Observations of Stellar Dynamos | Karel Schrijver

It's a school. We thought that this morning we'd have talks on dynamos—one on stellar dynamos and one on planetary dynamos. But unfortunately, as you will see from the schedule, Paul Charbonneau, who does dynamos also from the modeling side, couldn't be here until later in the week. So I'm going to stand in with an introduction that really focuses on the observational side of stellar dynamos. So that at least you'll have that information when we start listening to planetary dynamos and when we start talking tomorrow about stellar winds, stellar astrophysics fears, and the phenomena that happened inside them.

My name is Carl Shriver, and I am, by training, a stellar astrophysicist. I did my PhD on stellar magnetic activity—of activity of stars like the Sun. So this is still on my turf. I tried to stay in connection with this, but I've drifted into the direction of the Sun because that's really the only star that we can see anything in detail in. And even there, it's frustrating just how little we can see. What I'll do is take you through a series of observational constraints on how dynamos might work in stars, and I'll end with the statement that, well, theoretically, I don't think we really know it, but at least you'll have an idea of the ingredients. What does it take to make a dynamo tick, and what do they do in general on different types of stars and on stars of different ages and rotation periods, etc. Are divided. I'll show contains figures that you've seen yesterday in Rachel's presentation, so you're all very well prepared, therefore, with questions. So do feel free to interrupt and ask questions. Okay, because at some point I will be asking questions—you of YouTube first.

I thought I should define some terms. When we look at stars and we want to know something about their dynamos, we can't really send a magnetometer in and measure the magnetic field. Now, on the Sun, we use the fact that light traveling through magnetic fields in a plasma environment polarizes the light. So we can use the polarization signature by looking at individual elements of a particular polarity of the field. But on stars, we can't do that. All we see is the integrated polarization signal, and all these polarizations cancel except if there are very large patterns on the star that has one polarity dominate the signal for a while. So we can see something, or if the star spins fast enough that so that the Doppler effect actually separates the polarities for us. Julian here is nodding because that's what he does for a living. So if you want to know about the thing called zoom on Doppler imaging, talk to him.

But really, most of what we know about stellar dynamos comes from looking at the indirect signatures. The fact that there is a magnetic field in the step threading the stellar atmosphere causes the atmosphere to heat up above temperate air temperatures—above the surface temperature. The details of that heating is another story altogether, but it puts energy in, and it means that these different layers of the atmosphere give us different signatures to look at. Some of them we can look at from the ground because they happen to be sent out in the optical; some of them we have to go to space too because they occur in the UV, UV, and x-ray domain, and that doesn't come through the Earth's atmosphere.

So the three traditional domains in which we see activity—the four that we see activity directly—are listed here. The traditional ones that we keep talking about: photosphere, chromosphere, transition region, and corona. Formerly, they are defined—ought to be defined—by an astrophysicist in terms of how opaque the material is. The photosphere is the first point in the star that it becomes transparent to most of the light, so particularly the visible light. The chromosphere is mostly transparent, but it happens to be optically thick in some of the low ionization elements that sit around. So when we look at images of hydrogen-alpha, that's still neutral, or of what we call calcium II, which is singly ionized—just to confuse you—and the spectrum has one higher number than the ionization state, magnesium II, which is singly ionized magnesium, those we can see from the—that those are signals coming from what we call the chromosphere. At even higher temperatures, we find the corona—that's typically what we talked—to talk about when we talk about temperatures that are sort of a half a million degrees or above, where the bulk of the material is fully ionized and the bulk of the plasma is fully transparent except perhaps at some radio wavelengths if the field is strong enough. And then there's the thing that we call in-between—the transition region—which really isn't in between at all. All of these domains are threaded; they're there; there's no simple stratification. So they're threaded; they're stacked in our minds in terms of temperature, but don't make the mistake of thinking that they're actually layered. I'll show you some examples of that in just a moment. And there are some parameters that you can look at on this presentation on the web that show you just how enormous the contrasts are in terms of particle densities and temperatures and therefore general conditions between these various domains. But these are the typical domains that we look at: chromosphere in the near UV optical; the corona always in the extreme ultraviolet or x-rays; and the transition region, which is in the sort of the vacuum ultraviolet domain mostly.

When we look at the Sun, and this is a set of images sliced by NASA to show this peacock feather—they call it—of images, we can look at every wavelength separately, and in every wavelength we see a different incarnation of this activity. And if you go through material like this—plenty of this you can find on the web—you get the real feel for just, first, everything is dynamic; second, particularly when we're talking about heights that are the first tenth of a stellar radius above the surface, the chromosphere, the transition region, and the corona really are interspersed in that domain. They all move up and down; the different locations will have different thermal signatures at different times, but in the end all of it is driven by the magnetic field, and that's the one thing that we can't see. So we go for these indirect signatures, and then there's a stack of structures that emit that contribute to that signal.

