Transcription
Okay, so let's go into talking about what we can learn about flares in different wavelength domains. And then I'll go into the second talk, and I'll probably end up just talking about the first couple of evolutionary time scales in the interest of time. So the blue optical continuum is for studies of M dwarfs. This was a sort of—this is how I know Hertzsprung discovered his first stellar flare—and because of the contrast, the flare compared with the underlying stellar atmosphere, the blue optical continuum flares are have been studied most from M dwarfs because because of this contrast issue. And you can see that demonstrated here. This is so this is a relative response versus wavelength, and I've shown you the wavelength regions that are covered by some standard astronomical filters. Also, the Kepler mission, since all talking about mentioning flares on observed with Kepler. But you can see here this very red spectrum of an M dwarf outside of a flare, and this blue spectrum is the spectral energy distribution of an M dwarf when it's flaring. So you can one see why these are called red dwarfs, and then you can see the the contrast of the flare against the quiescent emission is greatly enhanced at the shortest shortest wavelength. And then in green, which is probably kind of hard to see, is the the quiet sun spectrum, just sort of bracketing the blue continuum from the flare in the red, my—us an M dwarf.
These are some examples of flares on M-dwarf showing you what the time scales look like in the light curve. Intensity is a function of time; what the spectral characteristics of these flares look like during during the flare. You've got emission lines from the chromosphere of the star that appear in emission. You've got an underlying continuum, which is characterized by a blackbody with a temperature of about 9000 degrees. And then you've got this little extra component here, which has been interpreted as a Balmer jump, but there's no discontinuity; you actually don't see a discontinuity here where you would expect one to occur. So trying to understand how this how this black body is formed, what this nature of this excess emission is, it's a current topic of study. I won't go into a whole lot of detail. This is the evolution with time of some of these parameters during an M dwarf flare. So here's the temperature of that blackbody component; you can see it varies, but during the flare it's temperatures of 8000 Kelvin and above, and covering a fraction of the star that is, say, ten to the minus four of the area of the disk of a star. Hmm.
So in the light curve of the flare, this is the intensity of the flare plus quiescent emission divided by the intensity of the quiescent emission. So it's just a factor by which the flare increased the flux in this wave band in the in the x-ray. We see evidence during flares for very high-temperature plasma that ranges from 10 to the 6 millions of degrees to 100 million degrees, relatively low-density plasma that's described by a plasma that's in collisional ionization equilibrium. So when you look at the spectra, this is an example of a large flare seen over a range of a couple decades and energy from the soft x-ray regime to the hard x-ray regime. A relatively low spectral resolution on the right; you can see the spectrum of a flare and the quiescent emission from this star at higher higher spectral resolution with Chandra, where you can see actually individual lines plus an underlying continuum. You can characterize this plasma by a temperature, a volume emission measure, which is just the integral of the electron density squared over volume, the abundance—how much material is there, how much how much iron is there, how much oxygen, how much silicon—and electron density. And in particular for flares, you can probe their variations of these parameters with time, and that tells you what the heating—you—the heating and cooling processes and what their timescales are.
Here's another example of an x-ray flare where you can see intensity—this is just count rate versus time. This plot also didn't show up very well, and this is for this particular flare; this is how these parameters are changing with time. So in this left series of panels, you can see the emission measure as a function of temperature during quiescence. During the rise phase of the flare, you see the sudden creation and very hot plasma. And then during two intervals in the decay phase of the flare, you can see that the amount of that material is decreasing, and the temperature of the flaring plasma is also decreasing until you get to conditions outside of the flare that more or less mirror the conditions before the flare. And then when you try to characterize the abundance of the elements that are contributing to this coronal x-ray emission, you can see that outside of the flare the abundances of this coronal emission relative to the solar photosphere values taken from Anders and Grevesse—if any of you are spectroscopists—during the flare, particularly iron becomes enhanced during this flare. So it's a topic for a whole other talk that's not on heliophysics if it has to do with stellar coronal abundances. We say we know that these very active stars outside of flares have coronal abundances that are less than the solar photospheric abundance, and during the flares that that abundance becomes temporarily enhanced. That is also a signature of material being brought up from lower in the atmosphere, which is consistent with this scenario that I showed you in the beginning of the talk. Yep, that's a good question. I don't I don't know why there are two different temperature populations during the rise phase of the flare. Partial answer might be that the x-ray spectrum that may be illusion may well be a lot of emission measure completely 30 million; that could be it. It could be an observational signature; it could be related to how the how this particular flare is heating is getting heated. That's that's one way to answer question one.
