Transcription
So now that we've heard back from the giant planets, might as well get started. And I'll try to make up some of that lost time. My name is Luke Moore. I'm a research scientist at Boston University, and I primarily do modeling and planetary atmospheres, in particular Jupiter and Saturn. So this is a fitting topic. I'd like to thank the organizing committee for inviting me and also especially Fran and Rod for giving very thorough talks on Saturday, which have set sort of the background for what I'm going to talk about. And also, I have need to point out that Marina Ghulam from Imperial College London has helped out with a lot of the slides that I'll be showing today.
So the talk will be broken up into two parts. The first one deals with just the basic properties of the upper atmospheres of the giant planets, and the second one will deal more in depth with the interfaces between them—the ionospheres, I mean—in the atmospheres and the magnetospheres. So I recognize that much of this will be new, or you'll see this for the first time, for many of you because you're from very different fields. So I'll try to keep it at a basic level and keep it as jargon-free as possible. That being said, feel free to ask questions about anything special if I'm missing jargon or if anything else doesn't make sense. Okay.
Part one: The giant planet basics. I'm just going to review some of the basic theory again. Rob presented much of it that's relevant for the atmosphere already, and then I'll go into how you actually generate the ionosphere. What are the ionizing sources—photons and particles in particular—and what are the relevant ion productions and loss of the giant planets? How do those differ from other planets and so on? Then I'm going to give a brief overview of what remote ionosphere—excuse me—remote ionospheric diagnostics are available at the giant planets. There are relatively few, so we don't know—it's harder to make a measurement there than at Earth, obviously. Finally, some model data comparisons with those remote—your god—diagnostics, and I'll go over a few of them. Issues that remain unexplained, and it's important—it's really—mind you—excuse me, sorry—there may be some astrophysicists here, so I'm going to say things like H2 a lot, but when I say H2, I mean molecular hydrogen, not ionized hydrogen. I mean ionized, I'll say H+.
Okay. There are atmospheres everywhere in the solar system, and of course the different constituents give you different behaviors, but you can also have very dense atmospheres that we're used to thinking about, and then things like surface-bound exospheres, which are literally that—in the exosphere on top of a surface. So here's an example of the exosphere of Mercury being driven antisunward by radiation pressure—thousands of Mercury radii. And then here's the exosphere of the Moon, again being focused by the Earth and radiation pressure pushing it away. So on Saturday we heard sort of a lot about the Venus and Mars and Earth my atmosphere—so the N2 and CO2 atmospheres—and I'll talk more about the dense molecular hydrogen atmospheres of the outer planets and how things are different there.
So we've seen a slide like this already, but it's important to emphasize that when we say upper atmosphere, it's very different for what the average person thinks about when they think about the atmosphere. So, for example, this is altitude, and the boundary between the upper and the lower atmosphere at Earth is somewhere around 80 kilometers. But in fact, the X Prize—if you remember that, the Ansari X PRIZE, which was awarded to a non-government organization—organization flying to space more than once—that was awarded for someone flying to 100 kilometers already. So, in the words, space, under that definition, is the base of the thermosphere—the bottom of the upper atmosphere. So the entire upper atmosphere is in this space region. Of course, this is where the shuttle used to orbit and other satellites do orbit, but there are a lot of interesting processes that happen here, in particular the deposition of UV and FUV solar radiation and energetic particles, and then forcing from below, that which we saw a little bit of on Saturday as well, and generally can divide the lower atmosphere in the upper atmosphere into two disciplines—meteorology in the lower atmosphere and aeronomy is a discipline of the upper atmosphere.