Just to get the terminology right, somehow the dynamo process manages to dredge up strands of magnetic flux that breach through the solar surface and cause opposite polarity pairs to form. Whenever those concentrations are strong enough and extended enough, they can suppress convection. When they suppress convection, you create what's called a sunspot because you stop—you inhibit—part of the energy transport to the surface. Radiation keeps leaving, so the temperature has to drop—that's why they go dark around sunspots. There's much more field that sits around in that domain that forms these bipolar regions. Technically, the jargon is an active region is something that's large enough to contain a sunspot or to have contained a sunspot at some point in its life. But the solar magnetic field is much more structured than the Earth's magnetic field at the surface, although in depth years magnetic field, as Oh, so being will tell you in just a moment, will have as much structure as the solar magnetic field that we see. It basically, what we're doing when we look at the star, we see the diet—the top end of the Dynamo domain—that's why we see so much structure. So we see not only these large bipolar regions, but we also see that entire spectrum of smaller and smaller, all the way down to the very smallest elements that we can currently observe, which is only a few hundred kilometers out of a one and a half million kilometer diameter object. Those we call ephemeral regions because the smaller they are, the more affected they are by the convective motions within which they are caught. So they live for about a day before they're shredded to pieces or run into opposite polarities and disappear. They form that pepper-and-salt pattern. In between is well, these active regions, subject to diffusion—are subject to diffusion—this is not ohmic diffusion; it's random walk dispersal that dominates it—disperses the field around and therefore you get the field to decay and spread out in these patterns that we call enhanced Network. And eventually, all of that will fade. I'll show you some examples of how that works. We think this is how it works on stars too, except that you change the spectrum of the size distribution of what you put onto the surface; you change the frequencies; and then in some cases you change the latitude distributions of how you put it onto the surface.

For a star like the Sun, we know that there's this thing called the solar magnetic cycle—the sunspot cycle. It used to be called the sunspot cycle before we actually discovered that sunspots were magnetic concentrations. And you can see this is a visualization of what that looks like going through the cycle from maximum, which is dominated by these frequent large dipolar regions that are the sources of all major flares and most coronal mass ejections and the seat of all sunspots; and in the distance you see the cycle minimum, which is when you—all you have—is that pepper-and-salt field, and then the new cycle picks up and you see the pattern change. And you see, if you pay attention here, that the polarities on the opposite hemispheres are in opposite directions, and in opposite and successive cycles the polarities changed. That's why it's called the dynamo; it's an alternating field system with a period of about 11 years. When you summarize that into diagrams like this, this is an alternate form of the butterfly diagram. What they've done here basically is take—take a full sphere magnetic map and collapse all of its longitudes on top of each other. So all you're left with is the residual flux as a function of latitude, and you stack 'em one right next to the other over the years. You can see on the north and south hemispheres these butterfly wings going towards the equator. But the other important thing that you'll see is that there's a signal drifting to the pole, and that's because every active region has a slight tilt to it—statistically it has a tilt to it; they have all sorts of orientations, but statistically the polarity that's trailing—seen from the rotational direction of rotation—is a little bit further from the equator than the one that's leading in the direction sense. And if you think about what that does to diffusion, it means that the trailing polarity is a slightly larger chance of making it to the pole than the leading polarity, and that's what causes these polar caps to build up. And the polar caps are the seat of the Heliospheric field; most of them, for much of the solar cycle, particularly at cycle minimum phases—can I point with this thing?—yes. So that cycle minimum phases, when there isn't too much field at near these low latitudes, you see that the polar fields are strongest, and they're more or less in anti-phase. So polar fields and mid-latitude fields are coupled—in a day it must be coupled somehow in a dynamo model. What I'll get to in just a moment is that we're not sure whether the polar field is or isn't an actual part of the Dynamo, but I'll come back to that in just a moment. The other thing I want to point out here is that when you look at where the strong fields form, rarely do we see active regions form poleward of about 40 degrees in latitude. Just remember that for just a moment.