So if we compare stellar flares to solar flares, x-ray flares where we can derive the temperature in the volume emission measure, this is a plot showing solar flares on the bottom and then stellar flares on the top. So they both have a scaling of emission measure with temperature which is very nearly the same power law index, but you can see that in the range where you have solar solar flares overlapping stellar flares, the stellar flares have more volume emission measure. So this illustrates these couple points that I've demonstrated that I've said verbally: these stellar flares tend to be hotter than solar flares; there's this contrast issue between solar flares and stellar flares; and this this relationship has been proposed by some of our Japanese colleagues as sort of a signature of magnetic reconnection that you would expect to see this relationship between temperature and volume emission measure. Okay, in the radio domain, here's a nice example of a large radio flare seen on an M-dwarf. In this particular case, we're looking at gyrosynchrotron emission from mildly relativistic particles that are electrons that are trapped in the magnetic loop. You can derive the spectral index, a few multi-frequency observations; this is just the flux; this index is just a flux ratio of those two assumed to be a power law, and how it's changing with time. You can see over here in the very beginning phases of this flare you had a very interesting increase in the spectral index, which indicates that in the beginning phase of the flare the radio emission is optically thick. And then during the decay phase of the flare, this index is decreasing down to smaller numbers, showing that the optical depth of the plasma—radio emitting plasma—is decreasing. And you can also measure the amount of circular polarization during this flare. These gyrosynchrotron flares from from stars tend to be unpolarized, as if you interpret that in terms of a simple coronal loop that has some net polarity pointing up and pointing down, that just suggests that they're you're seeing a complete cancellation of the polarization signature from the flaring loop. If you look at the radio spectrum outside of the flare, the radio spectrum is flat and falling, and during the flare the fluxes—right—the spectrum is rising with increasing frequency.
This is an example of a radio flare on an active binary system where you can see the sudden increase here in time. This is this is scale here; it's days. So this isn't them within a matter of an 15 minutes, the flare initiated, and the—this is the circular polarization with time of this flare. The red is a model where you have a mixture of quiet emission that has some amount of circular polarization and a flare that has a large increase in flux with time but no net polarization. If you put those two things together, you get this red curve, which more or less represents the polarization signatures, and then this curve is the these curves are the different spectral indices varying with time, showing that you start out initially being optically thick during the rise phase of the flare and then you were transitioning back to optically thin conditions during the decay phase of the flare. This is an example of a flare seen in the FUV where you're seeing this transition region plasma, and the flare contrast is not a red flare contrast; the image contrast is not particularly good here. So the the FUV region shows the impulsive response to the flare energy input in the far ultraviolet. With astronomical detectors, we have enough spectral energy resolution that we can actually deduce some velocities during the during the flare, and we can see redshifts and blueshifts happening during the flare, line widths getting broader indicating an increased amount of turbulence during the flare. Chromosphere emission lines—these are formed at temperatures below about 20,000 degrees—and these are formed during the so-called gradual phase of the flare. This is an example of another flare on an M dwarf where you can see flux with time for different chromospheric lines, and the thick black curve is that U-band continuum response, which is very fast, and the—temporal behavior of these other emission lines is much more extended. You can see this—I showed you this earlier—this sort of Newport effect relationship where you see some delayed response, and then it has a much longer time scale.
