Transcription
Activist: Slide. What I've got here are sort of a set of simplified equations that govern dynamos. So I've got a momentum equation, or conservation of momentum; magnetic induction equation; energy equation; and conservation of mass equation. Okay. Now, if we were interested in solving these equations for some planet, you might think you need to know everything you can possibly know about that planet. You need to know the density, the thermal expansion coefficient for the material, the viscosity—all these properties. And it is true, you do need to know those. But then if you go to another planet, okay, and a planet has some slightly different values for these properties, the question is: is there dynamo going to be completely different? And the answer is, well, not necessarily. And by non-dimensionalizing equations, what you end up getting out are the combinations of physical characteristics that are important that govern the system. And in our system, there are actually four combinations of these physical parameters that are important, and as long as a planet has the same values of these, their dynamos should work the same. Okay. And this is true whenever you do sort of non-dimensional analysis of equations.
So the important ones for the Dynamo problem: first of all, there's something called the Rayleigh number, and I know you probably can't read this from where you are, but the important point is it appears in the gravity force term, which is where all your buoyancy forces come in. Now, the fluid motions are going to be generated by convection, which are going to be due to thermal differences in the fluid and maybe even compositional differences in the fluid. So these are going to be due to buoyancy, okay. And the Rayleigh number is in that buoyancy term, and this essentially tells you how vigorous the convection is going on inside these bodies. Okay. So that's the Rayleigh number. The Ekman number appears in the viscous term, and it ends up being a ratio of two important forces: the viscous force and the Coriolis force. Okay. So this tells you essentially how important viscous forces are relative to Coriolis forces. Okay. Then there are two what we like to call Prandtl numbers that are essentially ratios of different diffusivities in the problem. So they tell you about how one field diffuses relative to another field. The standard one is the Prandtl number, which is the kinematic viscosity over the thermal diffusivity; so how fast momentum diffuses versus temperature, okay, our thermal anomalies. And then we also have a magnetic Prandtl number, which is viscous diffusion over magnetic diffusion. Okay. And these all essentially set time scales in the problem.
So let's look at planets in these four control parameters. Okay. I've written the Rayleigh number in terms of the Rayleigh divided by its critical value for convection. Okay. In Earth's core, we don't really know the Rayleigh number, but maybe it's around 5,000. You could change this by several orders of magnitude, and I don't think anyone could provide evidence that suggests you're wrong. Okay. The Ekman number, this ratio of viscous forces to Coriolis forces, is extremely small. If you're a solar person, you're probably familiar with the Taylor number. The Taylor number is inversely proportional to the Ekman number because it's Coriolis/viscous, essentially, and there's a square root somewhere involved. Okay. But the Ekman number is really small, and this essentially just means that viscous forces are really small inside planetary cores. Okay. You can ask, what's the viscosity of liquid iron at the core temperatures and pressures? Okay. Does anyone know? It turns out it's very easy to remember: it's the same viscosity as liquid water on the surface of the Earth. Okay. So when you're trying to think about the viscous nature of liquid iron, it's similar to liquid water, so it's very inviscid, right? So the Ekman number is really small. The magnetic Prandtl number is also fairly small—ten to the minus six-ish. This means that there's a vast difference in length scales and time scales of diffusion between the magnetic and the momentum equations. Okay. And the Prandtl number is point one to one. Okay. So these are the typical values in Earth. If I go to some other planet, these values don't change a lot. The Ekman number might change by an order of magnitude or so, but the point is still that this number is really small, which means the viscous forces are really small compared to Coriolis forces. Okay. These numbers might change by an order of magnitude, but but not by too much. And the Rayleigh number, again, we probably don't know so well anyway, but it's okay. All right.
So now you say you want to model this; you want to put these types of numbers in a simulation. And the problem is that a lot of these numbers, because of the horrible smallness of them, like the Ekman number and even this magnetic Prandtl number, mean that you need a ton of grid points in order to resolve the system, and you need more memory than is currently available on the planet to do this type of problem. Okay. So instead, what we do is we have to work with Rayleigh numbers that are much smaller than actually occur. Okay. So this means our driving forces are smaller. Our Ekman numbers—this is why I love my field—I'm working in an equity that's ten orders of magnitude different from the real Ekman numbers inside a body, but I still claim that I'm accurately portraying what's going on inside a planetary core, even though I'm ten orders of magnitude off in a certain parameter. I would argue that what's important here is the fact that these are numbers are still small relative to one, suggesting that viscous forces are still small compared to the Coriolis forces. We're getting that right in models, and some of the Prandtl numbers we get terribly wrong, like the magnetic Prandtl number, the regular Prandtl number when we get—okay. All right. So the wrongness or rightness of some of these numbers, or maybe probably this convinces you of the wrongness of them, makes you start, you know, questioning whether or not simulations are doing a good job of representing what's going on inside planets.
Okay. Luckily, there are another set of numbers which we call diagnostic numbers because you have to run the simulation, get output before you can actually figure out what these numbers are. And these are numbers that characterize the solution that you get, and we end up finding that on these numbers, some of them we don't do too badly. Okay. So some of the important ones: well, the magnetic Reynolds number, the one we were talking about right, and we said for Earth that's, you know, hundreds to thousands, and in models for planets we are able to work and in a parameter regime such that we can generate magnetic Reynolds numbers that are similar to what go on inside planets. This is very different from what people do in stellar dynamos and solar dynamo. Okay. The magnetic Reynolds number in the solar dynamo is like ten to the nine or something horrible like this. Simulations like this can't get to those numbers. Okay. But we are able to get to the right magnetic Reynolds number, so the right amount of creation of field relative to its diffusion inside planets. Unfortunately, we're terrible at the Reynolds numbers. So the Reynolds number is a measure essentially of how turbulent the fluid is; that's one way to think of it. And the fluid flow inside planetary cores is probably very turbulent, with a Reynolds number of like 10 to the 8 or 10 to the 9. We typically are around a thousand. Okay. So we aren't getting the turbulence right. The Rossby number, which Carl mentioned in his talk, gives you a measure of how important the Coriolis force is, or how important the rotation is in affecting your fluid velocities, okay, your fluid motions. This number inside planetary cores like Earth, for example, might be around 10 to the minus 6, and again we might be a couple orders of magnitude off in simulations, but these are small again, so rotation is important in our models just like they aren't that planet. And then finally, this number with this upside down—I guess a lambda, capital lambda—it's known as the Elsasser number, and it's a essentially a measure, a ratio of the Lorentz force to the Coriolis force. Okay. And this number is somewhere between point one and ten in planets, and we're able to get this right. Okay. So our models somehow are able to generate the right amount of field generation in the right field strength and make rotation important, but they aren't as turbulent as they should be. Okay. And there isn't as much separation of scale between the fluid motions and say the magnetic field generation and the thermal perturbations as there should be inside models.
