Transcription
Doctor, I'm not a professor, okay? Can you hear me? So I'm going to have a pretty much follow-up talk on Brian and Jeff's, and also on Rachel's talk from yesterday. I'm going to talk about the evolution of the stellar Astros fears in time and what Ryan and Jeff covered—what happens outside and in the boundary. I will discuss the changes from the star to the edge of the stellar system and how they—what's their impact on their different things.
The outline is essentially: I will start with just discussing the the what's—what's dominating the or controlling the structure of the Astros fear and how it—what—what are the parameters that change it in time. Then I'm going to discuss something that also was mentioned: cosmic rays—the transport of cosmic rays in particle—a high energetic particles in general in the solar system and the impact of the changes in the Astro sphere on the transport. I'll briefly discuss the effect of these changes on the evolution—disk evolution—when in early sort stellar systems—were the star system still evolving. So this will be the first part.
The second part will be focused on coronal mass ejections and how changes in time effect cone mass ejections. I will discuss the changes in the initiation, the propagation, and the evolution of CMEs with time—two different Astro spheres. Then I'm going to discuss or extend the effect of CMEs or the role of CMEs in stellar mass loss rates instead of spin down. Finally, I'll discuss coronal mass ejections and exoplanets.
The relevant chapters from the books are shown here. There are some parts of other chapters that are relevant because it's all plasma physics and space physics. So there are many things that are own other chapters, but these charts are really discussed—the topics I will talk about in the context of the solar system.
One thing I would like to—this is two comments actually. I may just transfer between stellar terminology to solar terminology—meaning solar wind versus stellar wind—usually I will mean the same thing. So if I transition between them, it's just a matter of the fact that I don't pay attention too much. And the other thing I would like to mention is that a lot of the stuff I will discuss here is ongoing research. We don't know much—these are kind of suggestions what will happen, but we don't know much about many of the things I will discuss about. So it's really cutting-edge research that is just starting. And because it's essentially an implementation of space physics and solar physics—astrophysics, we have very few observations—like Brian's—or Prime's observations that we can even constrain or the framework we work in. So this is an important comment to make.
So Astro stressing time—I won't spend a lot of time with that—already know that stars as they evolve, they move along the H-R diagram. They become less active—especially solar analogues. They're very active—they have fast rotation when they're young—have high stellar activity—and as they go—they grow older—they spin down and they lose some of their activity level. They become more quiet stars. And we have the—the M dwarf branch here, which are more active than the Sun, and we have the Giants, of course, which are—we can assume that these are different types of star—B stars—because they don't have the same kind of type of stellar winds and they don't have the same type of stellar corona.
So the focus of my talk is on solar analogues. Again, I would argue that we can—yeah, okay—hey, I would define the solar analog in this context as stars with hot Corona and thermally driven wind in general. So these are solar analogues as far as I'm concerned—where this scene is this plot that showed that there is a relation between the rotation of the star and the age and also the star activity here on the right—this is a function of the Rossby number, which is a representation of the stellar rotation. So in general, we have related—we do know—but with stellar relationship between the rotation, the age, the stellar activity, and magnetic fields.
Now if we think about the Sun and the solar wind, we have the solar magnetic field, which you can assume it's to first order that it's a dipole, and then we have the radially expanding solar wind that stretches the field—the magnetic field with it—because this is a plasma and we assume it's a—it's a—it's a pure MHD plasma, so the conductivity is infinite—infinite. So the field is frozen to the plasma because any—any motion—any changes in the magnetic fields that the plasma will do—the field will adapt really, really quickly. So if we change the—the plasma around a magnetic field, it will—we can imagine that the field is glued to this magnetic field. So the stellar wind stretches the magnetic field out with it, and eventually it opens up in a point where the wind velocity equals the local Alfvén speed. So we have this configuration of this stretched and eventually open field lines in the radial direction.