Okay, hard x-rays. So this is a plot from a solar flare, a schematic plot showing the contribution of thermal electrons, non-thermal electrons, and then very energetic electrons and ions. And you can see that the radiative flux of these thermal electrons dominates over the non-thermal electrons by factors of about 10 to the fifth. Okay, though for solar telescopes, you've got that advantage of being one AU from from from your star that you're trying to observe with hard x-rays. When you think about trying to look at stellar flares, you've got an additional complication in that astronomical hard x-ray detectors typically have sensitivity out to maybe a hundred to 200 kV. And remember what I said earlier about flare—stellar flares compared to solar flares—how what what's what was one of the differences? They're cooler, about the same temperature, they're hotter, or much hotter. So you're gonna see the thermal tail of a stellar flare out to higher photon energies than you would for a typical solar flare. And here's the same plot again that I showed you before. Here's an example where we've claimed to have seen an excess continuum emission at hard x-rays that we interpreted as non-thermal hard x-ray emission based in part on an energetic argument, based in part on claiming to see evidence for the Newport effect, but this is really—it's just—it's just a really difficult thing to do. You need a very energetic flare, very luminous flare, which doesn't happen very often, and you need to overcome the thermal tail that you're seeing from what can be—this is a hundred million degree plasma—and then you're looking for a non-thermal power law signature on top of that, right, in addition to that at high energies.
Okay, and then this is my last slide, and this part talking about processes. So evidence for stellar CMEs. I already said that we don't have any observational constraints on stellar CMEs, but astronomers are a very clever, inventive bunch, and we can take what we know about the Sun and try to extrapolate it by the several orders of magnitude difference between solar flares and stellar flares and try to make a guess at what the influence of these stellar CMEs might be. These are some figures from one paper by our—neo—I think—over—you're going to talk about this paper in more detail; you're gonna talk all about this; I don't need to. So you know, if you think about it naively, big scales—too big. So if you have big flares, you expect big CMEs; very numerous and energetic flares, you should have an enhanced rate of transient mass loss associated with these flares. Whether that actually occurs in reality, we don't know. Okay, all right. So and please tell me I don't have ten minutes left for the rest of my talk. All right. So all right, so I will not talk about some of this stuff. So going from thinking about individual flares to trying to think about—oh, it's a little better—thinking about synthesizing these—what I would—what I've been previously talking about is sort of detailed studies of individual events, trying to learn about that particular flare and then fitting it in with what we understand about solar flares. What I'm going to do now is sort of take a step back and then rearrange these studies of stellar flares so that now we're talking about things happening on evolutionary timescales. Okay, so I'm gonna be referencing a lot of flare frequency distributions because that's one way to to build up our statistics of flares and compare that with our understanding of solar flares. We can measure these flare frequency distributions in different wavelength regions as long as you pick pick one region where—region of the electromagnetic spectrum where flares happen—and then just count flares either from one particular star by just sitting on it for a long time or looking at an ensemble of stars that are similar in some fashion, either they're the same kind of dwarf or they're stars of the same age and build up a distribution that way. So so let's start looking at at these flares on this evolutionary with this evolutionary perspective.
These are some plots that just are meant to give you a sense of when we talk about stellar birth to the zero-age main sequence; we're talking about stars that have just formed; they might still contain the remnants of their formation processes or still be actively forming planets. So they could have a disk around them; stars that have disks are called classical T Tauri stars; stars that do not have any evidence for disks are called weak-lined T Tauri stars. These classical T Tauri stars are also undergoing accretion from the disk onto the star, so that is an additional process that can be occurring in addition to magnetic reconnection. And this just gives you a sense of where these stars lie in luminosity-temperature space before they arrive on the main sequence. This is a similar plot to what I showed you before, just showing that you can have these coronal loops that might be interacting with the disk of the star. You've got a whole bunch of other processes like jets and outflows; you can actually see one of those here in this image from the Hubble Space Telescope. This is a—there's a deeply embedded star in there; you can see that—see Ned Johns—you can see it's it's disk. The fact that there's a disk here in some of these young stars affects the star's final rotation speed, and these magnetic loops can potentially reach the disk and affect the star as well as affect the what's going on in the in the disk. This movie that's on the left is not an artist's conception; this is actual data; this is from a two-week long stare of young stars in the Orion Nebula cluster, which you can—if you go out and look up at the night sky—you can see you can see Orion. And all this what looks like flickering is not flickering; it's not flickering because we're seeing this light through our our own atmosphere; this is flickering because all those stars are flaring, and this one in the middle is gonna have a huge outburst. That's a roughly solar-mass star that's only about a million years old, though. During the process of the star's evolution, as it's going from having the remnants of that planet-forming disk, you have a case where you can have the signature of that disk be very present in these classical T Tauri stars. The weak-lined T Tauri stars don't show the evidence of this disk; it's the gas-rich disk that's still forming planets. The nature of that disk changes due to accretion onto the star, ejection from the system, condensation of the disk particles into larger bodies, and so the nature of this disk can change so that at later times it's referred to as a debris disk. Okay, and the time scale for this to happen, for this disk to disappear, is about 10 million years. Okay, so these very young, very active stars can still have still have a disk that can influence them.