Okay. What we hope is that if we're getting the force balances right, so if viscosity is still not influencing things too much, things like that, then maybe our models are telling us something about what's going on in core dynamics. And it turns out that you can use scaling laws that are out there to suggest this might be happening. Okay. So if we look at this—is magnetic energy as a function of some strange parameter which essentially is the amount of energy available to drive the convective motions inside a body—and these are results from hundreds of numerical simulations, okay, at different parameters. So these are all at different Ekman numbers, different Prandtl, and so forth. And the fact that on a log-log plot means that you can kind of plot these on a line means that they might be governed by a power law. Okay. And once you fit this line, then you say, okay, dynamos seem to follow this behavior. Where does a planet sit in this line? And then you kind of go to that point in here and you say that must be the value for a planet. Okay. Now the problem is that the planets are somewhere very far off compared to where these simulations are done, but you assume that if this line continues, if this relation still holds, then we're able to predict things for planets. Okay. So this is how models can be useful, even though we're not necessarily in the right regime for planets, is we might be able to use scaling laws to go from where we are in the models out to where the planetary regime is. And there are some suggestions that this works actually for planets as well. This is similar to have a plot; there's the scaling law; that line is the scaling law from this; and then there are a bunch of planets on here, and you can see that they seem to fit. There are lots of error bars because we don't really know the magnetic field strength in the core; we don't really know the buoyancy forcing, the driving convective forcing, but they do seem to work for some of the planets. You'll notice Mercury is not on here; that's for good reason; it doesn't work. Okay. There's—you may not have been aware that there are two Saturns in our solar system, right? Saturn 1 and Saturn 2 here. So this—these two numbers are different because again, we—there are some things about Saturn we don't know, and you have to make some approximations to get this type of thing. Okay. So the idea is here, maybe we're doing well, and there's actually—in the paper by Lily Christensen, he actually extends this out to the stellar regime and shows that there are certain stars that actually also fall on this line, although not all stars; the Sun does not fall on this line. Okay. So it's also possible that maybe these scaling laws are doing well at estimating the driving motions and the force balances in the magnetic field generation mechanism inside planets and stars. Yes, yeah. Neptune, you—it depends on if you're an experimentalist; you say older, but this cross is there, so I'm okay. But you're right; it is slightly—it is slightly lower. Yes, I have no idea; I should have looked that up before coming here. I'll look up in the paper and come ask me tomorrow or later today; I'll have the answer. Other questions? Okay. So scaling laws might be working.
Okay. So the other thing we want to do with planetary models: so we know we can't exactly work in the right parameters; maybe we have to use scaling laws to figure out conclusions based on that, but there are some things we can get right. Okay. We are able to work in an appropriate geometry for planetary cores. Planetary cores are spheres, okay, but they're typically spherical shells; there's usually an inner region that's not involved in the dynamo process. So in the Earth, for example, we have a solid inner core in the center. Okay. So we can work in the right shell geometry. Different planets have different shell thicknesses, right? So maybe the Earth—the inner core is about a third the radius of the total core; other planets might have a different shell thickness. Okay. So we could get that right. Other things we could get right: hopefully we're getting the force balances right, as I suggested before. Buoyancy sources: so what's driving the convective motions in here are different sources of buoyancy. So you can have thermal buoyancy due to things being hotter in certain locations; you can also have compositional buoyancy. So, for example, when the inner core freezes at the boundary, it releases both light and heat, and a light compositional element, so something that's slightly lighter than the surrounding fluid, and so that rises. We can mimic the convection driven by that compared to, say, convection driven by internal heating sources, radioactivity in tidal regions, okay, or just secular cooling—the fact that the outer boundary's colder than the inner boundary. Okay. So we can mimic the right sort of buoyancy profile inside bodies, and also external influences. Planetary cores don't live in a bubble; they are surrounded by things. So, for example, in Earth, we've got the mantle surrounding the core, and it has some effect on what's going on inside the interior. Mercury is so close to the Sun, and its magnetic field is so weak that actually magnetospheric fields and current systems can generate magnetic fields that might influence what's happening in the core. Okay. So these sorts of things we can model. Okay. And what we try and do is we try and use dynamo models to explain the differences we see between planets. So why is Earth's field look like this, whereas Uranus's field is so multipolar like this, or Mercury's field—you can't see the numbers on here, but the intensity—that field's much weaker than Earth's field. So we try and answer these order 0 or order 1 questions with these simulations. Okay.
So the plan now is I'm gonna kind of—we're going to survey the solar system now. In the interest of time, I'm not going to cover every planet; you can go through these notes and and look at them. I'm gonna hand-pick a few, but at this point, if there's one planet you really want to talk about, tell me, and I'll make sure I cover it. So calls for any of your favorite planet? Saturn. Okay. I will talk about Saturn. Let's do two more: the ice giants. Okay. I'll talk about the ice giants; that's two planets technically, but I'll let it go. Okay. Yeah, I'll talk about that. So that's a good question. So the question is—so I don't know if you know this, but Uranus is actually kind of tilted; it fell over on its side. And so it's actually—its rotation axis is almost in the equatorial plane. And the question is, if that affects—the short answer is probably not, but I'll give you more details on—okay. So I've got—we're gonna do Saturn, we'll do the giant planets; we should probably do a terrestrial planet; we'll do Mercury since it's new. Okay. I've got new data from Mercury, and I'll do Earth because we have to talk about a couple things about Earth. Okay. And then I'm around all week, so if anyone wants to talk about other planets, I'm happy to talk about them all week. Then after those planets, I'm going to go on into the the fringe or the frontier; we're going to talk about planetesimals and asteroids, and we'll talk about extrasolar planets. Okay. All right, here's hoping I can do all this. Okay.
