NASA's Heliophysics Summer School - August 14, 2024 - Tom Bogdan & Marco Velli

So welcome back. Uh, please, uh, welcome Tom Bogden, currently of the, um, National Solar Observatory, but, uh, formerly of UCAR. Yeah, formerly of UCAR. So, uh, and, uh, and, uh, a leader in the field for a very long time. We're happy to, uh, uh, he is a last-minute drop-in, uh, and we're happy to have, uh, thank him for his, his, uh, uh, work for today. Thank you very much.

It's a real pleasure to be here. I'm to tag team this, uh, along with Marco. Uh, this introduction, I want to first of all, uh, congratulate you all for being here. Um, there's very stiff competition for these positions, and you've all done an amazing job to get selected. So, um, be pleased and be proud of yourselves, uh, that you're here. Um, and the second thing I want to say is, put on your seatbelts. Uh, you are going to have an amazing ride for the next week. Uh, the lectures in this series are going to take you on a very diverse tour of a lot of wonderful heliospheric sites and processes and things that are going on. You'll be amazed by what is out there. Um, and my purpose here is to kind of try to unify what you're going to see by looking at the physics that sits underneath heliophysics. And, uh, I've grabbed this line from Shakespeare, uh, and modified it a little bit for my own purposes. Um, the two key ingredients you're going to see of heliophysics are the matter that's out there in the heliosphere and the classical fields of gravity and electromagnetism that connect those two fields. They're the two ways in which matter interacts with itself.

So here's my obligatory slide of the heliosphere. I took this with my cell phone. It's white light, fairly low resolution. It's about two or three arc minutes is the resolution on this slide. You'll probably be seeing better, uh, in some of the lectures coming forward in terms of resolution, but I think this gives you a big picture. You're here, you're in the heliosphere. And in this picture, although it's a little hard to see, there's an ionosphere above you, a thermosphere, a mesosphere, magnetosphere. There's solar wind coming out from that star in the middle of this picture of you. If you even look very far in the periphery, you can probably even find a heliospheric termination shock there.

So the classical fields, uh, believe it or not, the very last word on gravity and electromagnetism was written down in 1916 by none other than Albert Einstein, and it fits very conveniently on this slide. Um, there is, uh, one equation here for the, oops, oh, I think I've lost my pointer there. One equation here for the gravitational field. There's one equation here for the electric, electromagnetic field. These equations are exact. We have done nothing with them since 1916. So it's a sobering thought that, at least from this perspective, people could have started doing heliophysics over a hundred years ago.

If you are to measure the electric and magnetic fields in this room, what would you find? You'd find there's a DC component to both of those fields. There is an electric field that goes from up and down. There's also a magnetic field due to our magnetosphere. And situated on top of that are going to be a lot of wild fluctuations. That's how you're seeing me. That's how I'm seeing you. That's the radiation. So we tend to break the solution of Maxwell's equations in a flat, inertial spacetime into a deterministic piece, which we often call magnetohydrodynamics, and then a statistically fluctuating piece, which is the radiation field that sits underneath it. And in between is this really fascinating area where there's coherence that goes on, and it can be treated from either perspective, either by putting coherences and correlations in the random part of what's going on, or taking those Maxwell equations, allowing those time derivatives to be huge. And this break between deterministic and statistical is something that shows up a lot in our problem going forward. Um, and so that's why I wanted to emphasize it here.

The material is our problem child, as they say in French, our bete noir. Um, the fields, we know everything about classically. We've known about them for almost a century. But the matter causes us all kinds of problems, um, because it's very difficult to describe in the same sort of fashion. It too has a random component, the thermal fluctuations in this room, and it also has a large-scale component. As I move my hand, there is a flow that is coming by that hand and a turbulent wake that sits behind it. And turbulence is indeed that process which takes large-scale, ordered, laminar flows and turns them into heat in the background. And so we have ways to describe the gravitational field and the gravitational interaction, and we have ways to describe the electromagnetic fields. But the question is, how do we describe the matter? How will we describe the matter in a way that's consistent with those two?

And here are a whole bunch of descriptions of matter, starting from, um, the very tiny at the top. You could decide to set off and work out the wave function for the entire heliosphere. This would be a lot of work. Um, it would also require a very large computer code, probably larger than anything you have. And moreover, it probably tells you a hell of a lot more about the heliosphere than you could practically be interested in. At the other extreme, you could use the tensor virial theorem and work out an equation for how the change of the moment of inertia of the entire heliosphere changes with time due to the presence of the kinetic energy, pressure, magnetic fields, gravity that's inside. And this allows you to answer almost no questions about what's happening inside the heliosphere. So what we do is we pick something in between, because even the microscopic won't work. Anyone have a wild idea how many particles there are in the heliosphere? Take a guess. 10 to what power? Anyone? Fifty-seven. About 10 to the 57 particles. You would have to run forward with that Hamiltonian dynamics again. It's not going to fit on your computer, is it? And it certainly isn't going to make a PhD thesis.

So we picked this intermediate regime, what I call macroscopic, and at some point mesoscopic, where we treat the material in the heliosphere as if it is a fluid. Which is very silly, because at a certain level, very little fluid in the heliosphere, very little material in the heliosphere actually is a fluid. If you're studying the ocean, that's true. It is a fluid. It does act like a fluid. But we use it to describe the solar wind. We use it to describe the interior of the sun. We use it to describe the atmosphere. These are not strictly speaking fluids. These are gases and plasmas. But yet we adopt a fluid description for them. And what I want to leave you with is a takeaway message and something for you to sort of contemplate as we go forward is that this is unreasonably effective at describing our system. And I want to say it's unreasonably effective because look at how much information above that macroscopic picture we have thrown away. We've thrown away a hell of a lot of information about this system. We're keeping very little. The density is a function of position. The fluid velocity is a function of position. My God, we, of course, grained this. How is it that that description, which throws away so much information about the system, can give us reasonable answers to equations that are in, to questions that are interesting to us? It's kind of miraculous.

Now, a lot of you are working on particle distributions. Um, and so we cannot treat them generally in a fluid picture, but we have to move one level back to the mesoscopic approach where we look at distribution functions. So the physics of heliophysics, the underlying physics that's going to connect all the amazing places you're going to go over the next few days and the next few speakers that have come online are here. We make two assumptions. Number one, we assume we live in a flat Minkowski spacetime, that is, there's very little curvature of spacetime in the heliosphere that we need to take into account. We're trying to prove Einstein's theory and worry about deflection of light going by the sun. Yes, we need to worry about curvature. About no, um, for the sort of questions we're asking, we don't. Um, that means that in place of that alpha beta, which looked very elegant but contained a lot of information, we end up with Newton's equation. And I write it with a plus and minus because I want to say, beware, I have spent days trying to find errors in my calculations because someone was using a plus in that equation instead of a minus. Half the world likes to use a minus, the other half likes to use a plus. Figure out which it is when you look at it, because you can really get things screwed up. Uh, assumption number two is that there's very little motion in our heliosphere that is, um, relativistic. And so the gamma, the relativistic Lorentz factor, is almost always one in what we do. And in that case, we do have the flat spacetime in Minkowski equations for the Maxwell field, um, and we have a Poisson equation for gravity. And we adopt the macroscopic approach for how we describe our fluid. And this is the essential heliophysics that you use in no matter what lecture is going to be given to you this week. This is the underlying basic physics.

Now, you may take these equations and plunk them into a computer code which attempts to solve these continuum equations in a discrete fashion, um, or you may sit down and be brilliant and do this analytically. Um, however is how you're working on it. There are, um, two critical attributes of the heliospheric approach that I want to share with you and emphasize because they're very important. Number one is there are conserved quantities sitting in these equations. And those conserved quantities are incredibly important. They are incredibly important because it turns out that if your computer code and if your equations conserve the things that need to be conserved, quite often you will get more or less the right answers to the questions you're trying to ask. The second thing is that there's a very important frame of reference, and that is the co-moving frame of the fluid.