From now, one cycle is not the same as the next cycle; they're like our summer schools; every cycle is its own cycle. They modulate from cycle to cycle. This is an incarnation of the count that we have—the longest record—for the sunspot count: how many sunspots are there on the Sun at any one given time that we could spot? They were discovered, fortunately, just before the Sun went into that pause when the telescope was invented, and not too long after that they nearly vanished. Now, when someone describes to you the Maunder Minimum—that's what the state of largely absent sunspots is—they often will say there were no sunspots. This is incorrect; there was a Sun; there was a sunspot cycle going on; there just weren't very many of them. But then it resumed, and people will give names to the periods that we see in these diagrams; they'll say there's something like a ninety-year period, or that maybe a thirty-year period, or on a twenty-year period. Personally, I think we don't really know, given the observations that we have, any periodic—ROM will have some dominant periods—but there's no reason to think that they have any meaning yet because we don't know how this works, and we don't have a very long record. All we have is about 400 years of records, which is pretty good, but not very good for cycles that are hundreds of years or longer. This is the more usual incarnation of the sunspot diagram, which really counts sunspots. You'll see the same thing in the top end—now sunspots really above 40 degrees in latitude—and one cycle to the next the patterns change a lot.

No one way to look at Sun's activity cycles and stars would be, in principle, to look at the main signature that we've been looking at—the solar cycle—for, namely starspots. They do occur. If we look at the Sun and just look at the light coming off the Sun in the direction of the Earth over the years, we see a signature of a solar cycle. So we see that there is a—and something that mimics—in the total energy being sent into the direction of the Earth, a signature of the solar cycle. Now I'm being very careful as an astronomer here; I'm not saying the luminosity changes; we don't actually know whether the luminosity changes because the light doesn't come out isotropically, but in the direction that we're measuring it—towards the Earth—we see that signature. So here's a question for you: sunspots take light away, and yet the Sun is brighter when there are more sunspots on it. How does that work? The amount of energy being generated in the core probably doesn't really care about the sunspot cycle, and the amount of energy that you can store in the convective envelope is vast; the thermal timescale is hundreds of thousands of years. So if I blocked the Sun's light here and there by the sunspot, the amount of energy being generated or the amount of energy that sits in that—in the convective envelope—really doesn't care about that. So not really. I don't know that I have this—this is a magnetic view [Music] Well, I don't have a full picture of that now, but you should—that is—that is the key; that's what you should look at. If you look at a white light image of the Sun—of the solar disk—and you have an instrument that's sensitive enough, you see things other than just sunspots. Who said faculae early instead of actually a sunspot? If it's large enough—if the field concentration is large enough—extended enough and strong enough, it suppresses convective motions, and therefore, as I said, the light keeps leaking off; it goes dark. But if you make the concentration small, it still inhibits convection. So in the center the temperature goes down, and when the temperature goes down the stratification goes down; the material sums down. So there's a little depression in the atmosphere, but now what happened when I do this? There's these side walls, and the side walls actually are little leaks. So if the concentrations are small enough, these things are called faculae—hundreds of kilometers—extra light leaks out from deeper in the convective envelope, which is brighter than the surface, and you see these—not when you're looking straight down at them—but to the sides. So whenever you look at it at an white light image, you see the spots stand out very clearly at disc center, which is why you see these dips every time a spot crosses the central meridian. But the faculae, as they're called, leak extra light out. All of these smaller concentrations on the solar disk leak extra light out. So for the Sun, it gets brighter the more spots you put on it—averaged over a month—not instantaneously; you can still have these dips. For stars, if you go to very active stars, that balance changes; more field stays in star spots. So the active stars actually can get dimmer when there are more spots. So you have to be careful with this, but in order to measure this kind of cycle, you have to get people to give you telescope time and stare at it for the longest time with a really big telescope; that's not going to happen. So typically we look at signatures that have much more contrast, like in x-rays. The x-ray cycle that matches the cycle that I just showed you for the Sun is—depending on the wavelength band that you choose—and not looking at flares—of order a factor of ten to a hundred rather than a tenth of a percent. So it's much easier to spot. You think, unfortunately, getting time on telescopes—x-ray telescopes—for stars for a decade is even harder. So we have maybe one or two stars for which we have an indication that there is a cycle, and most easily you get telescope time on the most active stars, which don't really cycle. The Sun does, so we don't know about x-ray cycles on stars very well at all. We know most of it from the UV and the optical chromosphere and transition region diagnostics. So we learn about—yes, map—yes, you can; you can look at that cycle signatures in any wavelength, and getting light at time on any telescope is very hard. So getting decade-old cycles on stars has always been very difficult unless you have a dedicated telescope like my little son had for 40 years, and some automated small telescopes have nowadays around the world. I'll show you some examples of that in just a moment.