Earth: you've already seen some stuff about Earth so far. Fields mostly dipolar; it reverses in time, but chaotically. Models are very good at imitating Earth's behavior. Okay. The first dynamo simulations that came out in sort of the mid-1990s reproduced the Earth's magnetic field remarkably. Okay, maybe a little too well. All right, it got the intensity of the field right without even trying; there's no knob that tunes the intensity of the magnetic field. Yeah, this is a very early model compared to observations, and these things are roughly the same intensity. It got the velocities of the fluid motions right. Okay, again, no tuning involved. Okay. So things seem to be going right; this suggested that yeah, maybe we're getting some stuff going right. But models can reproduce a lot of features of Earth. What I want to talk about are two new findings that really affect studies of Earth's dynamo. Okay. So our naive picture before these findings is that the Earth's dynamo is generated in the fluid outer core. The outer core is roughly about two-thirds the total core radius, so there's a solid inner core about a third the entire thing, convecting, and yeah, and it generates a dynamo. Okay. So there are a couple—when he called me—threw a wrench in there; couple wrenches in the—whatever that expression is—but affect things. And the first thing is people are getting better at measuring material properties. Okay. Material properties at high pressures and temperatures are hard to measure. You know, if you ask someone what's the conductivity of iron at 150 GPA and thousands of temperatures—do that in an experiment; it's hard. Okay. And people nowadays are just starting to get better at this; they're also doing theoretical calculations using what's called density functional theory to say, you know, I've got this atom and this many energy levels, and what are the quantum dynamics going on here, and figuring out what the thermal and electrical conductivity properties of these materials are. And very recently, say around 2012, they did these sort of better simulations and have gotten new electrical conductivity and thermal conductivity for liquid iron. Okay. So we used to say, and we used to think that the conductivity of iron inside Earth's core is roughly around, let's say, 3 times 10 to the 5 siemens per meter. Okay. That figure is now 2 to 3 times higher. Okay. So the electrical conductivity of the core is higher than previously thought, and with the electrical conductivity goes the thermal conductivity because of the Wiedemann-Franz law. Okay. So there—those two things are proportional, so the thermal conductivity is also about 2 to 3 times higher than we previously thought. Okay. So this actually throws—this causes some issues. Okay. So let's think about the electrical conductivity. How am I making the electrical conductivity of the core larger affect some of the things we've talked about today? Let me start with a simple one: how would it affect the magnetic Reynolds number? Would the magnetic Reynolds number be higher or lower if you suddenly made the electrical conductivity higher? Higher, right? So the magnetic Reynolds number in the core is higher than we thought by two to three. Okay. What about time scales of the problem? So we talked about the magnetic diffusion time. The magnetic diffusion time was the length scale squared divided by the diffusivity, which means it's really the length scale squared times the conductivity. Okay. So suddenly all of your time scales for the dynamo diffusion problem have increased. Okay. So that means if you think some process was occurring on the time scale of magnetic diffusion in the past, no, you were wrong. Okay. Because the time scale for diffusion was actually two to three times longer. Okay. So there are issues for the con—that the changing conductivity has effects on our understanding of the dynamo. What's more important is the thermal conductivity. Okay. And here's why the thermal conductivity matters: the dynamo is run by convection. In order to have convection going on, you need to have more heat being outputted of the dynamo than can occur by conduction alone. Okay. It turns out in the Earth's core, conduction is very good at removing heat. You give it a lot of heat; it goes there, and it conducts it down to the—about—of the planet. That conduction is proportional to the thermal conductivity. So we actually just made it possible to conduct about two to three times more heat down the adiabat than was possible before. Okay. So then you ask, oh, that's okay, as long as there was a lot of heat coming out of the core initially. And the answer was, well, there wasn't. Okay. If you measure the heat coming out of the surface of the Earth, okay, it's about 44 terawatts. All right. Then you estimate how much of that heat's coming from the mantle and from radiogenic sources in the mantle, and you get about half of it. Okay. Then you're left with the core; that's where the rest of the heat's got to be coming from. Okay. And it turns out that the amount of heat coming from the core—people—this number varies; it goes from about ten to twenty terawatts or so. Okay. But suddenly the core ad—about—can almost take all of that. Okay. So suddenly we have a core that—
Shouldn't be convecting, okay? Yet it's generating a dynamo, okay. The way out of this that we currently think—but there's lots of work happening on this at the moment—is that maybe the entire core isn't connecting. The outer region of the core might be stably stratified thermally, and the dynamo might be generating much deeper inside the core, okay. And so it's surrounded by this nice, stable, stratified layer, and that has influences on the magnetic field that we see, okay. So that's a major problem, and people are really working out the details on how thick that stable, stratified layer is, okay. And I'm sure the number for the thermal electric conductivity will change again, but this is where this is going.
Another interesting thing to point out—you might not think it's very important—but the inner core is very important for our dynamo as well, okay, for two reasons. First of all, the inner core inside the earth, it's a good electrical conductor; it's solid iron, okay. So magnetic fields that thread the inner core are frozen into it on very long timescales, so they provide a sort of anchoring or stability to the magnetic field, and we think that's important in the timescale for reversals, okay.
Another important thing about the inner core is actually the location where a lot of the buoyancy source that drives the fluid motion in the core comes from. So the inner core is essentially the boundary—the boundary of the inner core is where you're at the right temperature such that iron at those pressures and temperatures starts freezing, okay. As iron freezes, it gives off latent heat, okay. The other thing it does is it turns out the core is not pure iron; all right, there's iron, there's some nickel, and then there's some light element; we don't know what it is—maybe sulfur, silicon, oxygen, hydrogen—all these things have been suggested. We're talking about ten weight percent in amounts, okay. And when the inner core freezes, the geochemists tell me that the frozen part likes to be more pure iron and kind of exclude the sulfur or silicon or light element from it. So that means that as you're freezing out the solid, almost pure iron nickel, you're getting a fluid at that boundary that's lighter than the surroundings because more enriched in the sulfur, silicon, oxygen than the surroundings, so it's buoyant compositionally, okay. So there's a source of buoyancy at the inner core boundary, okay. So that's why we care about the inner core. And what people have realized lately is that it's possible that the inner core itself is convecting, okay.
