 My name is James N. Letus. I'm Chair of the Department of Physics here at Berkeley. And it's my pleasure to welcome you to the 24th Annual J. Robert Oppenheimer Lecture. Now, the Oppenheimer Lecture, Annual Lecture was established in 1998, and it's made possible through the generosity of Jane and Robert Wilson, as well as Stephen Arlene Krieger. The series has brought a who's who of theoretical physicists. Past Oppenheimer lecturers have included C. N. Yang, Freeman Dyson, Helen Quinn, Charlie Kane, Andre Linda, Marie Galman, Stephen Hawking, Kip Thorne, Marvin Cohen, and last year, Lenny Susskind. Many prominent theorists in the fields of particle physics, condensed matter astrophysics, cosmology, and AMO have stood where I'm standing today. Now, let me tell you a little bit about Robert Oppenheimer, the person. He was born in 1904, growing up in an upper middle-class family in Manhattan. He graduated from Harvard, majoring in chemistry, entered Cambridge University in the UK in 1924 as a graduate student, hoping to work with Ernest Rutherford. But then he left in 1926 to finish his PhD with Max Born and Goddigan. I should point out that I try and tell my students that they could be the next Robert Oppenheimer in my own group, since Ernest Rutherford was a fellow Kiwi. But I usually don't tell them that he left after two years. Anyway, he published more than a dozen papers while with Born, mostly focused on the new theory of quantum mechanics. This included his most famous work, the Born-Oppenheimer approximation, that still is important in the fields of particle physics, condensed matter, and nuclear physics as well as many other areas. Now, he published more than 90 years ago, in 1929, after two years of post-doctoral study, mostly in Europe, Oppenheimer returned to the United States, and he accepted an associate professorship from Berkeley, where he remained for the next 15 years. During this period, he published his famous work with Volkov, establishing the Tolman-Oppenheimer-Volkov limit on the maximum mass of a neutron star, the mass above which a star must collapse into a black hole. Now, this area remains relevant today as we study gravitational waves from the mergers of black holes and neutron stars. At Berkeley, Oppenheimer's group typically was 8 to 10 graduate students in several post-docs, and Oppenheimer visited them every day, a standard that I try and avoid. But, no, or kidding aside, one of the most famous components about Oppenheimer's legacy is expressed by Hans Bethe, is that he probably had his most important ingredient of his science and to his teaching is his exquisite taste that he had in finding important problems. Okay. Now, the scientific leadership of Oppenheimer demonstrated at Berkeley complicated his later life and his role in science. In 1942, he was selected to lead the World War II Manhattan Projects Engineering Lab, cited in Los Alamos, near the ranch that Oppenheimer owned. His leadership of this effort culminated in the successful Trinity test, and later the political decision to use atomic weapons against Japan, a decision that troubled Oppenheimer for the rest of his life. After World War II, Oppenheimer became the public face of science and technology, featured on covers of Time and Life magazine. This period of his life came to a close with a controversial loss of his security clearance in Los Alamos in 1954, a time when a new Cold War and McCarthyism were at their peak. There was some resolution many years a decade later when President Kennedy presented Oppenheimer with the Nations Fermi Award. Now, Oppenheimer's legacy at Berkeley is a simpler one, summarized by a plaque on the fourth floor of Physics South Hall with another quote from Hans Bethe. In these corner offices, 1929 to 1942, J. Robert Oppenheimer created the greatest school of theoretical physics the world has ever known. Berkeley physics strive to continue this legacy today. Now, it is my great pleasure to introduce my colleague from UC Berkeley Physics, Professor Chris McKee, to introduce tonight's Oppenheimer lecturer, Dr. Hans Bilston. Over to you, Chris. Thank you very much, James. It gives me great pleasure tonight to introduce tonight's speaker, Dr. Lars Bilston. Dr. Bilston attended graduate school at Cornell University where he was a Hertz fellow. After that, he was a postdoc for several years at Caltech before coming here to Berkeley where he served on the faculty for a period of between four and five years. Unfortunately for us, he was then attracted to UC Santa Barbara and so he left and he remains there today as a professor of physics. Part of the reason that he was attracted to Santa Barbara was the presence of the Kovli Institute for theoretical physics there and he got an appointment at that institute. At that time, it was directed by David Gross, one of the most prominent theoretical physicists of this era and in 2012, Lars took over from Gross and is now the director. This institute is really a mecca for theoretical physicists and astrophysicists bringing in researchers from postdocs to senior professors for periods of several months to tackle some of the most