Okay. Again, we saw a similar slide like this where the different regions of the atmosphere are separated by density gradients in the thermal profile. So here is pressure versus temperature versus pressure, and then a representative profile for Saturn, Jupiter, and Earth, and a couple interesting points to note here is one—the Earth is actually as a higher temperature in the upper atmosphere than you burn and Saturn. That's a surprisingly common misconception that the Earth is cooler everywhere. I'm yeah. And then also, we want to describe exospheric temperature, which is the region at the exobase and above where you can have—you—your particles are still gravitationally bound, or you can have escaped, and the temperature profile reaches a constant with altitude, and it's called the TXo or the exospheric temperature. And of course, the thermosphere is the majority of the upper atmosphere, and it's associated with the positive gradient and temperature, and there are a significant amount of collisions, so you can treat the thermosphere with a fluid-like approach as opposed to a kinetic approach.
So here then is an example of the thermosphere of Saturn—altitude and number density—and the first—another important difference of the giant planets is, of course, there's no obvious solid surface to speak of. So we have to reference—when you've seen—whenever you see an altitude, it's referenced to some pressure level, and usually it's the 1 bar pressure level because that's the surface pressure at Earth. So, as Rod described on Saturday, in the lower atmosphere, convective turbulent mixing takes over, and the consequence is that the fractional abundances of the various constituents are all constant with altitude up to some point. In other words, the atmosphere is well mixed. If the—after that point—called the homopause or the turbopause—you'll see both definitions—then diffusive molecular diffusion takes over, and you'll start to see diffusive separation between the different constituents based on their masses. So the scale height of H2 is obviously a lot larger than the scale height of methane because methane is—law—harder—a lot heavier. And so at the outer planets, this is more of a distinction than say at Earth because the difference in masses between the main constituents is—is much larger. And so then that divides the atmosphere into a homosphere below the homopause and heterosphere above the homopause.
Brief facts about the ionosphere: Of course, it's the ionized portion of the upper atmosphere. It's typically coincident with the thermosphere, but in fact, anywhere you have an atmosphere and an ionizing source—which is pretty much anywhere we also have an atmosphere—you will have an ionosphere. In general, ion densities are much smaller than neutral densities throughout the ionosphere. That being said, even though the atmosphere—number density-wise—is minor, it plays a major role in terms of—it's a key layer for coupling between the upper atmosphere and magnetosphere, as we'll hear more about, and in particular it allows closure than my magnetic—magnetospheric current system through the conducting layer in the ionosphere, which we talked about on Saturday and we'll talk more about a little bit later today. And the currents that are driven through the conducting layer of the ionosphere lead to significant heating of the high-latitude upper atmosphere, and then that heat is distributed—gold—globally throughout the thermosphere.
So a few other parameters of the giant planets: Of course, they're all dominated by hydrogen—primarily molecular hydrogen—at Uranus and Neptune, then the heavier constituents play a bit larger role than they do at Saturn and Jupiter. All the giant planets are distant—between 5 and 30 AU—so they experience a much smaller solar radiation than the Earth, Mars, Venus. And they're all fast rotators—somewhere between 9 and 16 hours per day. That has important effects on both the ionization in the atmosphere and, of course, the coupling to magnetosphere as well, as you're rotating around a giant magnetosphere in such a short time. So, as Fran discussed on Saturday, there are widely varying dipole alignments—from Saturn where the dipole is essentially coincident with the rotation axis over to—Jim—to Uranus and Neptune where you have crazy dipole alignments relative to the rotation axis. And these all make the interactions between the ionosphere and the magnetosphere even more interesting and complex.
So the first thing we need to do is to generate ionization in the atmosphere, and to do that we have to ionize the main constituents—molecular hydrogen, atomic hydrogen, and methane. So here I've shown the ionization thresholds for those—Co—those constituents—12 to 15 eV, or alternatively, approximately all the ionization in the giant planets is for photons less than 100 nanometers wavelength. So solar UV and x-ray photons will ionize, and of course the solar proton flux goes as 1 over R squared. In addition, there are energetic particles from the space environment which can range from a few keV to a few hundreds of keV, and they'll produce two significant ionization in the auroral regions.