So you might think, well, if the inner core's solid, how can it convect? There is something called solid-state convection; it happens in our mantle—the rocky layer surrounding the core is solid, and it convects, okay. It occurs by processes that change the, you know, mold the crystals or move crystals along, okay, but it's still convection; it's still displacement of fluid—of solid particles—due to buoyancy differences, okay. The inner core itself is probably convecting, okay. If it's convecting, it turns out that the mode of convection might be very interesting, okay. Rather than having the small-scale plume-like things that we think of when we think of convection, the pressures and temperatures and crystal structures and properties of these materials are such that the pressure might have the convection actually just being a translational thing where particles start on one side of the core; they just move across, okay. So everything kind of goes that way, all right. So now we start thinking, well, what does that mean physics-wise, okay? If I have material kind of moving across the boundary like this, it turns out you'll have a hotter hemisphere and a colder hemisphere in the inner core. If you have temperature differences in the inner core, then you have gravity differences in the inner core; you have buoyancy differences. If you have gravity differences in the inner core, which is kind of positioned at the center of the earth, since liquid can move, so this temperature difference across the inner core actually causes the inner core to translate a little bit—to move to one side, okay. But as soon as you shift the inner core a little bit, what happens is you displace that nice phase boundary where the iron was solidifying from where it was, and what ends up happening is you end up having one side of the core that preferentially crystallizes. So suddenly you move the core; it says, "Oh, no, no, I want to be solid here," so it starts solidifying here; you take the other bit of the core and you move it to a part where the temperatures are higher, and so it melts. So we might have a very interesting inner core where it's crystallizing in one hemisphere and it's melting in the other, okay. And that has implications for the dynamo because it means that a buoyancy source might actually be hemispherical, so there might be one side that's releasing a lot of light element—so this side, actually the crystallizing side, right, because we get the buoyant fluid and you get the latent heat released—and the other side that's actually doing the opposite. And people are starting to do dynamo simulations of the effectiveness now.
You might think this is very far-fetched; why on earth would the inner core do all of this? And the answer is it was actually proposed by seismologists to explain something known as the seismic anisotropy—the seismic anisotropy difference between the eastern and western hemispheres—the Atlantic and Pacific hemispheres, okay. So there's seismic evidence; waves that travel through the inner core tell us that there's something fundamentally different on this side than on this side in the inner core, okay. So there's lots of work going on right now. Here's some output from an ice dynamo simulation that tries to capture some of this dynamics. This is the inner core, and the colors here are meant to represent buoyancy sources, so you have one hemisphere that's doing one thing, another hemisphere that's doing another. These kind of silvery things here are magnetic field lines; their thickness is proportional to the intensity. And what you're supposed to see from this—they're very complicated pictures—but maybe you see a best here; this is a North Pole here—is that you have more of these gray lines in one hemisphere than the other, okay. So there might be more active regions inside the core where dynamo fields are being generated just as soon as the inner core goes. So the question was, what would cause these temperature differences in the inner core? And the answer is, if the inner core gets to the point it says, "Yes, I'm convecting," and it happens to be in a mode of convection than where these particles travel across, then you have younger particles on one side of the core and older particles on the other, and their temperature will depend on their age. So as soon as it's convecting in this mode, this happens—yeah—reversals in general, like, okay. So maybe no one's really kind of looked at what this means for—would you have more reversals in this sort of scenario versus less? I think that's an interesting question, and people haven't yet done simulations of that.
So the question is, do we know why we have reversals in the Earth's case? The short answer is no. The—the cheating answer is, "Well, it's a complicated system; it's chaotic, and sure it could flip." The nonlinear dynamics answer is that there are two stable fixed points in the system, and it can either have answers in all a contraction; lots of people—so there are two stable solutions, and it can, you know, if the system is wandering around one, it might flip to the other, okay. But the real answer is I can't tell you. If you show me a picture of what the magnetic field velocity fields are like today and you tell me how they're going to evolve, I can't just by looking at it say, "Ah, that's going to produce a reversal," okay. Other questions, okay. So that's that's the Earth, okay. I'm going to skip the Moon, right, cuz Moon wasn't one of ours; was Moon—no, Mercury was—but I'm going to try and convince you—look at the nice pictures; the Moon's very interesting, okay. So we'll talk about—come see me if you want to talk about it. Let's talk very briefly about Mercury. We're talking about this because the MESSENGER mission has gotten new data of Mercury's magnetic field, okay. The Mariner 10 mission in the mid-70s told us that Mercury had a dynamo-generated magnetic field, okay. This was a surprise because Mercury is so small; we thought it would have just cooled and solidified, but that's not the case. The dynamo-generated field produces a very weak magnetic field at the surface, so you can think of it as the characteristic field scales at the surface are roughly around 200 nanoTeslas, okay. That's what we knew after Mariner 10. The MESSENGER mission has confirmed this, okay; has kind of pinned it down—the error bar used to be much bigger; the number used to be around 300—so it's pinned it down a lot. But the other thing that's been able to do is tell us a little bit about the smaller-scale structure of the field, and it looks like the quadrupole component—I know these are Gauss coefficients; their spectral coefficients essentially—but the quadrupole component is fairly big, so the surface field we see is about, you know, 60 percent dipole and 40 percent quadrupole, okay. So there is a large quadrupole component even though it's still dipole-dominated, all right. The other thing it's told us is that the tilt of the dipole—remember the Earth's is tilted by about 10 degrees—is very small, and all we can do is put a bound on this at the moment based on the data, so it's somewhere less than about 0.8 degrees, okay. So the field is fairly axisymmetric; there's a lot of symmetry with respect to the rotation axis, but the magnetic equator is offset by about 4300 kilometers or so north of the geographic equator, okay. Now, yeah, yes, so yes, in terms of the axisymmetry, the what we've measured so far is just the aligned component; there may be some component in the equatorial plane or in the other planes, but we don't have good measures of it, okay. But it does look like it's fairly axisymmetric. Now you do have to take data