challenging problems in physics today and the institute has flourished under Lars' able leadership. Dr. Bilston is a theoretical astrophysicist who is recognized for his work on the properties of stars, both while they are burning their nuclear fuel, which lasts over a period of millions to billions of years and also when they end their lives in spectacular explosion of supernovae. Most recently, he has been working on the variability of stars much more massive than the Sun just prior to their explosion of supernovae. He's also avidly engaged in the observational field of time domain astronomy by his longstanding collaborative efforts with the worldwide Las Cumbres Observatory and the Zwicky Transit Facility at Palomar. In addition to his university teaching and research, he has devoted significant effort to strengthening science and engineering in grades 7 to 12. Dr. Bilston has received many awards including the Alfred P. Sloan Foundation Fellowship, the Helen B. Warner Prize of the American Astronomical Society and the Danny Heineman Prize for Astrophysics. He was elected to the National Academy of Sciences in 2018 and was elected as a Legacy Fellow of the American Astronomical Society in 2020. Tonight, Dr. Bilston will present Hearing the Stars' new insights into stellar interiors. He will provide his insight into how theory together with space-based observations of stars within our galaxy have had a remarkable impact on our understanding of the universe. It gives me great pleasure to introduce Dr. Lars Bilston. Great. Okay, and everyone can hear me? So what I want to talk about this evening is a remarkable progress, both theoretical and observational, on really seeing with telescopes the fact that stars are varying quite dramatically. So as I go along in this talk, I will absolutely highlight what I want you to come away with from this talk, which is that when you look up at the sky, if your eyes were only able to detect changes in a part in 10,000 of the brightnesses of the stars, you'd be seeing a movie every night, not a still image. And of course, we're able to do that with telescopes, as I'll show you this evening, and use that information of how those stars are varying to understand their distances, their masses, their ages, and how big they are in physical size. So before I do that, I need to give you a little bit of a primer on the types of properties of these stars we're going to study, which is really standing waves in the star. So to do that, I want to first remind you of what a sound wave is. I'm going to give you a story of unusual things that happen in the Earth's ocean and how you can use sound waves to probe properties within bodies. I'm going to then tell you about the nearest star, the sun, and how we've learned how to do the science that I'm going to talk about by really studying in detail the sun, and then we're going to go outside of our solar system. So that's tonight's plan. I definitely will pause a few moments during the talk to take questions, because I think it's much more fun for me to get questions during the talk than to force all of you to hold them up, even though I saw that on the schedule. So pardon me, James, if I'm deviating from the plan. Okay. So let's first talk about what a sound wave is. Well, it's what you're hearing right now. It's the response of, in this case, air to compressing the air. And what it is is a compression rarefaction wave, but in this room, this is the speed of sound in case you can maybe see it. It's a little bit, sorry. It's about 350 meters per second. I'm sorry. I'm going to use mixed units this evening. I'll use, when I talk about the Earth's ocean, you'll see feet, which is unusual for a physicist. Thankfully, I took out the fathoms, because that's a harder one. But that's the speed of sound for the temperature of this room, which is roughly around 300 Kelvin. Those are the units we like to use. And you can use sound waves to actually triangulate, as you know. Let's start by reminding you what the wave is. So it has certain properties. So I will have some equations this evening. We're going to start pretty simple. But this is what a sound wave looks like. It's basically a propagating disturbance of an area that's rarefacted and an area that's compressed. The frequency of the wave is given by the sound speed. That's the CS divided by the wavelength. The wavelength is the distance between the peaks. And, of course, shorter wavelengths are higher frequency. And for those of you who have musical instruments, you know that the smaller the instrument, the higher the frequency, the larger the instrument, the lower the frequency. And we're going to do that in stars. Stars exhibit the same phenomena. Stars that are very large can have very low frequency response. Stars that are compact have very high frequency response. So I'm going to divert to an unusual thing, because it's a great story. And it's about sound and water. And it says nothing to do with the rest of the talk. But these three slides are so much fun, I can't not tell you. So first off, water is very different. The speed of sound and water depends on its compressibility. To you, water is incompressible. But, of course, it's not totally incompressible. If you compress it, it does resist. And that gives a sound speed. And it's much faster than the speed of sound in air. It's about 1,500 meters per second. So it's four times faster. But if I go into the ocean, there's some interesting phenomena that can happen. As I go down into the ocean, so here's my first question. So we're sitting here roughly in one atmosphere. That's the definition of where I'm standing. But some of you probably know how deep you have to go in water to have the pressure double. Are there any scuba divers? Not one. One scuba diver, how deep do you go? 10 meters. 