All right, so I have a question just to get a sense of how much you remember from Saturday and also maybe how much intuition you have on this topic—through a false—the first question is, all right, true or false: The higher the energy of a photon, the lower altitude it will be absorbed. So if you think true, raise your hand. So a small handful. So everyone else thinks this statement is false—not necessarily true. Okay, we'll come back to that. Yeah. And how about for the second one: The higher the energy of an electron, the lower and altitude will be absorbed in ionosphere—true? A few more people think that's true. Okay. Does anyone want to say why they think that's true? Yeah. So the—it depends on the cross-section, and that's true for both of them actually. They both depend on cross sections. So the main distinction is that photons, you know, when you—you send a photon through the atmosphere, it has a certain energy, and at some point the photon is absorbed, and then it's gone—that's it. Whereas electrons or other precipitating particles, they start out with some energy, they start colliding with the atmosphere, each collision they lose some energy until eventually their thermalized, and those collisions do depend on the cross sections of the with the different constituents, and those cross sections depend on the energy of the electrons and so on. So yes, the second statement is true—the higher energy electrons—the higher energy electrons are absorbed lower in the atmosphere because it takes more collisions to thermalize—to lose all that energy—where photons though it depends—is correct. So strictly speaking, the statement was false. The reason it depends is this equation doesn't look right here—it's close enough. Yeah. Yeah, it was—I had to switch computers. Anyway, that doesn't matter, but let's go to—so photon flux—that's right. Yeah, what is up and down mean? You can figure that out, but yeah, this is the attenuation of solar proton flux. It's fairly simple. Anyway, basically the photon flux at the top of the atmosphere is, you know, a certain amount of photons per square meter per second are going to be removed as some of the photons are absorbed on their way down into the atmosphere, and they're going to be removed at some rate that it's exponential of the optical depth. The optical depth is just some absorption—photo absorption cross-section—and then sort of the integral of the column depth basically—so the number density of the absorbers at this wavelength and then the actual depth through the atmosphere which depends on the solar zenith angle, which is right here—you can see—anyway—once—so you have a certain amount of photons at the top of the atmosphere and you continually remove photons through absorption processes. So then you can derive the number of photons per wavelength per altitude. Once you have that, and you can in a straightforward way, you can calculate the photoionization rate starting with the number of photons multiplied by the photoionization cross-section and so on and the number density. Yes, they wouldn't—there be a minus sign after that exponential? Yes, because you're decreasing [Music] yeah, it's—you look for the one online—hopefully—hopefully that has the—I'm okay. But so the problem is that the cross-sections—if they're even known—they might vary strongly with wavelength. So here's an example for molecular hydrogen—this is this cross-section—and term—in tend them—so somewhere around 10 to the minus 18 per square centimeter as an average cross-section versus wavelength. So here's the absorption cross-section, here's one of the ionization cross-sections, which cuts off at the ionization threshold of course, and then down here I show versus altitude and wavelength the resulting photoionization rate—here versus wavelength—and then summed across all wavelengths over here. So this is the total ionization rate of H2+ for these conditions. And so right away you can see that—oh, I haven't said—so this line here represents the altitude where tau equals one—in other words, where photons of this certain wavelength are absorbed in the atmosphere. So right away you can see that here we have some lower energy photons that are absorbed lower in the atmosphere, and then some higher energy photons—that's why you can't say a priori that a higher energy photon will be absorbed lower in the atmosphere. And just as a side note, you may come across this unit at some point—typically cross sections are given in units of megabarn—one megabarn is 10 to the minus 18 per square centimeter—and this comes from nuclear physics—if you're trying to hit the side of a barn with an energetic particle—say—varn far—yeah. So one megabarn—well, one barn is supposed to be already a big unit, and now we're dealing with megabarns. Anyway, some of the cross sections are not measured in the lab, and you don't know what they should be, and sometimes they get very complicated as well. So here I've zoomed in on this portion which is not shown here, but you can't—you don't—you can't read this off necessarily—this is cross section versus wavelength—and so this cross section is varying by five to six orders of magnitude over less than one angstrom—so it's going up and down in point-one angstroms or so—so you need sometimes very high-resolution cross sections, and then you need also very high-resolution solar inputs and so on and so on.