And if we look at the solar system from the top, the combination of this radial propagation with the solar rotation—because these field lines are anchored to the Sun on one end—gives us a spiral configuration. And you can imagine that this hand is the Sun and it is rotating like that and that if there is a parcel of plasma that leaves the Sun in the radial direction, but the Sun continues to move—so in the frame—frame of reference rotating with the Sun—this field line will be stretched this way. So that's what we have here. We have this Parker spiral—it's similar to a spring—rotating sprinkler. So we can write down the equation that describes this—this Parker spiral. If we assume that in the frame of reference rotating with the Sun at some point the field is open and it's fully radial, so we can equate the two components of the fact that there's a motor component and the radial component of the magnetic field with the same components of the velocity. Here we assume that there is no theta component, and this ratio that the radial speed of the stellar wind is simply the stellar wind velocity, and in the azimuthal direction is simply the—the solar rotation times the location in the radial direction, and we have the sine theta because this component goes to zero as we could get closer to the pole. We can assume that this is one and we're talking about the equator for the rest of the talk, but I will keep this sine theta there anyway. So we can re-manipulate the equation and get the equation for the magnetic field, and we—if we take the divergence of the magnetic field equals to zero, we get this equation for the structure of the magnetic field line in the hemisphere. And this is the—the Parker magnetic field is based on this Parker's spiral topology of the magnetic field of the—of the in the heliosphere.
One thing to note is that we have an R component that goes like 1 over R square—well, we have this extra R here in the Phi component, so the Phi component drops like 1 over R—so it works slowly. So as we go further out in the solar system, the—the azimuthal component of the magnetic field become to be more and more dominated, and at the Earth it's about 45 degrees, and by the time we reach Jupiter it's already essentially fully azimuthal field. So let's—one thing to note is that there are several parameters here that will determine the particular magnetic feeling. We have this Bs—and Bs is the magnitude—so let's start—we have Rs—the Rs is the point where we assume the field line is radial. You can think about this—this distance as the often point where the velocity of the slow in equals the Alfvén speed—so the field line is open. You can also think about this R—R naught as the point where the wind is fully developed and is not accelerated anymore—it has achieved its asymptotic speed at that point. And Bs is the magnitude of the magnetic field at that point—Rs—R naught. So where these two parameters here—we have the stellar rotation which can change for other stars, and we have the solar wind velocity which can change as well. So let's discuss how the different parameters may affect—there is the Astro sphere—our switch to Astro sphere—which is like the heliosphere but for other stars—and see how these parameters change with time and for large distances. I eliminated this R minus R naught here and left with only R because R is much greater than R naught.
So how does their stellar rotation affect this structure? We know that young stars rotate much slower—much faster than the current Sun. The current Sun has a rotational period of about 26 to 27 days. Young active stars can have rotation periods of to one-half a day—rotation—they rotate really fast. So let's see how this—the—the field line structure in the heliosphere changes for fast rotations. Here on the right, I show a simulation of a dipole magnetic field with stellar wind, and here the rotation rate period is 25 days—solar-like—and you can see that overall the field lines are simply radial—at the domain size is about 24 stellar radii—the radius of that particular star—which in that case was Sun or the solar size. If we boosted the—we repeat the same simulation, but we simply boost the rotation period of—of the star to half a day rotation—there are stars that rotate with that fast—you can see that even within the corona, they azimuthal component—a component of the field completely dominates the corona. We have this raft field all over, and there's—there—there are many consequences for that structure, and I will discuss it in the next few slides. And here I just did a solution for a Parker—for a spiral where I changed the rotation period from 18 days—no, sorry—25 days for the blue line—it was 10 days for the yellow and 4 days for the—for the red. And again, you can see that the tangling of the field lines is much—increases that we increase the rotation—and of course for the extreme case of half a day rotation, you can see that it's completely dominates the core now. So the rotation—the change in the rotation periods have a clear—is a clear effect on the structure of the health field.