10 meters, exactly. So if you go 10 meters into water, the pressure is twice that of this room. And as the pressure increases, as you go deep, the sound speed actually increases due to the pressure increasing. So you have to go pretty deep to have a big change. But that's one reason the sound speed increases. But the sound speed also knows about the temperature of the water. If the water is hotter, the faster the water is colder. Those two things end up giving you a very unusual arrangement for the speed of sound in water. And it looks like this. So this is an unusual plot. Oceanographers plot things, at least to me, that's sort of backwards. The sound speed is on the x-axis, and it's in this beautiful unit of feet per second. But notice a very small dynamic range. It's 5,000 feet per second, 4850. So it's almost a constant number. And then this is depth. So as you go deeper in the water, generically go down to 13,000 feet, the sound speed is faster. However, as you get to the surface, depending on your latitude, the sound speed also rises. So if you're near the equator, it's hot, and the sound speed rises up to a value which is almost the same as the sound speed at depth. And this is because the surface of the water is hot. If you go to northern latitudes, this is different because it's colder, and this is the profile. So the reason I'm telling you this is because in stars, and in this case, if I have a wave that's moving, and let's say it's going down, into a region where the sound speed is changing, that wave will get deflected. It gets deflected via sort of an optic snowslaw for those of you who've done optics, and the same thing happens in this case. So what happens is, as the wave is going down into the ocean, if it's a grazing wave, it's going to get reflected at some point and come back up. And again, you sort of know this, the fact that sound bounces off water. That's again, it's going into a place where the sound speed is four times higher. We're now talking about something much different. But what this means from this is that if I go to this location, let's say I'm at 19 degrees north latitude in the ocean, and I'm at 3,000 feet down, I go to this place, and I send out a sound wave that's moving exactly this way. It'll just propagate happily. If I send it up, it goes into a place where the sound speed is increasing, and therefore it gets bent back. If it goes down, it gets bent back as well because it's moving into a place where the sound speed is increasing. So this ends up making a channel. So how many people know how we measure the Earth's ocean temperature at 3,000 feet? It's this phenomena. If you really want to measure the temperature of the Earth, you can measure this channel. So you can do the exercise, and that is the busiest plot I will show, which is what I put at the beginning of the talk. What this shows is I'm sitting over here to the left, so that to the right is just moving down, going across the ocean. So I'm sitting here at, in this case, now here's fathoms, I'm sorry, I didn't get rid of fathoms. So here I set off an explosion. The ray that goes up 15 degrees, which is the scales are compressed, the 15 degree ray just off the horizontal goes up and reflects, and the ray that comes down 15, so it's showing you that these rays that are nearly transverse just keep propagating. So you take what would be a three-dimensional event, and all the rays in a narrow channel stay and they spread as a two-dimensional spreading. So if things are spreading in two dimensions, instead of three, they propagate and keep a large amplitude. So this was discovered by Ewing in the 40s. A few pounds of TNT in the ocean off the coast of Africa was detected in the Bahamas. And it's all because the rays were spreading into just a two-dimensional sheet. Okay? So how many people knew this? One, two, awesome. Okay, so I'm doing really well. Well, you'd like to make use of this. Does anybody know how this was used during the war? Yes. Not at this time. Yeah, no, not at this time. Submarines are a good idea. Yes. Rescueing pilots, jackpot, rescuing pilots. So pilots were given a small charge and given their latitude, they knew where to set the depth charge so that if they landed and didn't want to land, a.k.a. in the ocean, they would drop their charge and it would set off an explosion at the depth associated with that minimum. And it would send signals, this is from popular mechanics, 1949. This was me kind of Xeroxing