like this with a grain of salt; the MESSENGER spacecraft—it's—it's fabulous, okay—but the orbit it's on puts it very close to the planet in the northern hemisphere, and then it's on a very elliptical orbit, so it goes very far away and then comes back in close to the northern hemisphere, so we really only have magnetic data in the northern hemisphere. And it turns out it's very hard to do direct data of what's on the surface. And when instead we do is we look at the magnetosphere and where certain equatorial plane crossings are and stuff like that, so the data is somewhat indirect, and hopefully we'll have a lot of good new data coming if BepiColombo, which is slated to take off, does so, okay. All right, so new data: large quadrupole, small dipole tilt. You might think, okay, so as a dynamo modeler, we're trying to reproduce these features, and it turns out that after Mariner 10 we knew the field was weak, and that's already a problem. And if you do scaling analysis—one of the problems that questions asked to do a scaling analysis—you'll find that it's hard to explain this weakness of the field, okay. So people—I'm not going to go over this—but people after that came up with a bunch of different possible scenarios for what's going on in Mercury's core to explain the weakness of the field, okay. And these are all different models, and you can look them up, and I'm happy to talk to you at some point, but none of these models explain the offset of the dipole or the axisymmetry. And it turns out that it's hard to generate a dynamo that does both—have a large offset, a large quadrupole, and a very axisymmetric field—and the reason for that is if you look at what sorts of fluid motions stimulate or excite certain magnetic modes; as soon as you excite the axial quadrupole, you tend to excite the equatorial dipole, which gives you a large tilt. So I can show you dynamo models that have large quadrupoles, but they'll all have large tilts, and this is a case where we have the opposite, okay. So new models are working to explain the combination of those two parameters, and I'm just going to put up two here; the one of them came out about a week or two ago in GRL by Hu and Cal, and they basically—so this is output from in their models—and you can see the equator's offset northward by about the right amount, and they explained it by saying that the core-mantle boundary on Mars—on Mercury—actually has thermal perturbations on it such that the equator is hotter than the polar regions. And when they do this, they're able to generate a dynamo that has a symmetry breaking that offsets the dipole upwards, okay. It's no good reason to have that signature—the thermal signature—but it works, okay. I've also been working with a student, Jenda and Ken at MIT, and we're working to publish this; we've done a similar sort of thing, so we have a dynamo model; we've got thermal perturbations, but we've got a different kind of thermal perturbation; we have it a degree one zero—hotter in one hemisphere versus the other—and there's some evidence from past volcanic activity on Mercury that this is actually happening—happened—so and we can also do that, but we can also get the intensity of the field right and also the axisymmetry. So it looks like there are some explanations out there, but a lot of details are going to continue on this in the future. Any questions on Mercury before I move on? All right, so that was Mercury's nice slides about Ganymede, okay. I'm supposed to talk about Saturn, okay. So gas giants—Jupiter and Saturn—if you look at their interior structure, we talked about the fact that the dynamos are generated in metallic hydrogen regions. In Jupiter, that region that transits that phase change from the molecular to the metallic region curves very close to the surface. And in Saturn, the curve is much deeper, okay. But in terms of geometry, the dynamo regions are still pretty much a nice thick shell; there might be some rocky core on the inside; probably doesn't affect the dynamo too much, okay. You look at their magnetic fields; Jupiter's field's a lot like Earth's field, okay—fairly dipolar dominated; somewhat of a 10-degree tilt, okay. If you looked at the spectra for Jupiter's field and you look at all the higher-order components, you see it looks a lot like Earth's field, okay. Saturn is dipolar dominated, but it's almost perfectly axisymmetric, okay. So there's very little—well, with the data, we don't think there's any non-axisymmetric features in the field needed to explain the data, okay. And a perfectly axisymmetric dynamo is a problem, okay. The problem is due to Cowling in the 1930s, who said that—or who proved that—a dynamo cannot generate a perfectly axisymmetric field. Yeah, we have a 60,000-kilometer radius planet that does it, okay. So you need to somehow explain this, and the answer comes in with Saturn if you realize that you're making observations of the field out here, right? You're orbiting Saturn; you're flowing by Saturn; you're taking data here. Cowling's theorem applies in here, okay. So as long as there's some non-axisymmetric components of the field in here and they somehow don't make it out here, then we're okay with Cowling's theorem and the observations, okay. How do we do that? I have to skip Jupiter—Jupiter—Jupiter—Saturn, okay. So the way we do it is with an interesting thing that happens in the phase transition from the molecular to metallic hydrogen region, okay. In the late 70s, early 80s, Stevenson and Salpeter looked at the properties of helium and hydrogen at these temperatures and pressures, okay, and realized—so—so this is mostly hydrogen; there's like what—like a 20-something percent helium fraction in here as well, okay. At the pressures where the hydrogen goes metallic, helium becomes immiscible in the hydrogen, and what that means is above it the hydrogen and helium are well mixed, and you kind of have like a one-component fluid, but here suddenly the helium dissociates from the hydrogen, and they act as separate fluids, okay. And the helium is heavier than the hydrogen, so it sinks, all right. So you suddenly have some region where you've got helium sinking down, okay. And once you do that, you end up getting a compositional gradient in here that works against what convection is trying to do—buoyancy is trying to do—to remove heat out of the region, so you might have a region that's stably stratified—known as the helium insolubility layer—helium rain-out layer—surrounding the dynamo, okay. Now what this means for the dynamo is that magnetic fields are being generated down here; they might be fairly complex; there might be lots of non—non-axisymmetric features, but before we see them at the surface, they have to pass through a layer of electrically conducting, stable fluid, okay. And you're going to get attenuation of the field through this layer, okay. And non-axisymmetric features in the reference frame of this layer, if there's any sort of shear going on in this layer, are going to look like time-varying components. And so what you're going to end up getting is an electromagnetic skin effect where you shield out the rapidly varying time components of the field, so what you get left out here is just the axisymmetric component of the field, okay. So that's the theory; you can try and model this; people have, including myself, and they've shown that if you take a dynamo that would normally produce an Earth-like field—10-degree tilts or so—and you put this stable layer surrounding the outside, you can—you can actually symmetrize the field; you're going to make a field that has a much smaller dipole tilt than was previously known. Yeah, oh, I'm so