Another thing I would like to mention is that if they're wrapping—or increasing the wrapping of the azimuthal field line—this will increase the overall magnitude of the magnetic field because we compress all the field lines together. So you—you boost the—the magnitude of the field line of the Astros pheric magnetic field everywhere just by increasing this rotation. Let's now discuss how the changes in this B—the source B magnitude—changes with time and with stellar evolution. Keep in mind that that equation describes a single field line, so of course we have a collection of magnetic field lines in the Sun, and each one of them may have this different value of B—and indeed if we look at the magnetograms during solar minimum—so maximum—during solar minimum—you can have this dipolar structure of the solar magnetic field. These are measurements of the radial magnetic field at the surface of the Earth—at the photosphere—from the Wilcox Solar Observatory. You can see the dipolar shape during solar minimum, and your solar maximum you can see it's—it's not dipolar anymore—it's tilted and it has many different things. You can imagine that if we collect each field line here and here, the overall structure of the heliosphere will be very, very different. And indeed we have many, many observations that infer that indeed the solar wind structure essentially follows the structure of this magnetic field at the surface of the Sun.
Now, in addition, we also have a dependence of the solar wind speed on this—this value. So not only we have a specific value for Bs and each point, we also have a different value for U—for the solar wind speed. So that has another effect on the structure of the particular field line for each and every given point in the solar corona because it will be different from one another. Yes, of course, and we really—I will show it—yeah, but of course it—because there's a motor component becomes very dominant all the way almost to the surface—yeah—yes—yes. The comment was that this is not really the radial field on the surface, but it's a—it's a—it's a representation of that based on that particular measure. And this—this kind of measurements that we use to drive the global models for the solar—in stellar Coronas—well, usually this is the input or one of the inputs.
Now, in the next few slides, I will discuss—if—in the context of stellar evolution—how to change—you know—what's the effect of the change in rotation period or rate—and I want discuss changes—a short—relatively short period changes in the magnetic field—like the solar cycle. I will discuss more how the overall structure of the magnetic field we observe in different stellar types will affect the distribution of the structure of the heliosphere—for Astro sphere. As we just mentioned—young active stars—you know—their first rotating and they have their magnetic activity concentrated at high latitude—and that was shown by Carl yesterday. And here I'll show two examples. We have a B star—it's a young solar analog with a rotation period of half a day—just like I showed—and this is the Zeeman Doppler imaging map that was mentioned here—taken by Getty Hussain—that shows the radial component of the magnetic field of that star. The Zeeman Doppler imaging method essentially combines Doppler imaging that tells us where there are darker spots or darker regions with Zeeman measurements of the magnetic field or the Stokes components that—of the polarization. And from that we can reconstruct tentative low-resolution maps of the magnetic field of—of stars. It can—it can be done mostly for fast-rotating stars that we can see these features coming back many times within the time of the observation was taken. And you can see that the red and blue cause representative opposite polarity, but you can see that the high concentrations are located at around 50 or 60 degrees from the equator. On the Sun, we usually see the active regions—not more—not higher than 30 or 40 degrees in latitude. So—and we see it also in other stars that the—the—the magnetic activity seems to be concentrated at high latitudes from the equator. So again, it's a combination—structure of the radial component of the photospheric field—which is again tricky—again—they combined the Doppler measurements that give you where regions of darker and brighter areas—and then on top of that they take measurements—and that gives them—they measure the Stokes components—which is the polarization of the light that goes through a magnetic field. In principle, you should measure six components—they measure two—or they have certain two components—and actually this is the reason why there's a lot of criticism about this method—or there's a lot of uncertainty—but we use it just to get a general idea about the structure. And the combination of these two measurements enables them to reconstruct these kind of maps—and of course it's very low resolution because you're trying to resolve a point source—but with that respect they claim to have enough resolution to do this kind of match. Yes. So the question is—is there another way to obtain the magnetic field—essentially—and the answer is—it's extremely hard to measure magnetic fields in—in other stars because they are so far—the signal is so weak, etc.