Thank you. This is a light curve from of one of these stars that shows evidence of a disk. This is the x-ray count rate versus time; you can see numerous x-ray flares here during this two-week long stare from the movie that I showed you earlier. And I picked—so I broke up these evolutionary time scales into a couple of broad time bins to kind of illustrate—to give you a sense of what we know about flares on stars and these and these time bins and how that relates to some of the major fundamental things that are happening to the stars during these during these processes. So the zero-age main sequence is not a strict time per se; it varies depending on the mass of the star; it's about a hundred million years for a solar-mass star; it's longer for lower-mass stars, but this is the critical time when there's a lot of other stuff going on in the in the life of the star. So this slide addresses one of the questions earlier about what do we what can we know about stellar flares by looking at the decay phase of these flares? So when we're in particular looking at x-ray emission, coronal radiation from these flares, we can study the decay phase and actually get some constraint on what the physical size of these flaring loops might be. We have to do that by reference to hydrodynamic models of the response of a flaring plasma to the input of heating and cooling by radiation and conduction, but it allows you to use a couple of relatively simple observational measurements: the decay time from the light curve, the evolution of the temperature with time, the evolution of the density with time, and from that you can infer what the maximum temperature in the flare was, and you can infer what the loop length was. And there are some simplifying assumptions you have to make to use this approach, but it gives you a length scale that you can't access otherwise, since we can't spatially resolve stellar flares. So this is an example of a flare on a young star; you can see the light curve here; this is the temperature with time; this is actually log temperature with time, so it got up to a peak temperature of about 30 million degrees; this is the time variation of the emission measure; and then this is the synthesis of a number of these types of studies for different types of stars: so stars that are still embedded in their in their disk, these stars that's that still show evidence of their disks, stars that don't show evidence for their disks. And one of the results from this paper, which is still a little bit controversial—other people have followed this up with different data sets—and as you can see here, it's definitely affected by low-number statistics of flares. The top plot shows the number of—number of flares—number of stars, and the x-axis is the inferred loop length, okay, and the top plot is stars that show evidence for a disk; the bottom plot is stars that do not show evidence for a disk. So the conclusion of this paper was that stars that have a disk appear to be producing flares that have larger loops, which can potentially connect to the planet-forming disk. This is loop length in units of ten to the ten centimeters, but these largest loops here are 30 to 40 stellar radii in length, which is pretty large; the Sun doesn't do that. And you can ask a question of how applicable the solar flaring loop model that was used to derive these numbers is; that's certainly a valid question, but it gets at the an issue of whether flares on these young stars can connect to the planet-forming disks and affect the disk by something other than just the radiation that they're producing. On the left, you'll see a flare frequency distribution from young stars that are about a million years old that are solar mass, and they have a flare frequency distribution that's roughly similar to what we see on the Sun. This power law index is about the same as what we see in solar flares, except these are much more energetic, and they happen—they're happening much more frequently. These flares have a maximum
Energy of 10 to the 36 ergs happening one to two times per week. This plot on the right shows a comparison of flare frequencies on solar mass stars, in the filled diamonds, and low mass stars, which are significantly lower in mass than the Sun—0.12 to 0.3 solar masses. Their claim is that they see essentially no difference in the flare frequencies of these low mass stars compared to these solar mass stars. So, this stars—the stars don't know—the flares don't know what kind of star they're on; they're producing flares in roughly the same rate regardless of their mass at these very young ages.