happy you asked me. So the question was, why doesn't this happen in Jupiter? My next slide—why Saturn and not Jupiter, okay? The short answer is because Saturn is a little bit smaller and further out and therefore a little bit colder, okay. The long answer is this boundary where you start getting helium dissociation—this immiscibility layer—depends on pressure and temperature, and people have been trying to understand where this occurs in phase space. So this is temperature, pressure; these are some old studies—old studies put this line here. So you look at this blue line here, and what it means is if the temperature-pressure profile inside the planet is below this line, then you will get helium immiscibility. This is Jupiter; this is Saturn's adiabatic—great temperature profile essentially. So this is the temperature-pressure profile in Jupiter and Saturn. These are much higher than these, so this—that was not good, right? This suggested there was no helium. So a year later, neither—these are also some former work—also no good—no, not that they weren't good; they aren't good at being able to explain this difference. This is the most recent work; these green lines—the different lines are for different helium fractions—but the point is these green lines end up lying below Jupiter's adiabat and above Saturn's adiabat in this region here, which corresponds to the outer layers of the hydrogen metallic region, okay. So it's possible that it's happening in an outer region in Saturn but not Jupiter because Jupiter is just a little bit hotter, okay. Now planets cool over time, and what this also means is that over time Jupiter is—about—it's going to start falling in this picture, and in my next—you can see here we got pretty close; there might be a thin helium insolubility layer in the top of Jupiter's metallic hydrogen region, and that layer may actually grow over time. Yeah, oh, okay. Yeah, you're right; I said that off the fly and [Music] okay. So those are probably much more important to us. The reason I suggested it is because these profiles have to extend out to the surface of the planet, and so there is a boundary point at the outer surface. So so the Saturn one will start at a lower outer temperature profile to go in, but you're right that those factors are probably much more important than the actual temperature, right? Okay, I—okay, I will never say that again. Other points, okay. So I should explain that the dipole tilt is actually the non-axisymmetric dipole component; it's the dipole that lies in the equatorial plane, so it's completely non-axisymmetric, cuz if you average over this, you get—it's much positive as you get negative, so by definition the dipole tilt is the ratio of the equatorial dipole to the axial dipole, so it's directly related. Does that explain—okay. Other questions, okay. So that's Saturn—just a hint to—to make you look forward to things happening with Cassini in the future; there probably is some non-axisymmetry in the field; we just haven't been able to have measurements that observe it yet, okay. And you could ask where is it; all of the Cassini data to date for the magnetic field—you have to be close to the planet to do the magnetic field—and that all happened fairly close to the—in the equatorial region—so about plus or minus 30.
Degrees latitude from the equator. Okay, so we were getting tons of data in the equatorial regions. Okay, so, so this is a model that produces a surface field for Saturn that has the same amount of that has less intact non-axisymmetric components that could be measurable today. If I subtract out the axi-symmetric component, that's what the non-axisymmetric component that's left looks like. Okay, and you look at this and you look in the equatorial regions and you realize that someone weaker here, the most intense stuff happening here is in the polar regions. Okay, we don't have good data from the polar regions.
Okay, will we have good data from the polar regions, or at least from higher latitudes? And the answer is maybe. Okay, the Cassini is slated to eventually be crashed into Saturn. Okay, on the final orbits, I've been told that they will actually try and get into a higher polar orbit, and so we might actually get data very close to Saturn at higher latitudes, and I'm hoping that they use those orbits to take magnetic data because if so, it might be the first time we have the possibility of seeing non-axisymmetric features in the magnetic field.
Yeah, the tilts you mean? So it doesn't—that's correct because the if you look at this, you can notice that the non-axisymmetric features are in higher modes, so they aren't in the dipole; they're much stronger, same quadrupole or octopus. That's absolutely true. So the current data gives you an upper bound on the dipole tilt, right? So it's possible that there is a tilt which would be okay for any problem, but again, it's also possible that any non-axisymmetric features, even in the dipole component, get shielded by the helium in solubility layer, so you're okay, but none of Cowling's theorems apply to the observed field outside of the surface; they apply to what's going on inside the dynamo region. So as long as you can shield the observations from any non-axisymmetric features, you're right that zero is probably not going to happen, right? Because even attenuation through a layer doesn't give you zero outside of it; it gives you an attenuated amount, but the question is, can you get it below the noise? Yeah, so, so that's a hard one. Oh, I'm sure that there are their variations in that layer that have influences. I don't think it can be, but like it's it's it's a fluid planet, right? So you expect sort of equipotential surfaces to look a certain way, so there's probably not a ton of differences, but they're certainly a bulging due to the the rotation of the plantings like that.
All right, in the interest of time, how much time do I have left? Five or ten minutes? Okay, I'm gonna skip the ice giants, but I will happily talk to anyone who wants to talk about the ice giants after. The only thing I will say about the ice giants is because it will apply later is that a new phase of water is in vogue now. Okay, if you take temperature pressure space and you say what does mont water look like at high pressures and temperatures, we already know at low temperatures water is very complicated; there all sorts of phases of water at low temperatures. Right, and high pressures you go from sort of molecular water to this ionic water I talked about. If you get even high temperatures and pressure, you have a plasma state, but there's this new state known as super ionic water. Okay, and these are 80 abouts for Neptune and Uranus. Okay, and you notice that deep inside the planets they get into this super ionic layer. What is super ionic water you ask? It's not well understood here, but the basic idea is it's a sort of phase where the oxygen atoms in the water produce a lattice, okay, and the hydrogen atoms flow freely in the lattice, so it's almost like what you think of a metal with sort of a proton lattice with electrons flowing except that this is a hydrogen ions flowing. Okay, so we really need to understand the properties of this material, viscosity, densities, conductivity x', and all these things before we can understand how this new phase of water affects what's going on inside Uranus and Neptune. It turns out that where we expect this layer to occur inside Uranus and Neptune seems to be aligned with where we think there's a stable region inside Uranus and Neptune. We don't know why super ionic water might be stable to convection, but there does seem to be a coincidence of those things.