So let's talk about conservation laws. You can, in your calculations, select the origin of time, um, however you like. Right? There is not a universal, universal time. You have to put down, like, Julian days to begin your calculation. And the fact that there is no origin to time means that energy is conserved in the system. You can also flip the direction of time in many of your equations. Right? The dynamics, the Hamiltonian dynamics is, um, invariant under time reversal. I once saw a lecture by Sir Roger Penrose. It was very fascinating. Um, he had an egg and he was standing on stage, and he took that egg and he dropped it, and of course, it hit the floor and it broke into a million pieces. And he said, what if, if you saw a movie of a million pieces coming together of that egg and it amazingly coming up into my hand, could you say it was going backwards or was it going forwards? That movie, technically speaking, you couldn't. I mean, it is cosmically unlikely that all those pieces of egg should have the right momentum all at the right time to assemble an egg which would then be flying up and come into my hand. Um, but technically speaking, so much of what we see out there, we don't know whether the movie is going forward or backwards. That leads to conservation of entropy. Likewise, we can pick an origin to our coordinate system wherever we'd like. We don't have to set everything by Greenwich or some other position on the globe that you like very much. And that means momentum is conserved, three components of momentum. We can rotate our coordinate axes however we like. And we can even watch movies of the fluid going on in a mirror. Right? There are reflection symmetries that we can't tell the difference between whether we're looking at something in a mirror or not. Um, that leads to parity and angular momentum conservation. And finally, we can relabel particles, and that relabeling is conservation of mass. So these conservation laws, energy, momentum, angular momentum, and mass, are built into the heliophysics equations. They conserve those quantities, and they conserve them two ways. They conserve it locally within a certain volume of fluid. It's possible to exchange energy between these different reservoirs, between kinetic energy, between gravitational potential energy, between the internal temperature, right, Joule heating of currents leads to internal heating of the material, viscosity takes kinetic energy and turns it into thermal. Look at the other arrows. The magnetic induction equation allows fluid motions to create magnetic fields through a dynamo, going the other direction. The Lorentz force allows the magnetic fields to push on the fluid and cause it to move in different directions. All of these are contained in the heliophysics formalism, and the rates at which they occur are computable in that formalism. We can also conserve all these quantities between different parcels of fluid. And the idea here is that we have a system of systems. That there are small little blobs here which are locally at a constant pressure, temperature, and density, and they can exchange energy, momentum, angular momentum, and entropy with their neighbors. This too is encapsulated in those MHD equations and in the heliophysics formalism. And if we take a system, stir it up, and leave it alone, it equilibrates. First, it does so dynamically. The first thing it'll do, it'll move around and accelerate until the pressure is constant everywhere within that total volume. Then the thermal conduction will kick in, and it will now equilibrate until the temperature is constant everywhere within that volume. And the final step is the chemical equilibration, where the same type of material sits in every one of those little blobs. Um, that equilibration is also contained in the heliophysics equations. They're very remarkable for what they do.

Let me talk a little bit about the co-moving frame. Um, on one side, um, I have the electromagnetic fields, the current density, and the charge density as seen by an observer moving along with the flow. Right? So there's a parcel of fluid that is moving about here. And on the other side here, I am fixed in the laboratory, watching this parcel of fluid move along. And I also can measure the electric field, the magnetic field, the current density, and the charge density. Now, the important thing is the interaction between the material and the field must always, always be reckoned in the co-moving frame. And in that co-moving frame, if I have a lot of mobile electrons, which I tend to have in the heliosphere, um, it's the case that any charge density I might like to build up, any imbalance in charge between the electrons and protons, quickly disappears on time scales of which I'm of interest. So I would assert that in my moving frame of reference, the charge density is zero, precisely zero. Right? There is no charge density in the co-moving frame. But notice that me, here in the lab frame, I believe there is a charge density in that blob of fluid that's going by with velocity U, and it's the dot product of that velocity with the current density that I'm measuring there. So there is, in fact, a charge density as seen from the laboratory frame. Likewise, in the co-moving frame, if I look at the current, it's proportional to the electric field that's measured in that frame by a conductivity tensor of some sort. And so in the limit that the conductivity is incredibly large, sigma becomes huge, in order that J prime doesn't go through the roof, and I don't want a huge J prime, what has to happen to E prime? E prime has to get very, very small, doesn't it? So the electric field has to be very weak in the co-moving frame. And if I go up to the top equation, E prime being zero means that E is very close to minus U cross B, as seen in the laboratory frame. And that's how we get MHD. And here's what MHD looks like. Notice that to do heliophysics, I needed special relativity because I needed that transformation between the fields in the co-moving frame, where I reckon how they interact, and the laboratory frame, where I typically solve my equations.

So let me conclude with this very rapid, but I think review for most of you, introduction to the physics that sits underneath it. Um, and remind you that if you conserve all the things that need to be conserved in your problem, and you ensure that entropy increases for an isolated system, it need not increase for a system that's not isolated. Notice that your refrigerator takes warm air and makes something cold out of it. Um, then things often work out much better than you had any right to expect them to. Always be certain that in your little systems, your little subsystems that are going to exchange things, that the number of particles in there is large. Doesn't have to be 10 to the 57, but it certainly needs to be 10 to the 10 or 10 to the 12, so that the fluctuations are tiny, and that that physical system can sample all the microstates that are consistent with that macroscopic state of a certain pressure, density, temperature, flow speed. Always, and remember this, please, if you remember nothing else of this lecture, always evaluate your interactions in the co-moving frame. This is especially true for the radiation field, but you get to solve your equations in whatever frame you'd like. That's the beauty of physics. That's the beauty of relativity, is that any frame is as good as any other frame. So I should probably have retitled my talk, "The Unreasonable Effectiveness of the Macroscopic Description." Um, and I picked a different line from Shakespeare to close on. Um, if you find things don't work sometimes in your calculations or your thesis that you, you're working on, remember you should always blame the stars instead of yourself. That's what he tells us. So it's been wonderful to give you this brief overview. Um, Marco is going to come up and kind of take you through more of the heliosphere that's out there, but I'd be happy to take any questions you might have. Um, and I'd also be happy to hear from you why you think that the fluid description works so well. Um, there's my email. Um, stay in touch. And thank you very much. We've got a, we have in the schedule a Q&A session at the end of the morning lectures, um, usually. So you can ask questions then. But if you have any immediate questions for Tom, anybody not sure, uh, how relevant this is, but I need to ask it while I still remember, uh, the equation for the number of electrons, uh, going into the charge density, I noticed it had the subscript e. I'm assuming it had to do with electrons. And I was wondering if you're arguing that the number of electrons, rather than the total, like number of electrons plus, uh, number of, uh, ions, presumably the total charge density, is that zero, or are you asserting that the, uh, charge density of the electrons is zero in that argument?

Great question. And it's my fault for putting a subscript e on rho to mean electronic instead of density. So I mean, it's the total charge density which has to be zero of electrons and ions. So e does not refer to electrons there. It refers to electric charge density. Okay. Yeah. So you got it right. That's the problem by combining various fields is that we don't have enough symbols for things. Right? We end up using the same symbol over and over again, and subscript it, and put primes on it, and then we look back at our notes years later and we think, what the hell was I doing? What is this quantity actually? Other questions? Yeah. Could you elaborate a bit on what you mean by evaluating the interactions in the co-moving frame but solving the equations in a different frame? Like, what do you, how do you distinguish those two?

Great question. Um, so in terms of, um, E&M, I guess I can go backwards with this one, right? Where do I apply Ohm's law? I apply Ohm's law in the co-moving frame of the fluid. Right? The idea is that moving along, if I'm in this co-moving frame, I often don't even have an idea that I'm moving. I mean, take all of us in this room. We are moving at a hell of a large velocity, aren't we? But it doesn't really seem like that to us. And so it's in this rest frame of this room that I would take the current and multiply it by sigma, or take the electric field, multiply it by sigma, and determine what the electric field should be. In the laboratory frame, I can solve the equations in the co-moving frame. There's no reason I have to go to the laboratory frame to solve those equations. On the other hand, the co-moving frame is a non-inertial frame. So I have in my fluid equations, acceleration terms have to sit in there. Those are the things that become the gamma, the Christoffel symbols in Einstein's formulation. So I would, I should work out Ohm's law in the co-moving frame, and then if I choose to work in the laboratory frame, which is often more useful because that's where my apparatus is set up, for instance, um, I need to make sure I have the right equations for the electric and magnetic fields in that frame, which I get from these frame transformations. Another example is the radiation field. In the co-moving frame, often an emitter will emit isotropically into space, okay? But in the laboratory frame, I'm moving, and therefore the emission is beamed in a certain direction. And so, in fact, in the laboratory frame, the emissivity of the plasma is not isotropic. It knows about the direction of motion of the fluid. And so here again is another example where I want to work out my interactions between the matter and the radiation in the co-moving frame, and then if I wish to solve the problem in the laboratory frame, use the Lorentz transformations to transform the intensity and all the other radiative quantities I want back into the lab frame. And mind you, I can pick any other frame I want to work with. If I have a spacecraft that's moving through the heliosphere, I may want to solve the equations in the frame of that spacecraft because that's where I'm making my measurement. Again, the Lorentz transformations are your key to go between any of your frames. And so it's essential to know how fields, intensities, um, velocities, temperatures, all those things transform. That helps. Yeah, that makes sense. Thank you.

