Yeah, yes, right, yes. The top of – oh interesting, I didn't know that. That's interesting. Okay, H, I'll have to start reading some coronal physics papers. Great, thank you. I learned something. Okay, I'm I'm trying to get there. Okay um I'm gonna skip this. We've got a movie. Oh look at this – Ganymede does a great job, but I don't believe any of it, to be really honest with you; boundary conditions are wrong, we don't get fingers like that. But it's a very sexy movie that everyone loves. Okay okay um I'm going to let's go to Uranus and Neptune. Totally weird.
Um magnetic fields are in the pressure never gets high enough to have metallic hydrogen; you have to use this water, ammonia, methane, Wham as I like to call it, um conducting region. And you have this very non-dipolar magnetic field, and um highly tilted is one way of describing it, or maybe it's just non-dipolar, multi-component. Um we flew through and we as I said maybe for some reason Uranus was empty; there was more material at at uh Neptune actually partly a sourced by by Triton perhaps. Um but you know, one flyby – what do you learn from one flyby? Very little. And because Uranus is tipped on its side with a spin axis on its side, it goes around very strange seasonal behavior and who knows. I mean, could be because of the high order uh complexity of the magnetic field that we go back and it'll be very different – not necessarily flips – but but the high order components could have changed and you may end up with a different configuration. So this is a very interesting magnetosphere. Um we really need to go back and observe it. It's not easy to get to Uranus and Neptune; they're way the heck out there. Um there are plans, there are studies – hopefully we can do it. Um maybe using SLS or Falcon we can get that sooner. But there was a big push; it was a high priority of the planetary decadal, and it and I suspect it might be mentioned in the heliophysics decadal. I don't know why, I happen to know that that might be the case.
Okay, so these comparative magnetospheres are very different. They're very different in size compared with the planet. You can see this range in magnetic moment; you can see this range in size compared to the planet. And then the coupling process – whether you couple the um the magnetosphere to the ionosphere or um the magnetosphere uh to the solar wind – you end up with very different uh Dungey-driven magnetospheres versus um uh co-rotating um dynamics versus who knows what actually at Uranus and Neptune because of the highly dynamic magnetospheres. Um so these are all very different beasts with very different time scales, very different source strengths, and very different structures. So finally uh missions coming up: um Juice will be going into orbit around Ganymede, and particles and fields instruments – they'll be measuring this magnetosphere, trying to understand what's going on. Um and similarly, Europa Clipper Mission, which is due to launch October 10th, 2024, this year, just a few months away – primarily interested in what's going on in the oceans uh and talking about habitability. I will preempt the discussion this afternoon and say this is outside the habitable zone, and it's the most likely place to find life outside the Earth. So those astrophysicists that bla bla bla about the habitable zone – it's complete BS. Go to icy moons; that's the place to go find life. So who knows? We'll see, we'll see um whether or not that brown stuff is well poop or whether or not it's just dirt. We'll we'll find out with Europa Clipper.
Um so planetary dynamos – they're really pretty complicated. What controls the non-dipolar field? Thinking about Uranus and Neptune versus the very dipolar Earth and Jupiter. Big differences between the dynamos of Earth, Jupiter, Sun – similarities and differences. The basic fundamental principles are the same, but the environments are very different. What controls variation with time? Uh we don't know what causes the flips. Okay, so the Sun is nice and steady solar cycle, but you saw what the Earth was like – it was all over the place, sometimes flipping very quickly, sometimes staying steady. We don't know what is going on. Jupiter – we're seeing a little bit the high order moments are varying with time, but it's basically been the same for the past last 40 years. And by Uranus and Neptune, we have no idea what it'll be like. Um so these are all different environments, very different sizes, very different um plasma sources, very different dynamics, and um all fun places to explore. So uh let's keep exploring. Thank you very much.
Wow, I can't believe it – it's cowboy time. 10, 10, 10. Sorry, Dave walks in just as I'm doing my – yeah, I'll be here, but we'll also some clarify. Let's get a mic. I'll go get the funky box. Get the funky box, because we need to like hunt each other as we figure out our capstones. So I was um kind of curious about the radial um transport problem at Jupiter. I had been taught that it was pretty much all driven by interchange uh instability, but it sounds like that's more theory than actually substantiated. Could you go into that a bit more?