Okay. Now let's move on to deposition of—or electrons—and how they differ. So here is the electron production rate from simulations of precipitating energetic electrons versus altitude, and each color represents a different mean energy of the incident electron distribution. So from green to cyan we are continually increasing the energy of the precipitating electrons, and you can see as we said before, they deposit—they peak lower and lower and lower in the atmosphere because they require more and more collisions to thermalize with the ambient population. And just know this equation came out okay, but just as before, once you know the intensity of the electrons at a given altitude at a given energy, you can then straightforwardly calculate the photoelectron production rate as a function of altitude, and it's worth noting that that—that—that is proportional to the flux of precipitating electrons at the top of the atmosphere, just as the production rate from photoionization is—well, somewhere here maybe—it's proportional to the photon flux at the top of the atmosphere as you might expect.
How do solar and particle precipitation ionization processes compare? Here's an example for a high-latitude simulation—so production—electron production rates versus altitude. First, the dashed curve is from solar-produced ionization, and then the solid curve is from solar secondary production. So when a photon is absorbed by a neutral and it ionizes the neutral, there's usually some leftover energy because the electron and ion mass ratio is so widely different—most of that excess energy is given to the electron—and so you generate an energetic electron then called the photoelectron. Those photoelectrons, if they have enough energy, they can go on and produce further ionization, further excitation and so on, and so that's what this extra bit here is. The Sun produces some photoelectrons; those four electrons produce additional ionization here, giving you another ledge. On the other hand, if we compare to two different populations of precipitating electrons—there's a soft precipitating flux and a so-called hard precipitating flux—soft and hard just referring to the relative energies of the precipitating particles—you can see that those are orders of magnitude more important. So at least in the high-latitude precipitation region, precipitating particles produce all the ionization that matters. Black—solar protons—the dashes—primary ionization from protons—green and blue are electrons, and then the red is just the sum of those electron ionization x's. Yep. Okay. So I always say something about solar protons is a sort of source of ionization, but there are other photons—why don't we talk about stellar photons as the ionization source? Any ideas? Right. So the first effect—the first reason—is that the stars are much further away than our star in the Sun, and so the photon flux is much smaller, but there's also another important reason why stellar ionization typically isn't considered—has to do with the ionization thresholds that I talked about earlier—exactly. So higher-energy photons—in other words, say 912 angstroms and below—are already absorbed by the interstellar medium before they get here. So that being said, stellar photons can still generate something like a 10 to the 3 electrons per cubic centimeter ionosphere in the Earth's region at night, so they can be important sometimes if you have constituents with that I have ionization thresholds above that 912 angstroms.
Okay, so I just want to take a little bit of a pause here and talk about the—the fact that there are two populations of electrons that we have to worry about in the ionosphere. So there are thermal electrons and suprathermal electrons. So first of all, let's go through what happens with the photon again—it can ionize, associate, or excite neutrals as I just discussed earlier. The excess energy from ionization from with the photon and neutral is given to the electrons, and those produce four electrons which then join the suprathermal electron population. With suprathermal electrons are any electrons that have more energy than the thermal population. So those can also be the—world—energetic particles, and those—those suprathermal electrons can excite and ionize and dissociate further. Then the eventual emission from the de-excitation is the airglow if it's—if it's generated from photons originally—or C—or if it's generated from energetic particles originally. These suprathermal electrons are also colliding with the ambient thermal electron population through Coulomb collisions, and they impart significant heating of that thermal electron population and also the thermo-ion population. So thermal electrons form the bulk of the electron population—so almost every electron belongs to the thermoelectric population—and we can consequently assign them macroscopic properties—we can treat them as a fluid—maybe, you know, their energy distribution is a Maxwell-Boltzmann distribution—you can assign a temperature to them—you can evaluate conservation of momentum, mass, and energy and so forth. Suprathermal electrons, on the other hand, are just the high-energy tail of the electron energy distribution, and their energies depend on their—their cross-sections of interactions depend on their energies and not—have energy that's lost through collisions depends on their energies, and there are relatively more energetic and fewer collisions, and consequently you can't just assign a distribution of energy to the suprathermal population; instead, you have to calculate that population explicitly using the Boltzmann equation.