Great. Everyone, uh, my name is Marlli. I come from University of California, Los Angeles, where I teach plasma physics. And a few of you have followed my courses in the past, so some of you might recognize some of the things that I'm going to say. See if this, I can get this thing to work or not. Okay, well, the clicker seems to work. Okay. So the playground for this week is going to be our heliosphere, and possibly other astrospheres. And I just want to remind you a few things. Is that when we look at the Sun and we think of the Sun, uh, we basically think of the star, and that star is what gives us life. And that is the 1.36 kilowatts per square meter on Earth which sustains us every day. And what, what we're going to discuss today is something that might sound completely irrelevant because really, everything that we're talking about comes from somewhere between two to five thousandths of a percent of the energy that sustains life on Earth. And so you might ask, why is this really important at all? And the point is that the magnetization means that even though the energy is so small, it can be focused, and it can be focused in very small intervals of time and space. And it also affects what happens from, from the outside. And so this cavity that is created by the magnetic activity of the Sun actually protects us from cosmic rays and allows things like life to exist. So solar magnetic activity plays a major role in any kind of endeavor in space, but also affects the possibility, the very possibility of life as well. This is like a general introduction, and this holds for all stars, um, that have planets around them.

So I was thinking that I would follow on on Tom's talk with a, with a kind of geographical historical tour. And I don't think I'm going to be able to get through everything at the end of this lecture, but since I'm going to continue tomorrow morning, and then in the afternoon, um, we'll be able to get into more details of things a little bit later on. So, um, I'll start with this, uh, kind of geographical historical tour with some stellar references, mention solar and stellar activity, then discuss, um, an elevator pitch as to what a plasma is, hopefully with some interesting things for you, and then some of the observational properties of the solar Corona and solar wind from both in situ and remote sensing explorations, coming all the way back from Mariner to Parker Solar Probe.

So let's start with Douglas Adams. Far out in the uncharted backwaters of the unfashionable end of the western spiral arm of the galaxy lies a small, unregarded yellow sun. That's us. And we are immersed in, sorry, I guess the pointer isn't working. That's okay. So we'll do without a pointer. So the Sun is immersed in a very complex interstellar medium. And in fact, this interstellar medium changes because the Sun is orbiting the galaxy. And so as time goes by, if we're interested in what happens over geological or longer time scales, um, the environment in which the Sun's magnetic activity occurs is going to be changing. As you can see, now we're at the edges of a, of a large dust cloud. We're at the edges of various supernova remnants coming together. And that medium is extremely complex and extremely interesting. In fact, from, from the, from a physics point of view, luckily, we don't care too much about the details of that unless we want to study them, because of the solar wind, that is the heliosphere, represented in the bubble in the third picture that you see there, which is a little bit of an outdated picture. Voyager One and Voyager Two, as you know, have crossed the termination shock of the heliosphere. But you see that there's a bow shock extending around the heliosphere in this picture, and we're not so sure that bow shock actually exists anymore because of complex physical processes occurring, um, such as mass loading and things like that. So, in fact, that first, um, bow shock is probably not even there.

So let's come back to the Sun again. Bird's eye view of the Sun. The Sun is a G2 subdwarf, as they like to call it. It's a convective star. Convection plays a major role in the Sun's magnetic activity. There's a radiative zone extending about two-thirds of the radius, then there's a convection zone. Radius of the Sun, um, 700,000 kilometers, more or less. Escape velocity, 600 kilometers per second. We're sitting at a nice distance of about 215 solar radii, 150 million kilometers. And the Sun differentially rotates, as observed by us, um, 26 and a quarter, seen from the Earth. It's about 24.9 in sidereal motion, so if you don't take into account the rotation of the Earth around the Sun. And about 29.8 at the pole. And of course, in the stellar astrophysics course, you would learn that at the photosphere, the pressure of the medium goes to zero, and that's it, the star ends. But of course, we know that's not the case. We see eclipses and we see material sitting out in the Sun, and that has to do with magnetic activity of the Sun.

So let me give you a brief, brief history. The reason I'm doing this is in part to show that, like in all fields in physics, controversy, polemics, um, are part of human nature. They are part of the basic progress of science, and it is what helps us to go forward. In fact, and so we should be mindful that none of the things that we actually know come easy. And, uh, most of the things we don't know. Um, another leitmotif, I think, of the lectures that I will give you is that we really know so little about, um, the interaction of matter and radiation. We think we know a lot, but we actually know very little. And so I encourage you all, never to take anything for granted, even in what I say, for example, as a teacher, because once you scratch the surface a little bit, you'll find new things. In any case, sunspots have been observed for a very long time before Christ in China. Then Fabricius, Johan, uh, first saw sunspots and provided an indication of solar rotation. I don't know if this is going to work or not. Let's see. I don't see it. Sorry. Try to go back here. I don't know how to get this thing to click. Okay, well, whatever. There's a movie there. So if you can click on that there, right? So solar rotation. But, um, a Jesuit priest, Christoph Scheiner, was actually the first one who did a systematic analysis of this. But he was a Jesuit, and so he didn't publish. Um, but he wrote letters anonymously because he saw spots on the Sun. The Sun was rotating. The Sun wasn't perfect anymore, you see. And he was a Jesuit, he couldn't very well publish that the Sun wasn't perfect. The Pope was going to be on his back. So he sent these letters to a German merchant, Marcus Welser, who happened to be also a member of an, a very important academy, like the National Academy of Sciences here, the Academia Lincei. And Welser said, well, who's this guy sending me this stuff about sunspots? I don't know what this is about. Let me talk to the token scientist that we have in our academy, one of the founders, actually, Galileo Galilei. And Galileo, a very important scientist, but not a very nice person, like many very important scientists, immediately turns around, immediately turns around and says, wait a minute, no, no, no, no, I've done all this already. And so he publishes the *Historia Solarum*, in which he shows about solar rotation in three letters responding to this anonymous publication that Welser had sent him. But nonetheless, poor Scheiner manages to publish in 1630, so 20 years later, his book. And what I'm showing you here is he did a lot of very detailed work, although he wasn't a scientist. So he had some very strange ideas about what sunspots were, but he actually measured the inclination of the Sun's rotation axis to the ecliptic, as you can see in this beautiful drawing here. And by the way, if you're interested in his book, you can find it on Abebooks for $145,000. If you are. So he realized that sunspots never occur at the poles, and they rotate more slowly at higher latitudes, and the inclination of the ecliptic, of course, a very important thing.

And then the history keeps going and starts to connect with other aspects. Um, Schwabe was looking for an inner planet and in fact understands that there's a 10-year periodicity in the appearance of sunspots, very similar to the way we need to understand solar oscillation so that we can tell planets around other stars, you know, when you're looking for planets around other stars, is really important. Then, of course, Carrington, um, and Hudson saw the white light flare, and there was this big auroral display a day and a half later. Carrington abandoned, of course, because he had to take over his dad's brewery, unfortunately no longer in existence. FitzGerald in 1892 asked himself, well, maybe, maybe the reason we had this beautiful display was that matter starting from the Sun with explosive velocities, great acceleration, several times solar gravitation, could reach the Earth in a couple of days. But William Thomson publishes his response on the same occasion. He's been turned into Lord Kelvin. And he says, well, wait a minute, no, I don't think so. And the reason is, he's, he does a calculation of magnetic induction. He thinks about the variability of the magnetic field and how much energy would be involved in trying to get that to work directly, and it doesn't work. And he's right, but he hadn't thought about particles, really. But that actually kind of stifled studies on the connection between the Sun and the Earth in the UK, um, for a number of years. So when you have a person of authority saying no, be mindful, you shouldn't obey. Um, Wolf sunspot number now is the longest record, a continuous record now held by the, is now the archive is now being held by the Belgian Royal Observatory. Then Spörer in 1816, um, the latter, the drift of sunspot, and the, the butterfly diagram. And here we have it in, in all its glory. And we know that the Sun has a cycle, an 11-year apparent cycle, a 22-year real cycle, um, known as the Hale cycle. And of course, magnetism is fundamental. And George Ellery Hale, who's a fundamental figure in the history of astrophysics in general, but also in solar, because you invented the spectroheliograph. Now, not only did he invent it, um, for use, um, uh, at Mount Wilson, he discovered sunspots. This showed that they were Zeeman effect, and therefore that they were, um, due to electric. He considered that they were due to electric vortices. That's not very far from the truth, in some sense. But he also, um, sent his spectrograph to Arcetri Observatory in Florence, mindful that Galileo had observed the Sun from Florence, and in fact helped solar physics, um, uh, be born again in Italy.