All right, in the last—yo, and the most annoying thing about super ionic water is that any text editor you put that in things you mean supersonic water, and you have to change it every single time. Okay, so I want to talk a little bit about planetesimals and asteroids, small bodies, and then I want to talk very briefly about extrasolar planets. So for the small bodies, what am I talking about here? So the problem is the problem, the thing is that there are magnetic fields in ancient meteorites, so meteorites that we know come from very early in the solar system, earlier than 4.5 billion years ago. Okay, and they have very strong magnetic fields that imply that they cooled in the in the presence of a field that was tens of microtesla strong. Okay, if you wonder how strong that really is, well, so the earth is somewhere—so this is microteslas here—so the earth's around fifty or sixty microteslas at the surface. Okay, we're talking tens, okay, same order of magnitude as the Earth's field strength. Okay, four point five something billion years ago. Now, in order to explain the magnetism in these bodies, you also have to have the magnetic field in the wherever it's coming from being very stable, so not reversing a lot, not having lots of fluctuations on timescales of thousands to millions of years. Okay, the problem with that is some of the mechanisms that we think were around early in the solar system that would produce strong fields don't have this stability property. So if you say, well, you know, around those times you've got the Sun being in its T Tauri stage, but if you've got some planet, a small floating around or some body floating around in the presence of a solar field or something, it's going to experience different field directions and different intensities, and it's not going to be stable on those time periods. Okay, and it seems that the only way to explain the magnetism in these very old meteorites is for them to have formed on a body that had its own dynamo, but this was before planets were around; the only things around at this time were planetesimals, smaller building blocks of planets. So what this suggests is that there were small bodies, things with hundreds of kilometers radii or dimensions that were able to produce dynamos early in the solar system.
Now, another piece of ambulance coming from meteorites are from meteorites, the way that we believe to be from Vesta. Okay, Vesta is one of the big asteroids in the asteroid belt. Okay, it's not the biggest one, but there is a series of meteorites known as the HED meteorites; the II unit stands for u Crites, and one of these u Crites is called Allan Hills a 81001 has is believed to be from Vesta, and it has a very strong magnetic field that suggests a paleo field intensity of roughly two microteslas around 3.7 billion years ago. Okay, so this suggests that Vesta had a dynamo sometime then or before then. Okay, so you suddenly have evidence in smaller bodies, asteroid-sized bodies, planetesimals-sized bodies that there were dynamos on these bodies, and the question is, well, how do you explain this? Okay, the hard thing to do with planetesimals and the reason why this is, you know, people didn't suggest this, you know, hundred years ago is first of all the smaller bodies; first of all, you have to say, well, they're gonna be hot enough to differentiate, cuz you need to have a core. Okay, in order to get a core, you need the thing to melt. Okay, so are they gonna hot be hard enough to differentiate? Is convection gonna occur in these of course? Okay, you're gonna get the fluid motions; how long is that convection gonna last, and what sort of magnetic field strength could they produce? Okay, so people have done some studies, first of all looking at the time, looking at how long convection can last in these bodies. So I should mention first of all that the fact that there were some radiogenic particles like aluminum 26 early in the solar system allows you to melt these bodies and produce cores fairly straightforward. Okay, then it turns out you can keep the core super adiabatic for some amount of time. This picture has shows you the conductive value for the heat flux down here, and the fact that all these lines are above that means that they were convective during this time, and this can last for, depending on the size of the body, first, you know, several to ten million years or so. So we can get convection; then you can do the magnetic Reynolds number criterion, say, you know what are the velocities and length scales of these bodies; the hard part is the length scales again, right? These things are smaller, but if you do scaling arguments and so forth, you end up finding—I'm going to skip the details here in the interest of time—but you end up finding this is just sort of a phase plot of the convective energy, rotation period, and core radius for all sorts of bodies; you could have this side; the things that we read here are most likely to have had dynamo generated fields that could explain this magnetism. Okay, so you are—there it is possible that small bodies for a short period of time early in their histories had dynamos that generated magnetic fields, and this means that if there are any remnants of these bodies around like these meteorites, they're going to have crustal magnetic fields in them, and it means that asteroids, some of the bigger ones, might actually have surface crustal fields, and it's a shame that the dawn mission doesn't have a magnetometer on it to measure magnetic fields as it goes to Vesta. Okay, because there are predictions of this, or the investor would have a crustal magnetic field. Okay, so that's small, but it's quick questions about small bodies; I know I've sped through that, I'm sorry; I want to get to extrasolar planets. Yeah. Oh, all right, it's it's dangerous; it's dangerous in my shoes to make a prediction, right? But I have a 50/50 chance, and I'm I I am somewhat of a a better, so okay, so so what do you need to have a dyno? Well, let's let's think about this; what do you need? First of all, you have to have a substantial core. Does Pluto have a big enough core? We don't know, right? Right, but so half rock, but how much of that is iron? Yeah, so the core is probably small, so that's the first problem. Then, where the heat fluxes ever high enough to generate a dynamo? Who knows? If so, was there any crustal was there any rock around to actually keep the magnetic field? So could we see any crustal dip? My guess is if you if you forced me to bet, and I would probably say no, we won't see anything, but I would love it if we did. That's my feeling. Other questions?
Okay, just very quickly about extrasolar planets because I think this is a field where a lot of work can still be done, and it's the sort of field where you don't have enough data, so you can make you can say lots of things. Okay, so why do we care? First of all, several things. So as you're probably aware, there's been all of these detections and observations of extrasolar planets; a lot of these planets aren't like the ones in our solar system, right? They occur in different environments or they have different physical properties and the ones in our solar system, and you can ask the question, what does that mean for their dynamos? Why we might care, things you might put in a grant proposal, well, we seem to believe that having a magnetic field is important for habitability. Okay, so it might be something we want to look for; if we want to suggest an exoplanet might be habitable, we might want to look for one that's got a magnetic field, and also there's actually a way to detect this; it provides a mechanism to detect extrasolar planets; it's not currently in use; well, it hasn't it hasn't worked so far, but we know that we get radio emissions from interactions between planets and the still stellar winds or solar winds. All right, in our solar system, the same thing probably happens in other stellar systems, but they're very far away, so it's a much harder signal to detect, but people are looking. Okay, so maybe we can actually detect extrasolar planets by detecting things like radio emissions from from particles spiraling along they made field lines. Maybe we can also see stellar planet magnetic interactions, and people have shown that you can get these; so a lot of these planets are very close to their parent stars, so the magnetic fields might actually interact, creating, for example, heating signatures in the atmospheres of the of the stars that can be observed. Okay, so there are reasons that we care about this.