Yeah, so we don't measure flux tube interchange; it's hard to measure. Um sometimes we've seen empty, emptier flux tubes – only a very small percentage of the time. You don't really see that interchange. So if you think about it, if they're if they're very empty and very full, you could see them interchanging. But if they're only a little bit difference in full and empty, or just a little difference in density, we can't measure that, right? It's not really a radial flow, right? So it just becomes a diffusion – it becomes a diff – and it's well described using a diffusion equation which has a diffusion coefficient and a gradient in the flux tube content. And that Des you can use that math to describe the distribution. It's also true for the Earth's radiation belts, by the way, right? Um and yet we don't actually see that process; it's just a good ma mathematical practical way of describing it. You move further out, then you begin to get the ballooning mode and other instabilities; you begin to see flows. And we are seeing that now with Juno know. Uh in fact, I gr student Wang has got three or four papers on that. Yeah, thank you.
Question though. Got another question – oh, question here. Got the box. I'm a I wanted to know about different theories there are regarding why different rocky planets have magnetospheres or don't have. For example, the idea that Mars is just smaller and Mercury is still has magnetosphere – it confuses me a bit.
So yes, absolutely, it is a big question and I don't think hey – mataas – do we know why the dynamo was shut off at Mars and still going at Mercury? Yeah, Dave, no right. And why is why is Ganymede the only moon that has a magnetic field? We don't know these things. I mean, dynamos are cool and neat, but they're difficult, right? Right. But but the bulk one turned off 3.8, 3.3 billion years ago – 3.8 billion years ago. So it was a long time ago.
Yeah, yeah. I just want to ask about the plasma torus at Jupiter. So at Earth we have like the plasmasphere which is sort of more um belt-like; it sort of fills up all the space and uh it doesn't it's not just confined to the equator. But Jupiter really looks like it is very equatorial. I thought if you would have sort of higher pitch angle they would kind of fill up all that space and become more of a belt rather than just sitting as like a little – it's it's a bit simpler than that, right? Um where at Earth does something that is orbiting go around in 24 hours? How far out do you have to go from the Earth where a orbital period is 24 hours? Yeah, gravitational orbit 6.6. Okay, so that's the geostationary point, right? It's always overhead. Jupiter that's 2.2 – much closer in. So once you move beyond that distance, the centrifugal forces take over and the stuff goes – it's not gravity that confines it or simple um simple uh distribution along a a field line that's stationary – you've got this centrifugal effect that confines it to the equator, the furthest point along the field line. So that's why the Io torus and the plasma sheet is at the furthest point along a field line right from the rotation axis because of that centrifugal effect. Okay, that's the difference.
Yeah, uh I have a question about you have shown the slide of that Io's density of different planets and it's question about radiation belt of ice giant planet because they don't have that low energy significant low energy plasma source that we have for Jupiter and Earth, but they have the VLF modes waves in the magnetosphere that Voyager had detected. So what's the mystery and you have told about that the pulsation that during the Voyager passage at Uranus – so that's the reason for that uh radiation belts? So that's a good question. So we think the source of Jupiter's radiation belts is material from Io that has gone out, heated up, and some of it comes back in and accelerated to high energies. And so you end up with these me electrons and ions in there. We don't really know what the composition is of the ions, unfortunately. Uh we will soon be flying through when making those measurements. Um at Uranus and Neptune, that was a big surprise to have a radiation belt but no strong um plasmasphere plasma source, and we scratched our heads and said we don't know – you know, and people conjectured theories and ideas. Um but now Jamie has got us thinking: if you flushed out the thermal plasma down the tail at the time of the Voyager flyby of Uranus, then you wouldn't flush out the the the radiation belts because they're confined in the strong magnetic field; it's just the outer material that gets flushed up down the tail by the Vasyliunas cycle, if you like, or compression enhancing the Vasyliunas cycle then um or even the Dungey cycle for that matter at at Uranus. That might explain why you end up with a radiation belt but no plasma source. Um and and so you know we we're having to go back to the drawing and try to understand what what's going on, but but that was a just this summer – a few a month ago – starting to think about this. Interesting questions.
Do you have a comment? Um on that, Harriet, on Uranus's radiation belt? You've been thinking about this. Yeah, okay. I think we're all throwing our hands up in the air – don't know what's going on. Good question. Okay, time for break. Okay okay good.