Now we know, of course, that, um, this is what a solar cycle looks like. A Hale cycle, a number of Hale cycles look like. And I've put a yellow bar at a latitude of about 55 degrees, and you can see that there's something strange going on up there. We have, you can see this is a longitudinally averaged magnetic field. We have the sunspots appearing with your opposite polarities, and then you see what's called the rush to the poles, which changes the whole polarity of the Sun, um, every 11 years. And so that just about every 22, we get a full reversal. And so that's the magnetic activity of the Sun. And then we can look at the solar Corona, and we can pick up the story again of the solar Corona. Already when you look at the solar Corona, there's something that anyone can intuit. There's something wrong going on. First of all, it changes appearance depending on when it occurs, and second, it's heavily structured. The Corona is incredibly structured. Okay? But the other thing is that it's bright out to very, very large distances. Now, back in the 1860s, when emission lines were observed in the solar Corona during an eclipse by Young, you didn't really recognize those emission lines and thought, just like helium, that he discovered a new element, which was called coronium. But in the '30s and '40s, Grotrian realized that these were actually prohibited lines from heavily ionized atoms, and therefore the Corona is at a temperature of above a million degrees. And that's, you know, the big mystery. Now, you didn't really need to go into those details to understand that there had to be a very high temperature, because just by looking at how the emission is. Now, this is cheating because these are photographs that are heavily contrast, heavily increased. But if you saw a naked eye or a binocular eclipse, you understand the same thing, namely that the scale height of the density, the white light is coming from, uh, density is incredibly high, and you can get an estimate of the temperature of the gas that's required to have a scale height which is at least one solar radius. So you can actually do a back-of-the-envelope. I encourage you to do it if you've never done it in your life, trying to show what happens if the scale height of the gas that I'm observing in the solar Corona is one solar radius. You have the mass of the Sun. You can ask yourself, what is the temperature that that medium has to have for that scale height to be so large?

Now, as a result of that, of course, Chapman and Cowling said, if this is the situation, that means that the Earth must be immersed in the static outer atmosphere of the Sun. We're sitting in that atmosphere. In fact, we are. The eclipse changes, and this provides evidence that whatever causes the Corona is probably related to magnetism, because you could have thought that the Corona exists all the time, and therefore it's non-magnetic. But the fact that it changes structure and now it's heavily ionized means that it can interact with magnetic fields. The only animal that can produce structure in a heavily ionized plasma is the magnetic field. And so the fact that it changes means that the magnetic field on the Sun is changing. We know that from the sunspots, and its effect on the Corona is seen here. Um, you see very, very fine rays down to the limit of resolution, these things here. Well, sorry, we'll have to find a better way for the pointer, but you can see what are called plumes, you can see helmet streamers, you can see what are called pseudo-streamers that we'll discuss, um, tomorrow, and so on. That's the Corona.

Now, we remember the white light flare seen by, by Carrington. We have, we observe the Sun now in many different wavelengths, and we know that solar flares go off, energy is up to 10 to the 32 ergs, large flares. These are images now seen in different, in different wavelengths, um, X-rays to extreme ultraviolet to, um, to essentially H-alpha and calcium. And the Sun is really a star among others. I said it's a G2 subdwarf, and I like to show this image because it gives you a nice, I, nice view of what other stars might end up doing. So on the top image, you see, see the Sun. Next to it, you see the brightest star that we have in the sky from Earth, which is Sirius. Sirius is hotter than the Sun, about 9,000 degrees, radius about twice as much, two solar masses. Then if you put Sirius as that little ball on the left in the second panel, and you go to start getting to red giant type stars, Proxima Centauri, Arcturus, Aldebaran, you have temperatures that are cooler than the surface of the Sun, radii that start becoming massively larger than the Sun, masses that stay in the same order of magnitude. But even Aldebaran, which is a huge star, is a, is a very microscopic object when you compare it to Antares, um, the, uh, heart of the Scorpion. And Antares means the rival of Mars in the sky because it's a red star, and 12, 12 solar masses, 883 solar radii. And then, of course, you get into the semi-regular stars like Betelgeuse that actually pulsate. Now, all of these stars can actually have planets around them and act, can be active. This is from Haisch's lecture, um, at this geophysics summer school in 2015, showing where activity tends to, um, tends to, tends to dominate. And you can see that it occurs in convective and fully convective rotating stars, which are to the right of those series of pineapples. And, um, essentially all of the stars that I just mentioned, um, have an activity, um, and the, the dynamo. So dynamos and convection, and you'll hear more about that. Um, if you really want to understand the heliosphere from Abino, you need to understand how the Sun generates its magnetic field as well.

Now, planets. The top, the left diagram is now showing you essentially, um, a survey of the, um, stars with exoplanets seen by Kepler. And the, you can see the dots, the blue dots are along the main sequence. This, you see the surface temperature on the bottom, on the bottom. So we're going towards redder stars towards the right. And the dashed line is the, the separate subgiants from the red giants. And you can see we have lots of red giants with planets around them. And in fact, if you, um, the, the green circle, um, shows stars that have planets actually in what's called the habitable zone, where liquid water can survive at the surface. So you can see that, uh, for the Sun, of course, we're sitting in the middle of it. But for red giants, you can have multi-million year, 500 million or so years of, um, habitable zones at greater distances. So that would be what happens in an older Sun. So this is just to connect the physics of our heliosphere to the potential happening on, around different stars.

Okay, this is going to be tough. Unfortunately, you get that right-hand movie to play. So, um, another symbol, or one of the main features of the solar Corona is actually the presence of gas that is colder than its surroundings, called prominences. Let me start by saying that probably most of what you guys think about prominences is wrong. Most of what I think about prominences is wrong. The reason is that there is a complete disconnect between the theoretical models of prominences and what they actually do. Um, on the left, you see what's called a coronal cloud prominence. It's probably a different animal altogether from the quiescent prominence that you see on the right-hand side. The animal on the left, and just for, for dramatization, you have the Earth there for comparison. That's a good way to give an elevator pitch to make people scared of what the Sun does. Is really a prominence that comes from solar flares that haven't really erupted completely. So material that's falling back on the Sun, it gets trapped for, in ways that have not really been fully understood yet. So that's called a coronal cloud prominence. The animal on the right is a real quiescent prominence. Um, and I don't, if you can run the movie again, or try to run it again. It should be looping, but for some reason it's not. Anyhow, um, what you can see is that there are flows all the time. And what you're seeing is a basically quasi two-dimensional structure standing on the Sun. This is not a flux rope. Okay? This is not a flux rope. It's a sheet standing on the Sun with flow along it. I'm not saying there isn't a flux, but it's not where the matter is. Okay? So don't be confused. Why am I talking about this? Because these things exist on other stars, and apparently in a much more dramatic way than on the Sun. They're already dramatic on the Sun. Normally, all of magnetic activity is associated with this type of thing. Um, the matter is really incidental to all of this. Um, the eruptions are a magnetic phenomenon, not a mass phenomenon. The mass is on, is there for the ride, so to speak, and it's thermodynamics. But other stars produce things that extend much higher out, almost to what we could consider the Alfvén point, which is something that I'm going to have to describe later, to places where gravitational confinement isn't really working very well anymore. And in fact, some sit and hover there, and then get emitted outwards, um, in what are called slingshot prominences. So again, this phenomenon occurs over completely different range of scales when you go to other stars.

This is an image, um, in, uh, uh, X-rays, um, extreme ultraviolet, of a filament, which is that same thing, that serpent, that kind of Chinese dragon that you were seeing when it's seen on the surface looks like this very narrow channel. But you'll notice that you see what look like jellyfish surrounding it in the Corona. Those are called coronal cells, and they were first identified by Neil Sheehy and others, and they correspond to something that's also seen in the chromosphere, lower down in H-alpha, that are called fibrils. Those things tell you what the magnetic field is doing at the surface of the Sun. So that even without being able to measure the magnetic field, um, I have to tell you that if you try to do Zeeman effect, right, on that filament channel, as it's called, that dark region, you're not going to measure a magnetic field because the magnetic field is horizontal there. So you're not going to see a magnetic field coming out of the Sun there. However, the direction of the field is given by those cells around that, which show you that the field is essentially parallel to the photosphere in those regions. So these are insights into what the, uh, prominence is do, and it's telling you that the Corona is undergoing a process of relaxation. In other words, what's happening above the solar photosphere is not just simply driven by the photosphere on its own. There's an ongoing coronal dynamics which is reorganizing itself in some sense to, to, um, to react to what the magnetic field and the changes in the photosphere are doing. The reason being that the Corona is such low density, the magnetic fields and those particles are so important that their time scales are much faster than the time scales in the photosphere. And so this process can keep going on. It's intrinsically related to the magnetic structure of the lower Corona, which is given by supergranulation. Those are cells that are typically between 20 and 30,000 kilometers in diameter, and which dictate the way in which, um, magnetic activity occurs, um, around sunspots. So we have this two, um, million degree gas, it's completely ionized.