So we look at what we call direct signatures, but they're all photon signatures of the dynamos that are basically the signatures that I just talked about. You see line reversals that have to do with temperature inversions; you see the x-ray emission; you see the rotational modulation of the spots, etc. On the very longest term timescales, the fact that there is such a thing as magnetic activity causes magnetic braking. Rachel mentioned—there's a number—time—yet yesterday—that stars, as they age, they slow down. Why do they slow down? What's the magnetic brake that acts? They lose angular momentum; how—in the solar wind—matter streams out and takes angular momentum—that's one key ingredient. But if I can pick e—there's a second ingredient to this—if you—if you take material off the star, all you've taken—if you've done—is taken the angular momentum of that material off the star; that doesn't change the rotation rate of the rest of the star. There's a magnetic arm; you take it over an arm that's much longer than the radius of the star. So whenever matter leaves the star in a stellar wind, it takes angular momentum that's not just its own but a lot more by the torque applied through the magnetic field. So having a long arm—in many wind—in the solar wind and the stellar winds causes magnetic braking. There's my nuri star mergers. When you take enough angular momentum out of a star—a binary star emerges. Now why on earth would it do that—or why the universe would it do that—up to two active stars; both of them are losing angular momentum; both of them are slowing down. Why does that affect the binary star? Think of the Moon in the Earth—I owe coupling—that tightly coupled. So if you spin down the stars, you take energy out of these stars that somehow is now becoming to drain energy from the binary system. What does that do to the binary system? It speeds it up—not down—because it makes the orbit tighter and tighter and tighter. And as it gets tighter—some law of Kepler—the orbital velocity—angular velocity—will increase, but they'll still be tightly coupled. So a close tightly interacting binary over time increases its activity because it spins ever faster. A single star like the Sun loses angular momentum and spins ever slower and loses activity. That's one of the reasons why a binary stars—close binary stars—are as active as they are and can maintain that activity for as long as they do.

Astrospheres and winds—that's Brian—would Jeff Linsky will forego, and they'll talk about this tomorrow. So I'll pass on that. The summary of this is this: when we look at this—this diagram that astronomers make—I have to apologize at some point to Hertzsprung because I always forget whether there is or isn't a t in that—the Hertzsprung diagram—luminosity versus effective temperature—effectively shows here the colors of the stars. All of the stars that are—literally when you look at them—white, yellow, orange, red have something in common that makes them magnetically active. The bluish and blue stars are not magnetically active in the sense that solar-type stars are, and the reason for that is the internal structure—the partition at which we see stars be douche show.

Signatures like star spots and all of the activity structures that have to do with a sun-like dynamo occur at a transition point where there is a convective envelope that touches the surface. So any star that has a convective envelope that reaches all the way to the surface has a dynamo going. That means that any star that is about 1.2 solar masses or lighter, towards the cool side, the red side of the Hertzsprung-Russell diagram, has a dynamo running.

And does that mean that stars hotter don't have a dynamo running? We don't really know that much about them. They have a convective core like planets do, so it's fair to expect that there are dynamos running in them, but they have such a thick layer of insulating material above them—insulating in the sense that it is highly conductive—so it's very difficult for magnetic fields to get through, even on a stellar lifetime, that most of those hot stars don't have magnetic fields. Some of them have a large-scale dipolar field, AP stars; you can look at that in the literature, but none of them do things like sunspots, none of them do things like stellar cycles. So that's why the cool—that's why the name “cool stars” refers to the cool side of the Hertzsprung-Russell diagram—all of those stars have a convective envelope; all of those stars are like the Sun in some way.

So if I summarize that and take this HR diagram with all these measured stars in stellar positions in the HR diagram, I can draw this oval roughly where stellar magnetic activity occurs. Now I've intentionally not included the very highest part of those die—of those stars, although they are orange in red, and I just said all the orange and red stars have dynamos. So why did I—why would I have chosen to stop my little circle there? You have to know something about stellar structure here, instead, our evolution. Those are old stars; they've evolved and they've increased in size by factors of ten or a hundred or a thousand at the top end of that diagram. So what does that do to a star? Rotation is a key part of a dynamo; that's what I was just talking about about the binary stars. You spin up a star in a binary system; it gets ever more active. If you increase the size of a star, you're increasing its moment of inertia; with the same angular momentum, it's going to spin down; it won't rotate anymore, hardly at all. So of the stars that sit there, the only ones that are active are the ones that are still in tidally locked binaries, but the bulk of them are just actively dead, and as Rachel said, as uninteresting as the Sun would be if it didn't have its magnetic field, except if you're interested in winds, because—but that's an entirely different story.