Okay. So suprathermal electrons can be—just as a reminder—for electrons, but also overall electrons and/or secondary electrons. Secondary electrons I haven't described yet—those are any electrons that are produced after the first electron impact. So from an auroral energetic particle, this electron ionizes, then you have another electron that's a secondary, or if a photoelectron ionizes something else, and that's another secondary.
Okay, let's see—maybe I can switch to—no, I better go on—running short on time—even though this—this isn't quite right, it gives you the gist. So the thermal electron population—I said you can assign macroscopic quantity—so you can evaluate the conservation of mass, and here's the thermal ion continuity equation that you would write then. So the rate of change of an ion density is equal to the chemical production—the chemical loss—and then the transport of that species where the bulk velocity is—is u—here—transport being usually processes like ambipolar diffusion—so the ions and electrons just diffusing away—or also neutral winds can also drive transport in the lower atmosphere. When chemical loss processes occur much more rapidly than transport processes, you can ignore the transport term, and you can solve for what's called photochemical equilibrium where you—you simply set production equals to loss. So we'll see a few examples of photochemical equilibrium and when you can apply that. First, let's look at some of the chemical lost processes that you can expect to see for atomic ions—there's radiative recombination—so an atomic ion—an electron—we combine and you have
A photon emitted as well. This is an extremely slow process in general, and so instead, typically in atomic, on well charges change with some other ambient neutral well before this reaction has the chance to occur. So charge exchange, some ion exchange is charged with some neutral, and these reactions are typically very fast. So the loss, the loss rate, so number of reactions per cubic centimeter per second is a proportional to some rate coefficient, which sometimes it's measured, sometimes just estimated, and then of course the relevant number densities of the ion in the neutral.
And then molecular ions have, can also, they can undergo charge exchange, but they can also associatively recombine with an electron, and these processes are also fast. If you have the terminal ion in your ionosphere, if it's a molecular ion, then this is going to be the dominant loss process for that terminal ion. And in that case, if you have only one major ion, then you can set the loss equal to alpha; there's an alpha ne squared somewhere here. Basically, the electron density can be approximated as the ion density if you have a major ion species that dominates. And so then you can, under photochemical equilibrium, you have loss equals alpha ne squared, and you can very quickly estimate the electron density. All right.
Protonated molecular hydrogen. Does anyone know what that is? It sounds intimidating if you don't have a chemistry background. The "black and hydrogen" part is easy, so what is the "protonated" part mean? It means yeah, you basically smash a proton there, add a proton, or it's the fancy way of saying H3+, which is a major ion in the outer planet ionosphere. Just sometimes you'll come across this and it can be confusing. Most people will say H3+. Yeah, it sounds smart. As far as I know, it was first discovered at Jupiter, and that's now I have a line that says that later. Okay. But basically what happens in the giant planet ionosphere is photons or energetic particles ionize H2, because H2 is a dominant species. So you produce H2+, so 90% of the ion production goes to H2+, but that's very quickly converted to H3+ to this reaction because you have so much H2 present, and this is a relatively fast reaction rate. So you produce H2+, that's converted to H3+; you also produce some amounts of H+, but remember, as I said, radiative recombination is a very slow loss process. And so what happens is as you rotate, there's a short 10-hour day, say it's a turn, and so you don't have a lot of time for loss during the Saturday night, just five hours, and very quickly the Sun comes back up. And so slowly over time you build up a significant amount of H+ ionization, even though less than 10 percent of the initial ionization goes to H+, it's just you build it up slowly because there's a slow loss process. So the major ions that you predict would be H+ and H3+, and in fact, the initial models predicted that you would see a predominantly H+ ionosphere with essentially no diurnal variation, and the ionosphere would be approximately 10 to the 5 electrons per cubic centimeter.