Solar corona is a plasma, so most of you have taken plasma physics courses. But I figured I would give you, to start, a very quick class in plasma physics. So, first of all, plasmas are everywhere in the universe. Um, and we can define them as a system of charged particles interacting with electric and magnetic fields. Of course, there are also gravitational fields, as Tom was saying. But typically, a plasma is such low density that the gravitational field, or the gravitational scale height, is typically much larger than the gradient scales of the plasma and of the current, so it's not that important.

Now, as you can see there, the solar corona is sitting in there. But we have everything from aurora to fusion machines. And so, I would like to pick up our history again. We, we ended up in the 50s, but the 50s is when plasma physics is coming onto its own, mostly because of the discovery of the hydrogen bomb and the attempt to use fusion as a source of energy.

Now, a plasma is different for a couple of reasons. I think one of the most important things you need to remember in a plasma is that in a neutral gas, collisions increase as you increase the number of particles and with the speed that you move at. Suppose you're in a cinema and you're trying to get out at the end of the movie theater at the end of the movie, and you start running. Chances are you're going to collide more with people because the faster you go, the more collisions you make. As a result of that, you're going to slow down, and the people you bump into are going to accelerate a little bit. In other words, fast particles slow down, slow particles go faster. You can call that, you know, the basic way in which you go to thermodynamic equilibrium, or you can call it Robin Hood: you steal from the rich and give to the poor.

A plasma's different. In a plasma, faster particles see smaller obstacles and they collide less. The reason is that the collision occurs basically due to something like a Coulomb force, and the cross-section goes down with velocity. The faster you go, the smaller the obstacles, as though in your movie theater, the minute you start accelerating, people start becoming thinner, so you actually see a clearer path to get out. Now, if you imagine that you have some force acting on you as well, and you just got that head start, you're going a little bit faster, then now all of a sudden, you're not going to collide. So you get to go faster and faster and faster. The rich get richer, in other words, and a runaway effect is possible. Okay, so this is really important. This is one of the fundamental properties, anti-intuitive properties of plasmas.

The other, of course, is that the electromagnetic interactions are compensated. In a neutral gas, I mean, we're kept together by the residual of the residual of the residual of the electromagnetic force. That's what keeps us together. Um, but you know, we can cross a magnetic field, no problem. But if you're a charged particle, ah, not so easy. You have to rotate around that magnetic field. That's not the scale. Electron and a proton. I think the drawing is done correctly. So, proton is going around the field with a left hand, um, hand, and the electron with the right hand. Um, but there's of course a big difference in their radius that I had to exaggerate here. And so, at lowest order, the particles can't really move across the magnetic field.

Now, depending on whether the field is stronger in some sense that I don't want to quantify right now than the particles, it's going to be either the field dragging the particles with it, or the particles dragging the field. But to summarize: collisions decrease as temperature goes up. Faster particles collide less and can accelerate more. Charged particles lower must follow magnetic lines. Field lines to must follow charge particles. So, the self-consistent magnetic field provides structure and confinement. Then you put electric fields on that, and you can destabilize and accelerate. As I told you, if you go faster, you can gain energy. Result of that is that particles and fields are inextricably intertwined. And I like to ask people to repeat that 10 times fast, and maybe you get a feel of what it's like to be a plasma in a magnetic field if you repeat that phrase really quickly.

Now, because of what I just said, and because you can move freely along the magnetic field, well, it's easy to imagine that if you have an isotropic distribution and you put an electric field parallel to the magnetic field, you're going to get some kind of beam. Um, and so, going from what looks like a perfectly isotropic Maxwellian, you can imagine that you're going to develop anisotropies as well, things that, of course, in a fluid description, you won't see, but you would expect to see them in a natural plasma.

Of course, when the plasma was discovered, so let's backtrack a little bit. I was telling you about fusion. So, in the early 40s, Hannes Alfvén, only plasma physicist, received Nobel Prize, noted something that people hadn't really realized. People knew that electromagnetic waves in an ionized medium behave differently. There's a cutoff, there's a frequency. Marconi used that to show that you could reflect rays, sound waves, electromagnetic waves off the ionosphere in the early 20th century. But Alfvén said, wait a minute, there's a low-frequency wave too. And no one's really paid attention to that. But of course, Enrico Fermi did pay attention. And after he had a couple of discussions with Hannes Alfvén, he realized that Teller had been wrong. That cosmic rays were not all coming from the Sun. They must be everywhere. And he said, I even know how they get accelerated. It's Hannes Alfvén's fault. It's those magnetic perturbations that are all everywhere, and these particles are going knocking back and forth.

And this is the first page. I encourage you all to read that. Enrico Fermi was a master of clarity. Read any of his papers, you will understand them better than your physics professor. He, he was a master at explaining things. So, this paper, you can read it. You can read at the end, actually, you can actually read it at the end of high school without any trouble. So I encourage you to read this because it illustrates the Fermi mechanism of particle acceleration, of course. But as you can see, if you can read, you probably can't. He says, on the other hand, reacts on hydronics according to Alfvén and described saying, "line of force attached material density to the line of links of this." And he develops, um, the particle acceleration known with his name. And of course, he was right. Cosmic rays that had been discovered, of course, at the turn of the century.

So, let's get back to plasma confinement. So, there were a series of secret conferences held in the early 50s, trying to do fusion. And the Russians, on their own, the Americans, and the British, on their own, were trying to do that. Fermi himself did one of the first calculations of the instabilities that are associated with this thing. But the instabilities were so severe that Kurchatov ended up going to a series of public lectures. Everyone realized that trying to be secret wasn't really worthwhile because these instabilities were so intense that we weren't going to, we had to work together. And so, the space age is about to be born, remember 1957. And at the same time, although there's a Cold War, one of the, I think, most successful collaborations, international collaboration across a wall, occurs in physics of plasmas. And so, there's a huge burst of progress and of studies of magnetic field configurations. And there's a series of books and lectures, and people try to study magnetic configurations. And it's, I think, the Russians invented the tokamak, on the UK, the stellarator. There are many other protagonists that I haven't mentioned here, but people realize that there are instabilities involved. And in particular, one that we need to talk about, which is magnetic reconnection, of course, that you've all, that you've all heard of. And, uh, is really important for many, many reasons, because no matter where you are in a plasma, there are always, always regions where this thing happens. And this, and the result of magnetic reconnection is that you can get things like solar eruptions, and you can get very energetic phenomena occurring. And we'll get into the details of that, um, tomorrow.

So, let's get back to the space age. Um, I like to show this diagram because this is from an Italian outreach book from 1948. Okay? And it shows what we thought was happening between the Earth and the Moon in 1948. You can see that's we constructed V2. That's the one that was, you know, used in the Battle of Britain. You know, the Germans, that's the reason people were scared they were going to get an atomic weapon. They had the best missiles. It's the reason there was a race to capture von Braun at the end of World War II. Reconstructed, it was used for rocket flights, of course, balloons. And you can see the various regions that reflect various types of waves: stratosphere, troposphere, ionosphere. Various regions are defined by the wavelength of radiation of electromagnetic radiation that's reflected. And then you can see the temperature. And you see temperatures, um, first going down to minus 55. It starts going up again, 38, plus 100. Mark. And you see there, minus 273. It's absolute zero. So, there's no realization that there's actually a medium sitting out there which is hot.

But in the early 50s, who's also the Beerman of the Beerman battery? So, there's a nice overlap with Parker, who also developed, um, the first models of the dynamo. But Beerman, um, had realized that comet, looking at the comet tails, there's an ionized component that you can see very well on the right-hand picture. You can also see it in the left-hand, where there's going to actually be a disconnection going on. So, you can see that the one part actually curves away, following the radiation pressure modified orbit of the dust. But there's one that comes straight outwards from the Sun, blue on the, on the left, on the right-hand side. And he argued that that had to be ionized by something, by some.

Sorry, can you please use the mic? Recording. Thank you. Um, and, uh, and so he basically derived the fact that there had to be a medium there, moving it around between 400 and 500 kilometers per second.

Now, 1957, of course, the Soviets launch their first satellite, the Sputnik. And, um, immediately the New York Times goes into, um, defense mode, which means trying to convince people not to be scared. Of course, they were supposed to be scared. But the really interesting bit is that the Soviets themselves didn't realize what they had done. Pravda has nothing about the launch of Sputnik until the day after the New York Times publishes it. It's only then that they realize how important what they've done is. And, and, um, Korolev becomes a hero. But interestingly, the New York Times essentially lays out a program for exploring space weather. It's not going to be used for bombs or for spying. It's only going to be used to understand the nature of the Sun, cosmic radiation, solar radio interference, and static producing phenomena radiating from the North and South magnetic poles. And it's going to be of inestimable value for those who are working on the problem of sending missiles and eventually men into the vast reaches of the solar system. So here we have a program.