Okay, what about Betelgeuse? Okay, I'll have to go look up Betelgeuse. Yes, there are. Okay, I'm going to go back to this. When I say dead, I mean they don't have a global dynamo cycling like that of the Sun, but anything that convects will sustain a dynamo, and I'll show you that in just a moment. Okay, what is—what is the—what is the luminosity of our Sun in solar luminosities? That one is easy. Okay, so somewhere along that line, and it is on the main sequence, so that's pretty easy to find. If you want to know, it's B-V is 0.67 or thereabouts, the color, so it's—it's—it should sit somewhere. This isn't right; this is—this diagram. 0.67 is there. Okay. Okay, I'll get to that in just a moment. Yes, the answer is yes; it is a slow rotator, and I'll show you that in just a moment.

If you want to see confusing diagrams that you probably can't read from the back, all this is meant to show you is that we can measure activity in all these different diagnostics, going from chromosphere to coronal, and we can show them as a function of the stellar properties. And if we look at main sequence stars only, we can show them as a function of their color, their B-V in color, or any other color index or effective temperature. What you want to do, at any color, you see this big range in values; that's the key point here. So what the structure of the star is not enough to determine the magnitude of its activity; the second ingredient is rotation.

Now when we make a rotation-activity diagram—this is one that Rachel showed yesterday—on the vertical actual axis, we basically put how bright is the Sun in X—the star in X-rays relative to the light coming out as a whole, which is basically saying you're creating a dimensionless number; you're comparing what comes out in activity versus what comes out overall from nuclear reactions in its core. So that's a fairly logical number to look at. The horizontal axis is the ratio of the rotation period over the—what's called the convective turnover period. Now convection, of course, occurs on all timescales, depending on where you look in the star. Typically what people mean is the deepest layer of convection, the largest convective scale; what is the timescale of its turnover? Now why is that important as an ingredient for dynamo? A rate of energy release, a dynamo action, generation of magnetic field occurs in anything that convects. What makes a sunspot dynamo, a solar global dynamo, is something that makes it global. Convection is random, except in one condition. What makes it non-random? The fact that the star rotates; it rotates. This puts these—what is the English term for this? Apparent forces, non-inertial system forces—Coriolis force shows up. The Coriolis force introduces a preferential direction into the convective motions, and the preferential direction is a pathway towards cascading upward in scale from the small random motions towards a large-scale pattern. So horizontally there's the—there was—B number, that scale number of how fast is the star rotating relative to its convective overturning in—in the deep parts of its convective envelope.

Now here's a question for you that relates to your question: Is the Sun a slow rotator? Why aren't there—why are there so few stars in that part of the diagram? Okay, this—there's three things that can happen here. First of all, there's two axes on this diagram; is there—is there a problem with either of these axes? The vertical one is how bright is it in X-rays? Well, X-rays are hard to measure, and if you put a star far away and make it faint, the X-rays are going to get absorbed in the interstellar medium, so you might lose stars in your sample that way. So you can only see as a volume-limited sample. Well, if we think about that and said, well, all we see near the Sun are fast rotators, so all the stars near the Sun are young, and the Sun is old, that doesn't make sense, does it? So I'm going to offer to you, it must be the other axis. What's wrong with the other axis, then? Rotation period over convection period. How do you measure the rotation period of a star? Star spots. So when you look at a star like the Sun or less active than the Sun, there are—li—any sunspots, star spots on them, and they rotate so slowly that the star spots evolve more quickly than the repeat period that you need to see the period, so you can't measure the period anymore. Fine. So well, we can measure Doppler signals; we can measure the line broadening. So why don't we do that? The Sun rotates at a speed about two kilometers a second; it's thermal line broadening is of order five or ten kilometers a second; you can't see the rotation anymore. So all that happens to, in that direction of the diagram, is we lose the signal; we just can't—we don't know where to put the stars. We can measure the vertical axis; we can't put them on the horizontal axis. So there's nothing wrong with the Sun; most stars in the solar neighborhood are in that area; we just can't put them on those diagrams.