This is another attempt to characterize flares on very young stars by looking at optical flares and delineating weak line T Tauri stars, classical T Tauri stars—so stars without discs, with discs—stars that are on the zero age main sequence. The fact that these stars that have discs can be undergoing accretion in the optical sort of confounds things, as you could possibly have that blue optical continuum flare continuum component that I showed you, plus some kind of accretion signature. It's a little more clear in the x-rays. This plot on the right, which is maybe not so visible, shows the flare rate as a function of stellar age for stars that are in clusters of well-defined ages.
Just to show you something a little different that doesn't follow the solar analogy, this is a radio flare from a youngster that actually is a binary. In this case, this is another example of an interacting magnetosphere where the two stars are in an eccentric orbit, and when they come close to each other, the flares occur and their periodic on more or less the orbital timescale. Yep. No, so you can't—you cannot run on this scale—you can't resolve the flare from one star from the flare on the other star. So, where is the flare occurring in that scenario? Is it—is it anchored on one of the two stars, or is it somewhere in between as the magnetic field lines are reconnecting? That's a question that we're—we're currently examining.
So, what are the expectations for a flare that occurs on one star? We can use the solar model for that. What are the expectations for a flare that's an intra-binary flare? That's a little—a little less clear as to whether the solar analogy would still hold or not, and what the observational consequences would be. It's not if there is—if that process is happening on these binaries—these close binaries—it's a subtle effect; it is still magnetic reconnection. And here is another counter example to the radio x-ray flares that I showed you before that illustrate the Newport effect. This is just an example where these two young stars show radio flares and show x-ray flares, but it's not the Newport effect, and what could be happening there is an interesting question.
Moving on to the next big temporal bin, and the first two of these are where we have the most information because, remember, I said the kinds of stars that are typically targeted for flare studies are very young stars. So, birth to the zero age main sequence are the youngest of these stars—the most active—and then we still pick up considerable amounts of flares on stars in this—in this next category—the zero age main sequence to one Giga year. So, at this point, the star is pretty much established; its internal structure is established; it's in hydrostatic equilibrium. You've got this nice main sequence that all of us astronomers know and love. The time for a star to reach this main sequence is a function of its mass, and the time that it spends on the main sequence is also a function of its mass. So, a star that has a solar mass will spend about 10 billion years on the main sequence; lower mass stars will spend considerably longer on the main sequence. So, at this point, the star—the environment of the star—is more or less settled down, but the stars are still—are still relatively active. I showed you this plot earlier; the rotation rate as a function of age. Here is a slightly expanded view of this underlying x-ray luminosity versus stellar age for stars of different spectral types: G stars, solar mass stars, and here K stars, slightly less massive, and then getting to the fully convective M stars. One of the three spectral—three types of flaring stars that I said tends to be targeted most often are the M dwarfs, and they fit in this age range—zero age main sequence to one Giga year. These M dwarfs have timescales for the decay of their activity that are very long—has to do with dynamo processes—but it means that we can see flares on these stars—on M dwarfs—for much longer than we can for stars that are near solar mass.
This is an example of some flares seen from the Kepler mission, which is a very broadband optical filter designed to find exoplanets; it's very good at picking up stellar flares, actually, although that's not what it was designed for. And you can see the magnitude of these flare intensity increases is tiny; it's fractions—a few percents to fractions of a percent—to the underlying stellar light. Can target particular stars that have a high flaring rate and characterize their distribution. That was done down here in this study by Audard, who studied a G5 dwarf that has an age of 300 to 400 million years, and they find that the index of this frequency distribution is hovering around 2, which is a magic number where you might be able to extrapolate this distribution to lower and lower flare energies and explain all of the stars' coronal x-ray luminosity as being due to flares.
So, if you want to try to take some of these results and see if there are any dependencies of the flare frequency on other parameters, this was done by Audard, where he showed that there was a nearly linear relationship between the flare occurrence above an energy of about 10 to the 32 with the underlying stellar x-ray luminosity. So, the more active—then that's follows along with sort of what I described in the very beginning—that there are scalings of activity in a general sense with some of these stellar parameters. This is just saying that flares follow the underlying activity. If you—this plot is also not particularly—that's pretty washed out—but if you take—if you take observations of solar flares and then try to put these stellar flares on the same plot by correcting for some of this underlying dependence of flare frequency on x-ray luminosity, you don't—you don't get to the Sun. So, something else is happening that's more than just the scaling with the underlying x-ray luminosity.