And of course, soon after that, Gene Parker, having discussed with Beerman in Chicago, working with Simpson, realizes that the 400-500 kilometers per second blows that Beerman's talking about wouldn't, couldn't be going through the static outer corona that Chapman had said, because it would be unstable. There's no way that couldn't happen. And he says, well, wait a minute, how does this work? And he suggests that in fact, the static solution is untenable. I had the chance to meet Gene for reasons that you'll, I'll talk about tomorrow, and become friends with him later in his life. That's a discussion that we had at the launch of Parker Solar Probe. And below that is a discussion at a Solar Orbiter meeting where Gene wanted to go to lunch every day. And after a while, I said, well, let's go with my PhD students so you can get to discuss with them some interesting problems. And in fact, Franco Rapetti, the student on the right, is working with me on coronal heating. And we convinced Parker that our numerical simulations were actually a simulation of the, what's called the Parker problem or the Parker nanoflare scenario. And so, and Parker was so enthusiastic about it that his final two scientific papers were written with Franco Rapetti.

Anyhow, what does Parker say? Well, he does that scale height calculation that I just was asking you to do. So I'm kind of giving it away here. So, you know, if you define the acceleration at the surface of the Sun, GS, normalize everything to solar radii, then you have DP by DR is minus 2MP blah blah. And you can write out what the pressure has to be. P of R is P0 e to the minus, and you have 1 over TR squared. Everything else are constants there, but in the integral of 1 over TR squared. Now, the interstellar medium is very little dense, and so Parker says that pressure has to be zero. But if I'm, I've got one over TR squared in there, and I've got a plasma, so one of the things that follows from those low collisions, and we'll talk about that tomorrow too, is that thermal conductivity has to increase like T to the 5/2, which means that the temperature decrease with distance from the Sun is very slow. R to the minus 2/7 is less than R to the minus 1. But R to the minus 1 changes that integral, the exponent one minus one. So if T goes slower than R to the minus one, then that pressure tends to a finite value at infinity. But if T goes faster than R to the minus one, it goes to zero at infinity. And so Parker says, since we know no general pressure at infinity which could balance the P infinity computed from equation, which is the one up there, we conclude that probably it is not possible for the solar corona, or indeed perhaps the atmosphere of any star, to be in complete hydrodynamic equilibrium to large distances. We expect always to find some continued outward hydrodynamic expansion of gas, independently of the evaporation. If you have a Maxwellian, you always have slow evaporation, Jeans' evaporation due to the tails of the distribution function. But this is talking about something different. We have a supersonic expansion. You guys think you know everything about this, but you don't.

So this is, um, the famous Laval nozzle. It's exactly how a supersonic jet engine works. In the same way, you have gravity conspires to create a flow that, if you consider to be stationary, has a constriction. That's the one over A DA by DR term. Gravity on the, is on the right-hand side. Um, and that on the left-hand side, you basically have the flow. And you see that this is an equation which has a regular singular point where U is equal to VT. And if U is equal to VT before the right-hand side vanishes, you get these weird solutions that are double-valued to the left of that diagram. On the other hand, if U becomes, if the right-hand side vanishes before U reaches VT, then you have these curves that go, go maximum and then decelerate. But if those two terms on the left and right vanish at exactly the same point, then you get the same critical solution, and you get this supersonic acceleration from low speeds to high speed. That's, or in circle in that diagram, and that's the Parker transonic solution.

Now, for a reason which escapes me periodically, every 10 years or so, people say, oh, how can the flow decide that that's the solution? You have to. Well, you have to remember that this is really a stationary solution that's starting from a time-dependent problem. There is nothing magic about this singularity. It's a time-dependent problem. There is a lot of magic in this equation, actually, but we'll discuss that tomorrow. Things are not as trivial. We know that the interstellar medium does have pressure. I showed you where the Sun is. It's sitting in the interstellar gas. There's a magnetic field, there's density, there's pressure there. So what's going on here? Does it have to be supersonic? In fact, a person asked that question, but we're going to address that another time. The reason we're going to address that another time is that it was beyond point, of course, in response to Sputnik, NASA was born, the Space Act. And one of the first things the Space Act did was create a committee to decide what kind of things we were going to do with satellites. And of course, Simpson decided one of the most important things was to do a solar probe to pass inside the orbit of Mercury to study the particles and fields of the city of the Sun, something that's happened now, essentially 60 years later, with Parker Solar Probe.

Then Korolev kept working. And you can see on the left, Luna 1, it missed the Moon. It was supposed to crash on the Moon, but it's hard to do gravity orbits, really hard. Put yourselves in the late 50s, no computers, only people, people computers. So they missed the Moon, but their detectors were on, and they saw something: solar wind. And of course, a Mariner moving between Venus and Earth observed that there was a continuous outflow. And that's Marty Shabow. And that's the press conference. She's there, second from the left, on the press conference. And you can see there's flow somewhere in the range between 350 and 750 kilometers per second. We're in the orbit, we're in the ecliptic plane. And you can see, though, that there's a variability. It's not constant. It's somewhere between 350 and, um, 750 kilometers per second. If you're really, you know, after the fact, sino as we say in Italian, we kind of see that maybe there's some oscillation there, right? Indeed, there is. We'll get to that in a second.

The solar corona, let's go back to it a second. If you look at it in different lines, you can see that the temperature is not homogeneous. So, in the Parker, Parker, we didn't talk about magnetic fields with the Parker solar wind because he just, his model is actually hydrodynamic. There's no magnetic field there at order zero. And there's some issues, though. As you can see here, in the solar corona, we see hotter and cooler regions. And, um, the green is 2 million, the red is 1 million. These are electron temperatures. And what you can see is that the poles of the Sun, where the field, the field appears to be open, if you consider those to be charged particles, and therefore mostly electrons, and therefore you're seeing essentially things that are attached to field lines, then you can say that maybe the field lines are open there. You can see that it's colder there, and it's warmer in the, what appears to be a more confined kind of solar atmosphere.

Now, in all of this, I haven't really mentioned how dynamic the corona actually is. We now have a Solar Orbiter, which is the first spacecraft to send a remote sensing instrument, oh, really far away from the Earth and moving. And so here you see, so the left-hand side is also moving with a very, very wide imager. You can see here that, um, that, well, you can kind of visualize, if this is a plasma, you can imagine that you're seeing things that are associated with field lines. Of course, you see active regions that are associated with sunspots. And you see that there's intermittency, there's, uh, brightness, there are little flares, there are smaller flares. In fact, flares come in all shapes and sizes. They're distributed according to power laws in energy, in duration, um, in total energy, in duration, and so on. And so, you know, this picture of a sort of a stationary solar wind is perhaps, you know, unreasonable to maintain. And we'll try to discuss that further tomorrow. But it's really important to notice that in addition to the Parker solar wind, there is this kind of continuous, dynamic, kind of eruptive, uh, phenomenology going on as well. You should really stare at these things for a long time because there's nothing that can substitute actually looking at things to to really try to figure out how things are working. It's not, anyway.

And that, of course, changes along that picture of the ultraviolet corona. Ultraviolet extra corona changes with the solar cycle. With a moment in the solar cycle, the corona appears to be much darker at solar minimum and appears to be much brighter at solar maximum. And correspondingly, you would imagine the solar corona and the solar wind to look different. Proof that, in fact, the corona is of magnetic origin, or at least the X-ray emission is. This is a very old paper from the group P.S. of Alex Poveda. And it shows the luminosity as a function of magnetic flux. There are more modern versions of this, but you can see that you can very, you can fit the luminosity with the magnetic flux on the star. It's a power law here. The exponent is about 1.14, depending on the data you use. And, you know, more modern observations, people end up finding things that vary between one and two. And so you now have an idea that the origin, the origin of the corona has to be magnetic in nature as well. And the source of that magnetic energy, has to be essentially, in the end, a Poynting flux.