This is another one you saw, which Rachel attributed to Andy Skumanich. This is an incarnation that Tom Ayres made, but it's the Skumanich law of slowing down over time. The young stars are in the first part of the diagram, and Andy was in the audience yesterday, and I thought it'd be nice to point him out today, but he isn't here today, but you may see him. This is saying something interesting, too, other than that stars slow down; there's this big range in young stars, and there's a small range towards older and slower stars. This is basically telling you dynamos are nonlinear, and angular momentum loss is a nonlinear process, so that rotation converges all of them to very nearly the same pattern. So all of the stars that are sun-like in age really rotate at about the solar rotation period, because that's the way that they've been put into that physics, except if they're in binaries, and maybe Rachel has an exception. It's in black and white because every diagram that Tom Ayres makes is in color, but that's probably not what you mean. Okay. Okay, you've got me. I'm looking at the axis; what am I supposed to see? Oh, you're off—my—it's still age; it's in units of tens of Giga—. Okay. Okay, I will fix this. I will take the actual diagram that a nice good man is putting some of his papers—

Okay, I'm going to go through this fairly quickly. You can look at this; this is essentially an experiment that is—it has more to do with what atmospheres do with dynamos than about dynamos proper. We can look—I said that all these different diagnostics in X-rays and UV and the optical, and we can put a UV signature versus an optical signature, or in this case an X-ray in the vertical axis versus a UV chromosphere—excitature—and all these stars that are in this diagram line up. There's some scatter; part of the scatter is because you never get these two measured at the same time, because you can't get time on these telescopes; part of it is probably intrinsic. The Sun actually sits somewhere near that line; I've intentionally offset it slightly, not because it is necessary, but because we use different passbands and different instruments, and actually calibrating the Sun under the stars isn't all that trivial, and it sort of moves along that diagram, again intentionally offset a little bit, but all of these stars line up. And what does that say? These—these are stars that are half a solar mass to one and a half solar masses; these are stars that are rotating with a period of half a day to well over a month; they're stars with surface gravities that differ by factors of a hundred. What a diagram like that means is that once a magnetic field puts atmospheric energy into the atmosphere, it's the atmosphere that determines how it's being distributed over these various temperatures, but the nice thing about this is if you measure in one wavelength how active a star is, you can translate it to some other diagram, so we can accumulate all that information onto each other—onto two diagrams—and these stars basically go through diagrams like this from the top right to the bottom left as they age; they get less and less active.

Okay, cycles are an interesting other phenomenon. We have records of some 40 years because Olin Wilson started observing at Mount Wilson; no relationship—I don't know why he chose to work there—but it's an interesting comparison, coincidence that they're all called Wilson. And he actually looked at stars for like 20-some years, and then other people looked at the same sample until funding discontinued, so now we have a discontinuity in these records, and we see that there are cycles in some stars, but—so some—like cyclic behavior is observed in only one in three cool stars. So the Sun is typical of its kind, but some of its kind don't cycle, and most of the active stars, more active and younger stars, don't show an obvious cycle. Now this means either they don't cycle, they're more chaotic, there are multiple cycles on the surface—who knows? We don't really know what happens there, but they don't have an obvious cyclic signature, so that's something for the dynamo theorists to—to explain to us.

Now when we combine that information and say what sets the period of the cycles that we do see, you get diagrams like this, and I'm not even going to explain it; you can ask Paul Charbonneau about it. People try to hunt for correlations; they say, well, what is the cycle period relative to the rotation period, or the cycle period relative to the convective period? Can we find some form of patterns? And they find patterns, and we don't really know what to hunt for because we don't know the governing parameters in all these processes. We know it's convection, and we know it's rotation, but there are many other things that depend on the stellar internal structure, and we don't really know what this really should look like. What sets this dynamo cycle period? Ask Paul. The other thing, in the Maunder Minimum state—now I'm coming back to the fact that dynamos generate field no matter what, even if they're not rotating—is something like this. The bottom diagram shows you that butterfly diagram at the—in the Maunder Minimum. People have gone through—in this case the records in the Paris Observatory in Meudon—where they didn't note whether there were sunspots, and yes, there were sunspots in the Maunder Minimum, but not very many, as you can tell. The bottom and top diagrams are very different in terms of number densities of sunspots, and they were predominantly, but not exclusively, in one hemisphere, but interestingly, there were still aurorae, and there were still modulations of the cosmic ray signature that suggests that was still a cyclic dynamo working, even though it wasn't really generating very many spots. We don't know how this works; we don't know if the Sun is heading this way with its weakening cycles; might be an interesting experiment to see, although it'd be kind of boring for anyone interested in space weather because all the space weather would basically vanish.

Hang on, cosmic ray modulations track dynamo activity. Why is that? You've heard part of the answer; you'll hear more of the answer tomorrow. Does anybody know? This chain: Shielding—cosmic rays come from outside the Sun; the Sun's magnetic activity shapes the heliosphere, and these particles have a harder or easier time of penetrating the heliosphere. So the cosmic rays that form carbon-14 in your body and carbon-14 in the biosphere and beryllium-10 and chlorine-37 and other things are found in ice sheets and in trees and in rocks, and we can reconstruct the cyclic activity over tens of thousands of years and the trends in cyclic activity over millions of years. So there's a great tool there. They test—the 11-year cycle just continued through the Maunder Minimum, so it's an interesting conundrum. Somehow it chose not to make sunspots and not to make too many flares, maybe because aurorae were there but scarce, but it still kept going anyway.