So here's just an example of photoionization rates versus altitude. You can see that mostly H2+ is the dominant ion produced, but then it's a very minor constituent after chemistry. There are also hydrocarbons. So at the homopause, we saw the hydrocarbon number densities. Sorry, this is this is a model simulation. Sorry, I'll come—there are no direct measurements of the photoionization rates, but we have other measurements we can compare to it. We will—there are also hydrocarbons to worry about. They had, there, that the homopause, you have methane and other carbon and hydron hydrogen things, and there are a lot of reactions to worry about there if you want to do hydrocarbon chemistry correctly. But once you can account for a few reactions in your model, it's actually not much harder to add in hundreds of more reactions; it's just an amount of busy work to track down the reaction rates, and in fact, many of these reaction rates aren't measured, so you just have to estimate them. If you do want to treat hydrocarbon photochemistry at Saturn, for example, here's a brief summary of the chemical reaction chains, and there are hundreds of other additional reactions to worry about, but those hydrocarbons only—so these now are model simulations and to pattern or density versus altitude in each in each case. So here's the electron density profile, and then the H+ is dominant as I just alluded to, and then H+ is still a major ion as well, but the hydrocarbons only contribute some ledge of ionization in the bottom side. So if you're not worried about this ledge of ionization here, then you can safely ignore the hydrocarbon ions, at least to a first approximation. Additionally, you can also have meteoroid ablation in the lower atmosphere that produces metallic ions such as magnesium ion and so on, and that's similar concentrations to the hydrocarbon densities. So these are minor constituents in the giant planet atmosphere. All right. Now let's move on to some of the remote observation techniques.
The first and most common is radio occultations. So these have been used ever since the 1960s for basically every spacecraft that's gone to a planet, and they're still used today. Briefly, what happens in a radio occultation is: here's a spacecraft, here's a planet, here's Earth. Spacecraft is transmitting a radio signal to Earth, and as it moves behind the planet, it's occulted by the atmosphere. So the radio signal goes from no interference with the atmosphere to interference with the atmosphere, and so you have some refraction, some some bending, some time delay. And what you measure at Earth is a frequency that you're getting from this spacecraft, and you compare that to the frequency that you would expect to get if there were no atmosphere in the way, and then you have a frequency residual, it's called. So you construct frequency residuals versus time. Radio waves are sensitive to electrons, and they're also sensitive to neutrals in the lower atmosphere. If you make an assumption that the atmosphere is horizontally stratified, stratified, you can then invert these frequency frequency residuals versus time. So here's no atmosphere, no atoms here, and I'm sure then suddenly the upper layer of the atmosphere, and then each successive layer on the way down. So you can invert those and derive an electron density versus altitude profile. Ultimately, there's a lot more complication involved there, but we don't really have time to go into it. Yes. So basically the positive here is the ionosphere, and then you can't see this on this scale that would go way down here, but that's the response to the neutral atmosphere into the into the deep neutral atmosphere. So thus atmosphere is just a little bit of a blip above the main refraction that you see, the main response. So these can be used to drive electron density profiles versus altitude, and the only problem with the outer planets is that they're so far away, the only time that a spacecraft is going to occult the atmosphere is at the the local dawn or dusk. So you can only get dawn or dusk ionosphere profiles at the outer planets.