How, how is the energy brought from below? It can't be thermodynamic. The solar, the photosphere is colder than the corona above it. There are exotic mechanisms where the plasma from being collisional or fluid-like in the photosphere becomes collisionless further up. So there are exotic waves, ways in which you can transfer energy along the thermal gradient if you have a system where the mean-free path changes dramatically over the same or shorter distance than a gravitational scale height. Okay? It's a non-trivial problem. But if you think of it just thermodynamically, from a classical mechanics point of view, you say, well, I can't bring heat from a cold body to a hot body. So I have to do some mechanical. So that mechanical energy is in the convection, mostly, and in the magnetic fields in the photosphere. So it's a Poynting flux. I use CGS, unfortunately, sorry guys. It's C, C over 4 pi E cross B. And then if you follow, in fact, in the com frame, the electric to, and then calculate how much Poynting flux crosses the photosphere, it's made up of two pieces essentially. Of course, there's always flows also. Um, but most of that stuff falls back down or develops into shock in the lower chromosphere. So the only way you can bring up the magnetic energy is two ways essentially. You can emerge magnetic flux with velocity field and bring fields that are parallel to the photosphere upwards, emerging a system. Or magnetic field that's threading the photosphere, you can wiggle it. And by wiggling it, you produce those waves that Alfvén was talking about. And those Alfvén waves of stairs.

Now, if you actually take a view of what's actually going on, and this is our, it shows you the kind of complexity that's involved in the physics of it. That's dedicated missions to observing what happens in the chromosphere and transition region because it's such a complex, thermodynamic. But it's, it's complex not only from the point of view it brings all those physics that we were talking about together in a way in which you cannot make approximations because this is a layer where, as I'm saying, the mean-free path and the, and the scale height start to become comparable. The magnetic field comes from being essentially non-dynamically important in most of the upper photosphere, except perhaps in the very intense flux tubes that are formed at the, in the, um, supergranular network, to becoming dominant just above and therefore expanding dramatically. And so it's a very complicated place. Um, but the, that's not where coronal heating, coronal heating happens above that. It's above what's called the canopy, where you see canopy domain, where the magnetic field is now becoming dominant. And so coronal heating has to occur there. It's not sufficient to heat the layers below that. That gives you chromosphere, but it doesn't give you corona.

Early ideas of what happens, um, to, if you add a Parker solar wind to a dipole, you've probably seen simulations of this. You do this all the time. There are some non-trivial aspects here as well. Well, you know, what happens? Um, you have the corona. The corona tries to push on the magnetic field, therefore it produces this, um, subsequently solar rotation then wraps that field into something like that. Now, two things. Left-hand picture. That left-hand picture is a snapshot. And people used to think that there was a solution of the MHD equations that was stationary, which produced that picture on the left. Turns out that's not true. There is no stationary solution of that type that you see on the left. That is a cartoon. It has to do with the fact that you, people, when you did numerical simulations a while ago, had huge resistivities. And most of the codes that you are using today, if you're not careful, also had huge resistivities. But that solution doesn't really exist because there's no such thing as ideal MHD, point one. Point two, the magnetic field gets rotated this way. You can see that the R changes, of course, the, it doesn't, um, really wrap. But unfortunately, rotation axis and magnetic axis are not aligned. And so not only is the loss of component complicated, but the region where the polarity inversion in the photosphere changes sign gets warped. And you get what's this picture of the warped heliospheric current, which is also a very extreme idealization. And I'm probably going to stop here for today because I think we're getting to the final. I don't want to much more, but I want to convince you that these are interesting idealizations that have been examined by spacecraft, typically quite far away from the Sun, 1 AU. Um, somewhat closer. The Helios spacecraft came in closer than 1 AU, of course. Voyager went further out. And so our knowledge of that structure is limited both in space and time. Generically speaking, we know that the solar wind neighboring that structure is typically slower than the typical solar wind. And also that that's that layer where there is a current, of course, because the magnetic field is reversing. And so there's a current which is wrapping around the Sun. Seems fairly stable. It doesn't seem to be doing anything very, very dramatic. Magnetic field actually rotates around. It doesn't really go through zero typically. And so, but as we move closer to the Sun, and we'll see, things tend to become more dramatic. I think I would probably want to pause here because, yeah, I, that's the, I want to go. Oops, that's going forward. Let me stop here. Um, and then tomorrow we'll continue with some of the basic properties of the plasma and what we see in the solar wind. Then you're going to have a lecture on magnetohydrodynamics. And then I'll pick up, um, with the real structure of the solar wind and where we are more or less, with focus on questions rather than answers, unfortunately. Thank you.

I'm going to, um, I'm going to recommend, so we're, we're into a Q&A period now. I'm going to recommend that you take two minutes and, uh, think about any questions you have, either for Tom or for, or for Marco. Um, and, uh, you'll also discuss things at the table if you want to, to maybe, uh, help you formulate your questions. And then, uh, and then we'll start going or start passing a little bit. Kind of questions are, are out there. Give it, you know, want to give people time to sort of process what they've heard. Yes. And if you have to use the facilities, do so. They're in the back and corner over there. And grab some water when you come back. Okay, who's got a question?

Can I ask about helmet streamers? Or are those coming later? Okay. Where, where do those come from? Because I, are those from like closed magnetic fields on the Sun that create slow solar wind? Or I just never understood that.

A helmet streamer normally has footpoints in regions of opposite, of opposite polarity on the Sun. So it stands to reason that there's a, the inner part, the lobe, the lobe part of the helmet streamer is basically confined plasma. The confinement isn't perfect, and therefore there's a loss of plasma upwards from that. And, um, and there's an accumulation of density. There's an extended heating. And so you get a denser, slower plasma moving out along the helmet streamer tip. But typically, it's not occurring in a stationary way. That's, that's, I think, the new, well, fairly, I mean, it's not there. Nothing is a poster, as usual, a posteriori, with hindsight, everything is easy, right? But the fact that it's not typically stable should have been, I think it was. The problem is that when you do numerical simulations, you see something, you tend to believe the simulation, even though theoretically maybe you think that it doesn't, doesn't sound right. And then I think people finally, when they started reaching the resolutions that are required to get a hint of what the real system might work like, you get this transition to an unstable behavior.

Yeah, so, uh, I have a question for Marco. Uh, you have mentioned that, uh, after World War II, there were lots of fusion experiments, fusion labs. So it might be a cation, but I heard that after World War II, lots of nations had radars and radio frequency generators, so they had donated to the scientists so that they had fusion experiments, and that's why the accelerators and the plasma physics has taken a boom from that. Is it development of things like synchrotrons and things like that occurred in that time?

Yeah, yeah, for sure. Very, yeah.

Um, yeah, two more questions for Marco. Number one, why the pineapples? We're all very curious. And the actual more question is, you mentioned about the heliosphere may not have a shock. If you would mind elaborating on why or why not, and what the mechanisms would be to alleviate the necessity for one.

So, so, okay, so we'll discuss that a little bit more in detail tomorrow. So the sun is moving supersonically in the interstellar, in the local interstellar medium, it's almost about 100 kilometers per second, so it's quite fast. But the presence or absence of this is a collision, essentially a collisionless shock. And so it's mediated by all sorts of dynamics that can occur. In particular, there is charge exchange between ions and neutrals. And so if you, if you add sufficient mass at the edge, you don't need the shock transition, essentially. You can slow down. Normally, if you try to slow down a flow from supersonic to subsonic continuously, it's unstable. And it's, there's kind of, if you think of it, it's not, it's fairly simple to understand the reason is that essentially, if you imagine perturbing, you have a flow that's decelerating through the sonic point, and you perturb in the vicinity of this place. What's going to happen? That any fluctuation that tries to propagate upwards into supersonic gets, it gets slammed back. So perturbations can only propagate away from that. And any propagation that's coming in will stick to it. And by sticking to it, the amplitude goes up, up, up until you develop a wall, essentially. So, so that super, that transition becomes a shock. And once you have a shock, it becomes stable because now the sound wave coming in, it'll, it'll just wiggle the shock a little bit, but the shock will be, be stable. Um, but there's a way to stabilize that by changing the way sound waves propagate. And mass loading is one of those ways.

Okay, with the pineapple, why pineapples? That's you gotta ask Tom that question because I, I just stole the slide from him. That's my 2015 lecture. Yeah. And maybe he'll say why. So I consider myself an amateur in that area. So there used to be, um, in the early 90s, a famous dividing line between the stars that emitted in X-rays and stars that have massive winds. And I think that dividing line has kind of disappeared. I'm not sure, but they now have, it's so slightly more complex, as usual, you know, more observations you get, the more complex it looks like. Um, but it's basically where those pineapples are.

Another quick question for Marco. Uh, I wanted to know what your take is on about the heating that's in the corona. So you mentioned about the chromosphere and the corona and things happening in the, uh, corona which could contribute to, uh, coronal heating. But, uh, could you tell me your take about, uh, how much the chromosphere you think is contributing to this as well?