Okay, so what does that mean? Well, there was an interesting experiment that the Sun did for us in 2000—yes, ma'am—and someone at one point—at—did this that I think is not—what happens is that these part—these cosmic ray particles—there are ions; they're stuck to—gyrating around field lines, and they wander around the heliosheath; they got—the galaxy for millions of years, tens of millions of years if I remember my numbers correctly, and they wander around the galaxy because they're scattered whenever the magnetic field changes direction. So they're basically going in all sorts of directions, and they come to us from basically isotropically from any direction. Same thing happens in the heliosphere; whenever it finds a discontinuity, these particles scatter, and the more they scatter—it's a diffusive process—the less they diffuse, so they can't diffuse in as effectively if they scatter a lot. Now I've given you the pieces, so what's the final answer? Why is there fewer—where there are fewer cosmic rays coming down to Earth at times of cycle maximum? The field is more complex; the heliospheric field suffers from all these coronal mass ejections that are traveling through it, and they effectively form an additional complication, a lower diffusion coefficient of the galactic cosmic rays coming in. So as the field simplifies—the words—cycle minimum—it's easier for the field to come in, and then—and then if you really want to know the difference, there's actually the sensitivity of the—of the direction of the field—of the galactic cosmic rays; they have a preponderance of positive charge because it's the ions coming in; it's going to depend on the direction of the field, and you can think about drifts and all that; there are in fact asymmetries in the galactic cosmic rays penetrating depending on the sign of the cycle. You can read about that, I think, in volume three of the series.

Back to this here, some experimenting—experiment for us in 2008 and 2009; it said, "I'm not going to make any sunspots anymore for a while." In fact, it made no sunspots for longer than we had seen in a century from before we knew sunspots were even magnetic, so this was a pretty rare experiment, certainly with all the instruments pointing at the Sun now. There have been a question about, well, where does all that pepper-and-salt field come from? Is that just a decay product? Is that just the act of regions being spread out more and more and being torn up into the overall convective motion? And I think experiments like this were kind of interesting because it suggested the opposite. When we looked at that mixed field, in fact, some people—maybe some of you—will be as dedicated—had been looking at the same Sun—that's not the same person—it's a little harder for 40 years with the same telescope and the same instrument, just about every single day at something near disc center and measuring a signal—we're Livingstone—adenosyl—get that—and basically what he did—and the top end—what you'll see is he measured the total calcium H and K brightness, so the chromosphere and brightness of the Sun over these cycles, over 37-some years, same instrument, same person, same observatory, going up and down, showing the solar cycle, and then he pointed that instrument with a small window at the quietest patch he could find near disc center; that's the bottom set of points, the green line going through it, and it's just flat. So although active regions dispersed over the entire Sun and a timescale of less than a year or so before they really spread out or a few years before they cover most of the surface, those spot—there were areas near disc center—stay just flat. So to me this means that pepper-and-salt field is generated just by the fact that this convective motion is going on; it's a locally operating dynamo; it doesn't care about the big sunspots, and it doesn't care about the rotation. So when we talk about dynamos and stars, probably all stars, even the oldest, have at least that mixed field, that ever-present field going on, including the stars that very nearly have stopped rotating, the very largest of the stars.

Now if you go to a star like Betelgeuse, which happens to be a really big star, it has a really big, low surface gravity, so it has humongous containers—convection cells—on its surface, like a handful, two hands, four—I think is the formal estimate—sort of ten convection cells instead of the hundreds of thousands of convection cells that we see at the surface of the Sun. So if you put a pepper-and-salt field on top of that, it's easy to even begin to expect you might actually see sometimes a preponderance of one polarity over the other, just because statistical averaging over ten cells doesn't work nearly as effectively as statistical averaging over tens of thousands of cells. I'm going to have to start wrapping up. So in terms of dynamo ingredients, you now know the ingredients: What you need is essentially at least convection and—and kind of rotation strengthens the action and turns local action into a global pattern, and that's because the most basic recipe for a dynamo is stretch, turn, fold, ideally in a preferential direction, and that's how you get a dynamo in a star; that's how you—here in just a moment—get a dynamo to work in a planet. This is something you can stare at; I'm going to skip over it. The patterns—we don't really know much about patterns, except that if we look at the most active stars, they do something fundamentally different from what the Sun does. Some of these active stars can have sunspot groups—starspot groups—at their poles. Remember, the Sun doesn't do anything over 40 degrees in latitude; they somehow manage to do it at their poles. Some people do this with Zeeman-Doppler imaging—Dr. Julian Kŏrmendi, because he does this—with one of the very earliest experts in the field—and we can sometimes measure these polarization signals because the polarization is—I'm not going to get into this—but it's—it's a combination of large patterns and Doppler effects of a rotating star that you can actually measure, even an idea of the vector magnetic field, at least at these poles, and they have large bipolar or multipolar areas that are at their poles. How a dynamo does this is unclear. Last question—I'm going to ask.