So I said this before; these M dwarfs—they're the archetypal flare star. It's the most common type of star, and many field M dwarfs have ages in this—this range—this fairly broad range—but even when you look at observations of stellar clusters in this age range where you know the age—you know the ages of the stars—you still—when you look at them for their flares—these clusters—you still tend to find—tend to pick up M dwarfs more often than you do G dwarfs, due partly to their—to the numerousness of the stars in part, and also partly due to the fact that it takes M dwarfs longer for their activity to decay.
These are some—like herds—of some of these very large stellar flares that I was mentioning before. This is intensity increase in astronomical magnitudes, which makes sense to only astronomers. This increase in U-band intensity of six corresponds to a flux increase of a factor of 250 over a matter of an minutes or so. Um—and so yes. So, if you could go back to the plot that I showed earlier, U band is shorter wavelength than B; it's something like 3300–3400 angstroms to 3500–3600 angstroms. And here's an example of another example of one of these very large stellar flares where the x-ray luminosity of the flare exceeded the bolometric luminosity of the star. I won't really go over this slide in much detail, just to say that this is another example of a very energetic flare—that's 10 to the 35 ergs—from an M dwarf. This is a plot from a PhD thesis which was trying to observationally constrain the flare rates of active and inactive M dwarfs. So, most of what I've been talking about stars before, I've been concentrating on the active stars. So, this is a compilation of flare rates of different dwarfs, broken up by spectral type and then by activity level. So, what—what the underlying amount of chromospheric… 03:48:0p ours. Okay, how much time do I have? Five minutes. Okay. So, so I've already—the birdie talked in the previous slides about active binaries. I'm gonna have a particular fondness for them since that's what I did my PhD dissertation on. But once we get into what I'm calling the stellar adulthood range, where you're in the one Giga year to arbitrarily set the age range here at 4.5 Giga years to stop at our Sun, and then anything older than the Sun is stellar old age. So, stars that are binaries can maintain their magnetic activity and their flares for much longer than single stars can. And so, when you see flares from stars in this age range, you need to consider the fact that it could be a single star or it could be a member of a binary system and able to maintain its activity through—through tidal locking and fast rotation. So, these stars are outliers in that rotation-age relationship because they're rotating rapidly, but they're old and their—and their active.
So I mentioned Kepler. I think this is probably the point at which I will finish up, since this is talking about sun-like stars in the sense of being of the same temperature range as the Sun, roughly the same age range as the Sun, where we see evidence of flares, and these appear to be single stars, not members of binary systems. And Kepler has—is very good at finding exoplanets; it's also good at finding faint and rare signatures on stars like flares. So, there's been a series of papers by my Japanese colleagues exploiting the Kepler database to find examples of very energetic flares on sun-like stars that have rotation rates that are comparable to what we—what the solar rotation rate is, and they have a distribution of flare frequency with energy that's much steeper than we see on the Sun. And this paper by Shibayama tried to estimate how often these—what they called superflares—how often they might occur on these—on these sun-like stars, and they estimated that's something with an energy of 10 to the 34 to 10 to the 35 ergs happens once every 800 to 5000 years on solar-like stars. So, that's an interesting point to consider against our Sun and its current evidence for activity in the extremes of its activity. And this is a topic of considerable interest both from the solar physics and heliophysics perspective, but also from the astrophysics perspective—what whether the Sun can produce one of these extreme events. [Applause] So, if there's more questions, I'm happy to—happy to answer more questions. I can tell you—you know, I come up here during the break, I can tell you about there's on old stars if you're interested. Yep. Yes. Oh, so K stars—can—can things that are not stars—like brown dwarfs—produce flares? Yes, they can. So, so once you get below about 0.1 to the mass of the Sun, we don't really know whether those objects form in the same way that stars form or whether they're forming the way that the planets form, but they can—they can produce x-ray emission; they can produce x-ray flares, and they can produce ultraviolet flares, radio flares; they are—they're very interesting, and I didn't—didn't touch on those because they were different enough from the case of—of main sequence