—there are some attempts to measure the—the—the dipole components using radio measurements—with this method you need to have very strong fields and fast rotation—so you can even distinct a signal from whatever you have—so it's very, very hard. And as I mentioned, there's a lot of uncertainties, but what you can do is you can clearly see that you have more stuff—it's certain latitudes then in the other. Alright, and I don't know if you notice this goes all the way to minus 30 degrees, and this is because we don't—the inclination—so we don't see the other part of the star, but there is a clear distinction between this part which is pretty much blank to the high latitude here that is full of supposedly strong magnetic fields—and we—we see this kind of behavior occurring in many active—other active fast-rotating stars—so we were pretty confident that this behavior is pretty consistent. Okay, only 20 feet lower—well—so you combined—this is actually a simulation that Carl did with Allen Title in 2001 where they embedded flux emergence for this kind of fast-rotating stars, and they helped to explain why this activity is concentrated at high latitudes. So that's—that's what I'm showing here. This is not—will make observation. So the question is—how does the—the fact that for younger active stars we have the activity concentrated at high latitude—will affect the overall structure of the Astro sphere? And this is a simulation I did where I took a solar magnetograph with the active regions which are shown here in yellow and blue—this is an active Sun of the year 2000—and these are the active regions that are close to the—very close to the equator—and you can see the three-dimensional magnetic field lines in the inside a corona—and then I split the magnetic field between the weak dipole component and the strong active region component—and I shifted the—the active regions in latitude by 30 degrees and then by 60 degrees towards the pole—and you can see that the structure of the overall structure of the magnetic field in the corona changes dramatically only due to that. So the location of the actor—that the magnetic activity for young active stars significantly changes the overall structure of the heliosphere—or the—was Astros fear. You can imagine that in this case—a polar field—and all the way to the atmosphere will be much stronger than in this case here. We're talking about five Gauss—10 Gauss polar field of the Sun—and these active regions in a B star can reach two kilogauss inside—significantly stronger fields in the polar regions. This is actually an image resolution, but the initial condition was the potential field, and it looks pretty much the same at these distances.
So now let's discuss a little bit transport of particles in there—in the Astro sphere and how the changes in time modify the transport of cosmic rays. Again, it was mentioned by Carl yesterday and also by Rachel. Cosmic ray—galactic cosmic rays are generated—actually have a picture—there we go—we think they're usually generated in supernovae where you have short—very strong shocks that accelerate particles to energies that are very, very high—these are GeV. So you can see galactic cosmic rays—rays—energy goes from 1 GeV to 10 to the 21—very energetic particles—and they have a particular spectrum that has been observed—explained for many years by different models. The general transport equation for galactic cosmic rays was introduced by Parker in 1965. This is a very generalized equation, and overall it describes the diffusion term—and you can see this couple here—this Kappa—I think there's 30 years of work just to try to describe what this Kappa is and what—how it behaves—and trying to—using that—trying to explain what we see in the heliosphere. Wait a minute—vection term—this is the guiding center drift that was mentioned by Tomas—who already left—this is the overall drift that the particles have as they generate this kind of motion—and this is important for reasons that I will show in the next slide. We have an energy change term—and of course losses and sources—because we can have losses and sources—and again this is extremely generalized. We know that cosmic rays are modulated by the heliosphere. There's a clear anti-correlation between the solar cycles—which is showing here—and the flux of cosmic rays. You can see that the peaks are near solar minimum. The reason for that was essentially a homework—ongoing homework question yesterday—so I can essentially wrap it up. The reason for the reduction of the cosmic rays is—as we go to solar maximum—that the level of turbulence in the heliosphere goes up. We have more slow solar wind in the volume which is more sporadic than the fast solar wind—and overall we have much more turbulence going on—and that pushes away the cosmic rays via the—the diffusion term—via this Kappa. The other reason is that we have much more CMEs that generate shocks in the heliosphere—and this shock sometimes interact with each other—again—they—they increase the level of turbulence in the heliosphere—and again that pushes away galactic—most cosmic rays—and finally we have an increase of the polar field during—during solar maximum—that also pushes away the galactic cosmic rays. You can see here—this is
An interesting thing is that you have a transition between a peaked high intensity to flat high intensity and peaked and flat, and the question is why that occurs. So that that actually relates to the drift term that I just mentioned in the last slide. The drift term depends on the direction of the magnetic field in the heliosphere. The direction is flipped, flips every 11 years. And what happens is these are the drift patterns of cosmic rays, and it ripped, it, it, it's marked by the a larger than 0 and a smaller than 0. A, a is essentially the direction of the magnetic field. You can see that during periods that are smaller than zero, which is here, you can see that the cosmic rays get into the heliosphere along the equator. Word that it's just harder for them to get there; there's more turbulence, there's more stuff to go through. So you get these peaked flux during this time. While during the times that a is larger than zero, you see that the drift motion is inwards, coming from the polar regions where it's much, much easier for cosmic waves to penetrate. So that's a direct consequence of the consequence of the drift motion.