That's a very charged question. Because, okay, maybe not in this room here, there's no, they're not, it's a friendly room, exactly. So, um, if we were at AGU, it'd be contentious. I think, uh, anyhow, sorry, B, that's school. Okay, so put this way. So it all has to do with this issue of collisionality disappearing, right? So scale height versus things. So you probably heard of type one spicules, and you may have heard of type two spicules. So the type two spicule is a more energetic spicule that tends to disappear into the corona. And so there are, there is a school of thought that lays all of coronal heating occurring in the upper chromosphere. Okay? There's another school of thought that says that that doesn't, that can't work, and that, um, you have to have some source of heating already further up, above the transition region, essentially. And, uh, this debate is slightly different than the DC versus AC debate that dominated coronal heating, I would say, in the 80s, where the question was, is it slow motions or fast motions? Is it waves or is it slow motions? Which is what the debate that Parker, um, and the nanoflare scenario came out of that debate, you know, quasi-static versus, uh, waves. So what's my take? I tend to believe that that coronal heating occurs above the transition region. The transition region is a response to the dynamic behavior of the heating above and chromospheric dynamics below. So it's always a dynamic thing. Um, I'm not, I, but I do, I do believe that the thermodynamics of the upper chromosphere needs to be really done properly because of this Knudsen number effect. It starts going up very quickly. So let me explain what I mean. Um, so imagine that you, so there is an energy source which is in a convection, right? Okay. If you're, if you're completely collisional, you have Maxwellian distribution functions, fine. But now you start getting some particles that are fast enough that they're starting to see a decrease of collisionality. Now suppose they start gaining a little bit of energy, so you form a tail. So you have a non-Maxwellian distribution with a small tail. As you move up, you're going against the gravitational potential. So that tail contributes more and more to your distribution function. So now you can actually transport energy along the thermal gradient. If you think of it, because the core of the Maxwellian is vanishing, because it's low speed, so it can't lift itself up, but the tail does. And so you start off with something which has a very minor tail, so it looks cold. If you do the second-order moment of the distribution, it's cold. But when you go upstairs, you're left with only the tail. So if you take the second-order moment, it's very hot. So that's called, that's called velocity filtration. Was first pointed out by Scott and Albert. And I think there's demonstrations that it's actually working. For example, in the, in the outer atmosphere of Io, people have actually measured this effect. And it may not be fundamental, but it could play a role in the upper chromosphere. I think.

Thank you. Uh, I had a question for Tom. Um, one of the assumptions that you mentioned underlying how we treat plasma in the heliosphere, uh, was that we had a flat Minkowski spacetime. I was wondering if there were places in our solar system, like maybe very close to the Sun or something, where that assumption no longer holds and noticeably changes the plasma dynamics to have a curved spacetime.

You'd have to have a lot of matter, um, in a small area. Um, of course, if you believe the modern, modern cosmology, there's a whole bunch of dark matter all over the place here that, uh, we're not interacting with. Um, so no, I don't believe we've found any particularly dense places within our solar system where we need to do that. However, for those of you that want to be engaging, there's certainly no issue with trying to put planets around more dense objects. Um, the idea of treating the, um, gravitational field as a form of waves and static background, you can apply the same sort of heliophysics to more exotic places like that as well. Um, and so there, in fact, you might have to worry about that curvature. But I think, as far as I know, we're pretty safe here. Um, there don't seem to be any real curves.

Thank you. I have a question for Marco related to the, the bow shock not existing in front of the heliopause. So you explained a bit that mass loading could balance the shock transition and we could not have a shock. But what sort of observations have pointed to that? And would you elaborate a bit more about mass loading and how it's balancing the transition?

We're going to discuss that tomorrow in more detail. But that's, yeah, but so, so it's, it's a question of particle acceleration. If you have a shock, you have an electric field associated with a shock, and so there's a consequent change in the spectrum you see. In, um, the Voyagers have measured things, and we have indirect measurements from IBEX about energetic neutral atoms. And there's no signature, there's no obvious signature of the, of the bow shock in front of the, um, interstellar medium to heliopause transition.

I, I haven't thought a lot about this, um, as someone who just, uh, uses data and analyzes it. But I was wondering if there's, um, a case where we need to consider a transformation between the co-moving frame and the laboratory frame for, uh, data that you would use from satellites or from a, a ground-based station looking up into the ionosphere.

Uh, yeah, that is done. People do take into account the distribution functions change between those two frames. Um, and so those motions are should be taken into account when doing those comparisons. Absolutely. It comes back to the old question of, if you run in the rain, do you get wetter than if you walk slowly? Right? I believe it is. Yeah. There's a famous saying that all people that work with data don't trust anything to do with data and believe all the theories they read. And all the theorists discount every theory they've ever seen and completely believe what the data say. So, uh, it's, once you work with it, you understand how sausage is made.

So I'll open up with a sort of a light question for Marco. I've noticed you've used, uh, uh, phrasing of upstairs and downstairs to refer to regions of the solar atmosphere. Is that common lingo in plasma physics area? Made me think of tensors. And Tom, I had a question regarding, I just lost it. Oh, no, here it is. So you were mentioning that the origin of the convective electric field term, with, how can we develop an intuition for the co-moving frame having the low to no electric field within it and associated because there's a low current density, those terms go to zero? You've pointed out then that term turns to minus V cross B, right?

The idea is that in the co-moving frame, if you have a lot of mobile electrons, then it's very hard to build any charge density because they will disperse very quickly on a plasma time scale. And some people are interested in that. But if you're looking at large-scale global MHD, likewise, in terms of the current density that you would see in the co-moving frame, it's proportional to the electric field. Um, and again, if those electrons are incredibly mobile, you get a lot of current for very little electric field. And so it's that idea that the electric field is probably very small down here. If you were to try to do MHD, um, in the first 100, you know, kilometers, it wouldn't work very well at all. And, and I think it's quite a fascinating system that probably Fars can say a lot more about how the MHD of the magnetosphere transitions into something which is not MHD down at this level, because of course, there are sensible electric fields that are set up, and lightning is what the planet's doing to balance those electric fields and get charge redistributed within the atmosphere.

So Tom, I wanted to turn your question back on you. Um, so I couldn't think of a good answer. You asking why, why the macroscopic description works so well. What would your answer be?

I don't know is the honest answer. I think that there are some key points around it that I try to make. The first is that, uh, if you conserve things that need to be conserved, you're really doing a very good job. If you're not conserving things that need to be conserved, you're going to end up way out in left field. Doesn't matter how good anything else you do is. Um, the second bit is that at least this this separation, there have to be these small places, um, where local thermodynamic equilibrium is being, um, possible. So, for instance, if I were to look inside a flare kernel, I wouldn't expect the fluid picture to do a very good job there, right? Because as Marco pointed out, those very high energy particles are not interacting with anything, they're ballistic. Um, and so you have to have this place where the system is able to sample the microstates and find itself in the most probable set of microstates. And and that's what's giving you the answer for how the global system works. So, uh, I must admit that it puzzles me. I don't, I don't have a good answer for it. I see some of the ingredients that must be involved in that process, but, um, I challenge all of you to think more about why that comes about. And then, in fact, it's, it's wonderful that it does come about, or we wouldn't be able to do the sort of work we do.

Any other questions?

I just wanted to comment on this issue of the, there, I think Hans Alfvén was one of the people that, that wouldn't have agreed that the fluid description works well, even though he invented the flux conservation theorem. He, he then disavowed it, put it that way. And, and so depending on what you mean by fluid theory, I think that if you, if you consider fluid theory to mean fluid behavior everywhere except in certain places that are always there, unfortunately, but you find the right places where they are, then I think it works pretty well. Um, but if you discount that, then I think you go wrong very, very quickly.

Parker once made a very provocative statement, and of course, he was teaching at the University of Chicago, and it was that you could actually treat anything as a fluid if you wanted to, even collisionless plasmas. The catch was you needed to know the equation of state. And that's something I've kind of glossed over in in my lecture is that what allows the fluid picture to work is that you've got to find a way to relate the pressure to other quantities that you're carrying, like the density and the temperature. And so you end up with very high-order moment closures. Right? People will go to the next moment and say, okay, I'm going to, I'm going to solve for the pressure tensor. I'm not even going to assume it's isotropic because in general, it's not going to be isotropic when those mean-free paths get large. And I'm going to truncate my system of equations with, um, the heat tensor. Right? Again, you have to always, the no-free lunch theorem says that at some point, you always have to figure out how to take a higher moment and relate it to lower moments in the problem. And so, so technically, yes, you can always treat anything you want in a fluid sense, but you better be damn good at figuring out what that equation of state is. And typically, that requires doing the mesoscopic calculation with the Boltzmann equation and the distribution functions to get that idea. In radiative transfer, it's called the method of variable Eddington factors. You go in and do some local radiative transfer to figure out what the relation is between the radiation pressure tensor and, and the mean intensity and the flux. Um, and you can kind of do that locally. So, uh, yeah.