All right, I want to talk very quickly about two types of extrasolar planets, let's say three types of exercise planets that might be very different from our solar system. Okay, rocky planets; we have rocky planets in our solar system, right? Earth's rocky planet; one might be different in extrasolar planet, and the answer is the rocky planets in our solar system are small. Okay, or it's the biggest one; we now have observations suggesting that there are rocky planets that can be much bigger. Okay, we we dub these super-Earths. Okay, if you look in the literature, and super-Earths, the interesting thing about them is you put rocks under high enough pressure, they'll metallize—right? So in our solar system, the magnesium silicates that make up the mantle don't become good conductors at the pressures in the earth; if you put them in a five earth-mass planet, they become electrical conductors. Okay, if you suddenly have electrical conductors in the mantle of planets, that's going to affect their dynamos. Okay, so I'm not gonna I'm gonna skip the details; there's a paper by one of my students, Ryan Vilim, who's looked at some of the influences of having electrically conducting mantle layers surrounding a dynamo in a super-earth. Okay, so that's one thing, and that's all I'm gonna say about that. Water-rich planets. Okay, water worlds, things like Uranus and Neptune in our solar system, let's say. Okay, here again, I will call you to the phase diagram of water and the fact that we have this new phase of water that people are talking about, the super ionic water. If the planet 80 bats fall into this regime that they fall into this super ionic water phase, then there might be implications for the Dynamo just like there are the implications for Uranus and Neptune in our solar system. You'll notice this is one exoplanet, GJ 1214b; this is one from one of our compositional structure models, and this suggests that GJ 1214b doesn't ever get into the super ionic phase, which is over here; it goes from the ionic to the plasma phase, but the important thing to note here is if you change planetary properties just a little bit, so these are schematics of interior properties for planets where I just changed one property, the mass of the planet, but it's mostly water, and what you see is that the structure on the inside can be very different. So this is a body that's just got ionic water for a long time; this is a body with good ionic water and then super ionic water, and the thickness of the super ionic water increases; the red here is plasma. So if you change the equilibrium temperature of these bodies, you can have layers as well, and what this means is we might be able to actually if we could actually get measurements of magnetic fields from these bodies, we might be able to infer properties of their planetary interior structure from that. Okay, and the last one are hot Jupiters. Okay, hot Jupiters are these Jupiter-sized planets that are really close to their parent stars; what that means for them is first of all that they're in a much more radiating environment. Okay, and what that means for the atmosphere is is that some of the alkali metals and the atmospheres can ionize, so you can get a good conductivity, not a metallic or anything like that, but good conductivity is occurring in the eye in the atmospheres of these bodies. Okay, the other thing that's happening is if they're that close, they're probably tidally locked to their parent bodies, which means they have a constant dayside and a constant night side. Okay, so you have a hot side and a cold side, and atmospheric flows are going to try any equal a break that temperature difference. Okay, so your flows that go from the day side to the night side, so now I have an atmosphere, and I've got flows going around somehow, and I've got the possibility of these things being ionized. Okay, if these bodies have dynamos, the magnetic fields that thread through those regions are going to affect the flows in that region, and people are doing simulations of this sort of thing, and they found that for different magnetic field strengths—so this is work by Konstantin Batygin and myself and Dave Stephenson—and we've shown that with different magnetic field strengths you can go from having what are considered over the pole flow, so it flows from the day side to the night side over the pole, the zonal flows in this direction. Okay, and zonal flows are important because what's all those can do is they can take the substellar point, the point where the star is hitting the the planet most directly on, and it can shift it, the hardest point a bit, and there are some observations that suggest this is actually happening in these bodies. Okay, and people are doing all sorts of more complicated modeling of the atmospheres of these bodies. Okay, so with that I will end and take questions and just quickly say the future is bright here. Okay, we've got new mission data coming from all sorts of new missions; we've got we're gonna have better numerical simulations; simulations always get better as far as I'm certain; there will be tons of new experimental data on things like material properties plus all sorts of other things from planetary data, so I think we're going to get a lot more information about this in the future. Questions? Mm-hmm. Okay, so if I understand your question correctly, so it's the idea that ultimately the motions, the convective motions inside bodies are very small-scale, so the turbulence is small-scale, and the question is whether or not the dynamos generated the small skills and then somehow produces a large-scale field or if there are large-scale motions that are important in generating the large-scale field. Is that okay? So in yeah, so it's certain large-scale motions are important if you have strong differential rotation in any region, right? The tack of Cline of the Sun, it's a great place to have differential motions; those are very easily produced magnetic field, and there are no horrible theorem saying that you can limit the strength of the field or anything; if you if you take a magnetic field and do this a lot, you're gonna generate strong fields. So I think large-scale motions are important if they're there; there are some places you might not have them, right? And these fully convective stars may be in planets; you don't have as strong differential rotations, although from our simulations we tend to find it there are mechanisms to create strong large-scale flows as well, and they seem to be important. So if you have them, great; maybe you don't need them, but but I think they're they're very helpful. Other questions? Yeah. Yeah. Yeah, so that's so I know nothing about material physics, but when I talk to people who do, the way they explain it to me is that essentially you have a sort of an oxygen lattice, and it's the protons that are able to move freely between atoms or molecules, let's say. So it's a very different phase than what you would normally think of for water where, you know, when I picture water, at picture two hydrogens, one oxygen floating around like this, right? So it's a different structure for that material, but I don't think a lot is known about it, and I think we need a lot more work, and I should mention that I super ionic water has only been discovered in numerical simulation, theoretical simulations, so there is no experiment that's produced super ionic water, so you have to be careful about things like this when you only produce them theoretically. Other questions? I have no idea; that's a good question; I don't I will I have no idea; I mean, high pressures and temperatures are always hard, right? They've done it for hydrogen, right? There their hide their shock experiments and hydrogen and high pressures and temperatures that showed metallic hydrogen exists, right? People are working on what are called static high pressure experiments for rocks and things, so they can put things like mg something or other under high pressure and temperature and look at its properties; water is probably complicated; it always depends on how the water reacts with everything you try.
And surround it with how you put it under pressure. I'm sure that people are trying, but I don't know the details on what what the challenges are in that problem.
Oh, good. Okay, what's next?