flares on main sequence stars that I didn't want to completely confuse everyone, but they're an interesting bridge between what we see as stellar behavior and what we see as planetary behavior. So, we see that some of these objects can produce x-ray emission; they're very faint; the x-ray luminosity is decaying with these stellar parameters. So, they're—they're—they have x-ray luminosities that are less than that of the Sun, and they're at 10 to 20 parsecs away. Some of these objects can produce radio flares that actually don't look like those radio flares that I showed you; they look like auroral emissions that we see on Jupiter. And so, you know, what's—what's going on in that case where you've got potentially some—maybe some stellar-like processes, but also a mixing of planetary processes is an interesting—interesting topic. Let's see. So, the least massive object for which an orthodox solar flare—and that's an interesting adjective—so, so yeah, so an ultra-cool dwarf that has an evident—has some evidence for a flare that looks like it's a—some kind of analog of a solar flare would be something that's a spectral type of about M9, which is a temperature of say 3000 Kelvin. It's a failed star. Yeah. Yeah. Well, so it's not—it's not igniting its… [Laughter] Yeah, but those were stars at some point. A white dwarf used to be a—used to be a solar mass star. No, the best a brown dwarf can do is to burn deuterium in its interior; it doesn't—it's not massive enough to be able to fuse hydrogen. So, that's—that's the demarcation—that 0.1 solar masses is things that are more massive than that can burn hydrogen. Roughly 0.1. Yeah. Right. So, just flares. So, I'm gonna—I'm gonna go back to one of the slides that I didn't pay a whole lot of attention to at the very beginning. So, when you—so when you try to synthesize these flare studies, you have to count flares, and there are a couple of different systemic effects that can affect that interpretation, and I'm skeptical—I'm skeptical of whether the flares that you can observe can be extrapolated back to the flares you can't observe that could be powering the stars' underlying x-ray luminosity. So, one of the arguments is that you need to have the index of your flare frequency distribution be greater than two. Most of the studies that have looked at these flare frequency distributions, such as these two studies—these two—these two plots by Marco Audard—they can find alpha greater than two, but with a large error bar. And in fact, on paper that I'm currently working on, I was thinking about these—these are two prototypical flaring M dwarfs—82 Leo and EV Lac. They've had a flare frequency distribution in the x-ray measured, and they've had a flare frequency distribution in the optical measured, and not a lot of attention has been paid on doing a comparison of this—an intercomparison—intercomparison of these—these wavelength regions. So, if we think that flares form the way on these stars the way they form in the Sun, the optical flare and the x-ray flare should be representative of the same underlying population of flares; you're just looking at some—some different components of the energy partition in each of these different wavelength regions. So, I'm skeptical of the indices that come out to be larger than two because—because of this intercomparison that suggests that you don't have to have an index larger than two. If you have an index larger than two, and this is actually touching on the second homework question, that suggests that you have more numerous low-energy flares compared to high-energy flares. And for something that's less than two, you have the opposite effect. If you try to do a model of a flare-heated corona, it can be difficult to reproduce some of the light curves that show large x-ray flares. Another criticism that I have is that this assumes that the flare frequency index is a power law; you're typically only measuring a small dynamic range here at the very uppermost reaches of these flares. And if something is limiting the maximum energy that a flare—that star—can produce in a flare, you could be skewing your—the flare frequency distribution that you determine by assuming that it's—that it's a power law when it could have an exponential cutoff that is steepening, and you're erroneously interpreting that shape of that distribution as a power law with a steep spectral index. And say whether you like steel. Okay, there's the—okay. So, on the Sun—even on the Sun—for the flares that you can measure, it doesn't look like you can get into this—this regime. Yonder do actually. Yeah. So, the short answer is yes; you can—you can speculate that the CMEs—that any CMEs that might be accompanying these large flares would be themselves very massive. And I had one slide showing some results of one paper, and Overbye is going to talk in more detail about what you would expect to see if you try to model a stellar CME using the solar flare CME analogy. Oh, also on the—the event of in-scribe site. Yeah. [Music]