You you saw this one - I told you binary stars. Tightly interacting binary stars spin up as they age; they get more and more active, so they get more activity and also more polar spots. So you can make diagrams like this for Sigma probe, or is one of the stars I happen to write part of my thesis on, so I know that one too. Are they magnetically coupled? Why are they magnetically coupled? You're saying yes, so why are they magnetically coupled? What what is the one condition under which you can not have these fields interact magnetically with each other? Signals have to propagate from one star to the other. There is a case in which you can stop signal, magnetic signals propagating from one star to another; it's called the stellar wind. If you blow a wind out faster than the Alfvén speed, the signal can't get there any more. So if the wind of a binary star can be accelerated fast enough that the field of its companion lies outside itself in radius, they would be effectively magnetically uncoupled.

Now for Sigma Corona borealis, that's not the case; they're really close together. But if you pull them apart to something like 10 or 20 stellar radii, you might have a case where close binary stars are still gravitationally tightly coupled, but not necessarily magnetically anymore. But that's for others to consider; that's a nice case. Complications. The bottom line of my talk really is the bottom line of Mr. Slide: we have this long list above it of all the ingredients we know we go into a dynamo. Rotation and convection are above two; we don't really know if field coming to the surface is a part of the dynamo. We don't know if at the Sun we're looking at an essential ingredient of the dynamo, or if we look at these polar fields, or whether it's just a leak. And if any of it wouldn't leak is effectively what the same thing happened. This could happen if you look at ever cooler stars where the photosphere has become no more conducting and we get very dusty, and you can do something completely different to the fields. We don't really know if overshoot into the bottom beyond the bottom of the convective envelope is an essential ingredient; it's not an essentially green for dynamos because fully convective stars are but half dynamos, but it may change the mode in which the dynamo operates. We don't really know if what sets differential rotation as in yes we do: Reynolds stresses on convective motions in a turbulent medium, but we can't really parameterize it very well ab initio, so we can't know really. We're getting closer with with models what is the rate of differential rotation on the surface or in the interior of the star, so we can't really measure that that well either.

So all these parts are ingredients of the dynamo, and all of them come together, and there's a beautiful set of models that you'll run I think it is on Monday when Paul Charbonneau comes. And I'm gonna leave you with that's what we think happens in the Sun. Okay, thank you. [Applause] Questions? I was too difficult or was it that easy? Okay. Yes. Yes. If you pull them apart far enough, you'll get to be the state of them being magnetically isolated; the stick. It's the ones intermediate to it would be very interesting. The reason I brought this up from a dynamo perspective is these stars, these coupled binaries, close binaries or nearly merged binaries are active, but in fact they're more active than they should be given their rotation period. So it's it's not just that they spun up; there's something about the interaction between the two that makes their activity level even bigger than just the fact that they rotate. So they're an interesting dynamo experiment to do. The you're saying that some observations suggest that stars with close in, particularly the large planets that we can see there, have activity levels that are larger than they should be given their rotation period, and that's a very interesting thing to look at. It it seems to go in the same way whenever you offer some way to break symmetries to convection, you might increase activity. Tidal coupling does it, rotation does it, maybe the presence of a companion, even of planetary size, does something like that; there's a lot of exploratory space to do. Yes, active longitudes is something that people have looked at on the Sun; it doesn't seem to have it, not very pronounced and certainly not very long-lived. But stars, not only stars with planetary companions, but all very actives, many very active stars have persistent latitudes of preferred Sun star sport activity. That's well, it's been well known for binary systems, and it's now beginning to be known for planetary systems. First, we don't know; we haven't known about exoplanets for very long, so there's a lot of research to be done there. Somebody's gonna stop me. Shall we take 10 minutes? Yes, 10 minutes, and then Sabine is going to talk about dynamos and planets. Is it or is it this afternoon? I'm sorry, no, it's right after. Right. What is my schedule?