There's another remote observation technique that, so far as you need to Saturn, that's called Saturn electrostatic discharges, or SCDs. Briefly, these are broadband, short-lived, impulsive radio emissions that were originally thought to come from Saturn's rings due to the 10-hour, approximately 10-hour periodicity. Later, they're shown to originate in lightning storms in Saturn's lower atmosphere. So basically what's happening is you have a broad went broadband radio emission; some of those radio waves can transit, transit through the ionosphere and be measured by the spacecraft; others won't be able to transit, and they'll be reflected by the atmosphere, and then you look at where that cutoff frequency is between ones that can transit and the ones that can't, and that cutoff frequency tells you essentially what the peak electron density of the ionosphere is; it's a plasma frequency there. So using SCDs, you can drive then the peak electron density is a function of time at Saturn, and that's complementary to the radio occultation profiles.
Another major remote observation technique is CH3+, and as we just described earlier, it's predictably a major ion and outer planet ionospheres, and there are many emission lines in CH3+ available in the infrared, in particular in the K band and L band atmospheric windows, but I'm going to leave this for the next lecture. Let's look at some history of radio occultations of the giant planets. So there have been six spacecraft to take radio occultations of the giant planets: Pioneer 10 and 11, Voyager 1 and 2—they just had flybys of each of the objects—and then of course Galileo and Cassini orbited Jupiter and Saturn respectively. As far as I'm aware, there is no—I haven't seen one, but I could be wrong—Ulysses also passed by Jupiter. Right, right. Sometimes you don't have the ultra-stable oscillator that you required to do it. The other possibility is that radio occultation analysis is sort of a black art, and that there are only a few experts in the world, and so, for example, Jupiter, there were more than five measurements made; only five have been published and analyzed. So there are some just sitting around, maybe the Ulysses as well. At Saturn, we have 59 so far, just from Cassini, and then there will be maybe a half-dozen more before Cassini ends its mission in 2017. So in a flyby, you have an ingress occultation and an egress occultation, so you get two per flyby. So you can see that we just really have a handful of measurements of the radar, the electron density profiles at the outer planets, and this is a pretty stark contrast to say the Earth's ionosphere. We can measure all kinds of things all the time.
Now I'm just going to briefly go over some of the results from radio occultations. Here are two—or all—electron density versus altitude profiles, so from Pioneer 10, whereas your one, and then Galileo and Voyager 2. So the main point to get from these figures is that one, there's a lot of interesting structure present, and then there's also a significant amount of variability in these observations, but on average you might say that the peak electron density, so the peak value here, here, here, is of order 10 to the 5 electrons per cubic centimeter; that's called n max, and then the the altitude of the peak electron density ranges somewhere between 600 and 2,000 kilometers. So there's clearly a range of processes that are driving at least two different categories of ionosphere: Jupiter, a low-altitude ionosphere and high-altitude ionosphere, and we'll need to be able to account for that in the models. At Uranus and Neptune, same sort of idea; there only two profiles each; they look maybe sort of similar, but they also have these very sharp layers and sort of odd structure that will eventually need to be explained, and you might say on average the peak electron density is somewhere between 10 to the 3 and 10 to the 4 electrons per cubic centimeter. That's most of the extent of what we know about Uranus and Neptune in terms of electron densities. What about Saturn? Again, the same story; there's sort of a high-altitude profile that you see, and then a lot of these low-altitude sharp layers, and then some significant amount of variability on top of that, but if you just look for an average, then the electron density is something like 10 to the 4 electrons per cubic centimeter, and in the height, the peak of the altitude is somewhere between 1,000 and 2,500 kilometers. Well, that's further planning or Voyager radio occultations. What about for Cassini? Here are the first 12 radio occultations from Cassini. Okay, thank you. If you plot all them together, separate them into dawn and dusk, and what you see first of all is that it's kind of a mess; there's no clear overall trend, at least I would say there's no clear overall trend, despite the fact that all these occultations are within about 5 degrees of latitude of each other, so they should be sampling the same ionosphere, the equatorial ionosphere, but if you then squint your eyes a little bit and look back and forth between the dawn and the dusk, you might be able to convince