There are tricks. Most cosmic rays help us to think whether Voyager has already left the solar system or not. I just had a discussion with Margaret Margot about this; we don't know yet. It's still a debate whether Voyager 1 is outside of the solar system or not. But one thing we can clearly see is that as we're approaching the edge of the solar system and being inside the intermediate region, we can see a clear increase in the cosmic ray flux and a clear decrease in solar wind flux. So this shows that at least one and runaway two to be out now. Galactic cosmic rays have an effect on the evolution of the Earth's, and this is related to the early solar system and the fact that we would like to see how they ask us where the heliosphere used to be when the Earth was formed. In particular, galactic cosmic rays may have some important effects. First, they serve as an ionization source for production and creation of complex molecules. They also call the impact on cellular mutations, either direct or indirect. We know nowadays that cosmic rays trigger lightnings, which is very important. And there is a controversial issue that some people claim that cosmic rays have a net cooling effect on the Earth. So if you reduce the amount of cosmic rays, you can help get an increase in the overall temperature, surface temperature of the atmosphere. And that's related to climate change; it's considered to be an anti-global warming theory, but it's still under debate. There are some recent experiments in CERN that they try to confirm this process. The bottom line is that they confirm the experience, but atmospheric physicists claim that that looked nothing like a real atmosphere. So you know that science, but it's, it's, it's important to mention this aspect as well.
We're looking, we're going to look now at a period of the Archaean, about 3.8 billion years ago, and why this, this time. This is right after the late heavy bombardment where all this stuff in the solar system cat-eating the Earth. So at that time the source system was quite clean from small bodies, and that's the period where we have the first for science appearance. So that's the period where essentially life started on Earth, and it's important. So we would like to see how the side, the young Sun, used to be during that time and how the heliosphere looked at that time in the context of cosmic rays. The rotation period was probably about two to four times faster than the current 27 days period, in which we should expect a higher level of activity because it's a young star, so it's more active, especially if it's rotating faster. So again, I hear I mentioned again what I did. This is now a Friday theta, this display of the magneto-gram of the active Sun that I showed before in the three-dimensional view, and this is the original magneto-gram that I took. And this again are their active regions that appear in the original map, and then I just shifted these, their bells to bells of active regions by 30 degrees and by 60 degrees in latitude towards the pole to resemble a young active star or young active sun, if you like, based on the actual solar magneto-gram. And I used this, this input to simulate the structure of the magnetic field in the heliosphere at the time, and then I gave this solution to Joseph Kota from the University of Arizona, and we calculated the cosmic rays transport from this, the edge of the solar system all the way to the Earth, and we calculated the fluxes for different parameters of the young sun. So for each case we had this solution of the transport of cosmic rays or the spectrum of cosmic rays for a given set of parameters. And another thing I did for this solution, I boosted up, I had two additional cases where I boosted up by a factor of five the magnitude of these active regions and the magnitude of the ambient type of the weak dipole component of the magnetic field. So here are the solutions. This is the original solar magneto-gram, this is the magneto-gram where the spots shifted by 30 degrees, and here it's the spot shifted by 60 degrees. So this is a, this is a poor active regions, and you can see that there's, this is the interstellar medium cosmic ray flux. So this is the boundary condition for the intensity of the cosmic rays at the edge of the solar system. And then for a different rotation, you can see that way I have the different fluxes or different spectrum, and you can see that the most dramatic effect, of course, is, or clearly is due to the increase of rotation where you see that for a two-day rotation, but just, just by increasing the rotation we reduce the cosmic rays intensity and their peak by two orders of magnitude. So, so this is, this is the main effect. There is some additional reduction due to the latitude of the spots, but it's not that, that much. However, if I boost the magnitude of the spots by a factor of five, I get even further reduction. So the bottom line is that the cosmic rays intensity near the Earth during the, the, the period of the young solar system was probably significantly lower than the current days because of the fast rotation of the Sun and because of the stronger magnetic fields that it had at the time.
I'll briefly go through the effect of this transport on a stellar evolution and disk evolution study. I'll just, okay, accretion disk around T Tauri stars. These are revolving star, young suns that have an accretion disk around them, and this accretion disk eventually will form the planets around the star. So there's a problem of angular momentum transfer within this. This is a long-standing problem because it's important to determine this transfer of angular momentum within the disk if we want to explain the formation of planetary systems and the origin of planets. Now in 1991, and this was a quite open question for a while, in 1991, Balbus and Hawley introduced the so-called magneto-rotational instability. The idea was that we have magnetic fields in the disk, and these magnetic fields essentially attach to particles in the disk and their servers a restoring force. So these particles don't run away from each other; they keep, if attached to each other, and with a more detailed analysis they show that you can get the right transfer of angular momentum that was necessary at the time. This is an MHD formulation, so we assume that the disc is sufficiently ionized, but the question is, does the disc? So this is, this is something that is still under debate, especially recently. There are some recent, what, oh yeah, I know what you were praising me. No, I think that's the Frank Shu you mean. Yeah, I know what you're talking about. I'm not sure how it is related to that. Okay, let's, let's keep it to the end because I want to try to finish this before the break. Okay, it's not a direct question about this. So we can have different ionization source sources in the disk. This plot is more busy than needed. We can have simple thermal ionization at this part of the disk, the part that's close to the star because there is heat, there's also a lot of x-ray emissions from the hot Corona, so that can serve as an ionization source. We can have galactic cosmic rays, and we can have decay of nucleus within the disk, but in many cases the ionization will be mostly the outer part. So we can have these dead zones inside that are not fully ionized or sufficiently ionized, and the question is how does this instability work without, without sufficient ionization? So one thing me and Jeremy Drake did is to calculate the solution for there's the astrosmurf at a T Tauri star that we had a CDR observation for, so you can, we could drive the model, and then again we calculated the intensity of cosmic rays from the edge of the solar system based on as the standard ISM intensity all the way close to 1 AU, which is here. This is a log scale of the radius in 1 AU, and again we use different rotation periods, and you can see that even for a solar rotation period there is a significant reduction by the magnetic field, and if, if there's a, it is a faster rotation of four days, which is a very typical rotation for T Tauri stars with discs, you can see that there is a significant, even more significant reduction of cosmic rays in large distances where the disc occupies. So can the disc be sufficiently ionized? This is the work done by Cleaves et al. recently, where they tested their model, different sources of ionization. Here on the left you can see the x-ray ionization; it goes from a lower and is an x-ray luminosity to higher. I think this is 10 to the 27 ergs per second, 10 to the 30 and 10 to the 32 I think. So the x-ray flux increases, and you can see that the fraction of the disc that is ionized, the blue parts represent the dead zones, you can see that the part, the fraction of the dead zone is reduced as we go to higher x-ray intensity, as it should be. And here they also estimated the intensity of cosmic rays and the amount of ionization by cosmic rays where the plot goes from top to bottom; there the magnetic field increases. You can think about this this way, so you can see that as we increase the magnetic field, this dead zone grows, and for a high, this represented a typical T Tauri star environment, and they expect that the ionization by cosmic rays again will create a significant dead zone inside, and again the question is can we use, can we assume that the disk is fully ionized to take this MHD approach and do some work with that based on the fact that almost half of the disk is not ionized. Dinner, oh, that's it. I think I will stop here. Yeah, so this will be the second part. I think it's good time to stop, or are there any other questions? [Music]