yourself that there's a little bit of a dawn-dusk asymmetry, so the the densities are are lower in at dawn and larger at dusk. Maybe if you average the dawn and dusk profiles together, that's maybe a little more convincing. So here is electron density versus altitude, the average of the dawn profiles and the average of the dusk profiles. So this is clearly, on average, some dawn-dusk asymmetry, and that actually can be easily explained by the mixture of H+ and H3+ ions that we mentioned earlier. So here's an example simulation that could explain this: altitude versus local time, and then contours of electron density. Basically what happens is here the Sun is turned on; you start producing ions, and in particular you produce H2+ and therefore H3+ ions throughout this the daytime. Then at dusk you turn off the Sun, but you still have some ionization left, so you still have H3+ ions here, maybe throughout the nighttime. H3+ ions can just associatively recombine very quickly, so they're lost; therefore, at dawn, before the Sun comes up again, you're left only with H+ ions, which tend to peak at a higher altitude, and therefore you have a high-altitude, low electron density at dawn and a lower-altitude, higher electron density at dusk. Yes. So you said by following the timeline it's similar to what we used to infer maps. You yeah. So you might be able to imagine that the difficulty there I would say is we don't have measurements of the ion species per se; most of the time we'll get to that a little bit more in the next lecture. So most of we just have the electron density profiles at dawn and dusk, maybe some information about the peak electron density versus local time, but other than that it all has to be inferred from the modeling. Okay. There's also an interesting latitudinal trend in electron density. I'm just going to go through this briefly because they're running short on time. The if you separate—here are a bunch of Cassini radio occultation profiles—if you separate them by color, so the red is low latitude, the green is mid latitude, and the orange is high latitude, then you again you can see that there's some sort of trend with latitude, but the electron densities are increasing with latitude. Here I show the same thing, so except I'm instead of just the electron density peak, it's the the integrated column content of electron density, also called the total electron content, or TEC. So TEC versus latitude, and here are the points. You see there's a very clear trend with latitude where the minimum electron densities are observed near the equator and the largest entities are high latitudes. In fact, this is opposite to what you would expect from solar photoionization, because the Sun is overhead at the equator, so the peak of the photoionization is at the equator, and the minimum production from polarization is at higher latitudes. So actually the exact opposite trend. Does anyone have an idea what might cause that? So the peak of the production rate is at the equator, but that's also where you see the minimum in electron density. So you go in from peak production to minimum electron density. What's in between that could cause that? What if we set production equals to loss? So we're in photochemical equilibrium, and we want to solve for the electron density. We know the production; it's large, and we know the electron density; it's small. Sorry, a large loss. Exactly. So that's the current best guess as to what might be happening is we have a large loss at the equator, and that photochemical loss falls off with latitude. That loss is most likely an influx of water, so water or OH or some other molecules that can charge exchange with H+ and turn H+, a long-lived atomic ion, into some short-lived molecular ion. That molecular ion will then recombine, and you produce the electron density. Okay. So I think that's a good stopping point for now, and then we can please yes. This one—these are actual differences between measurements. Yeah, they're fairly large, but you still see either drastic variations or some—I mean, most likely we'll get into some of the possible causes a little bit later for these vertical structures, but basically it's nothing like you would expect for just a simple photon-produced ionosphere. There's a lot of structure induced. Yeah, you can sort of hand-wave your way around and explain, but you can't derive, you know, the answer, one answer for one profile that will then also explain all the other profiles. You need to sort of re-derive the answer for each profile. These are uncertainties in the mean; there are uncertainties in individual measurements. You know, sometimes they're large, but you can see, you know, like here's a green profile, and then here's another green profile, and these are wildly different, even though they're at similar latitudes. You know, very nice. Yeah, so there are very few measurements; it's a giant planet; the measurements are taken over many years, sometimes separated, and somehow you need to describe the entire ionosphere from those measurements in a self-consistent way, so that's the problem. It can be yeah.