two different little, but it's showing schematically, here's the poor downpilot, they here see 4,000 feet, so they told you where it was. And then they had listening stations at different areas, so for those of us in California. There's no way to actually geolocate downpilots during the war. Okay, so that's nothing to do with stars, but it's just such a cool story. I can't not tell it. Okay, so now let's go off the earth and let's do a star. How do you understand a star? Very simply, it's ideal gas that is holding itself up due to the pressure of the gas. So what that implies is that as the object changes its radius, so what I'm showing here is the big M is the mass of the star, this is the radius of the star, this is just the mass of a proton, G is a gravitational constant, this is the Boltzmann constant and this is the central temperature, the mean temperature of the gas. And the need for it to hold itself up ends up basically demanding that the temperature be of order with the gravitational energy, what we call the virial theorem. And so as a star gets more compact and radius, the temperature rises or if the mass is less, the temperature is lower, but this relationship pretty much holds for all the stars I'm going to talk about today. It works well for the sun, this tells you the sun temperature is about 10 million Kelvin. That's what sets the temperature, it's the size of the star. Nothing to do with fusion, just to be clear, it's the size of the star. So let's just do the math of I've got a star, it has a certain temperature, I know how to calculate the sound speed if the temperature is higher, the sound speed is higher, what's the time it takes for a sound wave to just go around the star or go through a star if I'm being a little bit loose. Well, because of this relationship, it's the same roughly as the time it takes for a particle that's orbiting at the surface of the star to do an orbit, what we call the dynamical time. And for something like the sun, this is roughly an hour. Okay. So if we're going to think of sound waves going around a star, this is the time scale that's going to matter. And so let's start with the nearest star, the sun, for which we have a big advantage. Not only is it bright, but you can look at small spots on it. For all the other stars we're going to talk about, you cannot do the latter. You're stuck seeing the whole disk. But let's start with the sun because this is where we really cut our teeth as a physics community, astrophysics community, and understanding how waves get created and propagate in a star. So in the sun today, there's a core in which the fusion is occurring of hydrogen to helium. We're about halfway done. So in about five billion years, the core will burn out. It's hydrogen, and there'll be a ball of nearly pure, well, it's basically will be pure helium with some other elements, but no hydrogen. There's a layer in which the heat is escaping just via diffusion of heat. But then the outer, roughly one-third of the radius is vigorously convecting. It's impossible for the heat to get out via just slow diffusion. Instead, it triggers convective motion. So this is vertical and transverse motion that is transporting the heat out via vigorous convection. So that's the structure of the sun. Back in the 60s, it was discovered that there were really worse of persistent oscillations. There was very distinctive timescale scene, roughly, in this case, about five minutes for the sun, is what was detected. And all of these motions, also when you would look at patches, had pretty large coherence. So you could see waves going around. You could distinguish waves that are going through and coming out the other side. Today, when there's a sunspot on the backside, or an eruption on the backside, waves come around and we can see the waves come around the front side. You can actually use that maybe to predict if there's going to be a coronal mass ejection. But the sun is nearby. The understanding of this presence of all of these ringing and oscillations completely has to do with the fact that this is a vigorously convecting object, which is really, really noisy. And so many of you, well, not today, but we used to have cars that at certain speeds would rattle. I think this is somehow gone. At least my car still doesn't. But there's resonances within anything and the noise ends up creating resonances and those resonances get to large amplitudes. And so how we understand what we see in the sun in terms of all of these waves, which are really standing waves, has to do with the fact that convection over time creates an amplitude spectrum of many, many waves. And if you want to think of it, it's really a musical instrument with many possible tones. I can have a wave which has four or five nodes to the center. I can have a wave of much higher frequency where there's higher frequency oscillations. I can do the same thing going around the star. Not all of these are going to be available to us for distant stars, but some will. So what did... What do these waves look like when they're propagating? Well, this is important because this is going to help us understand what we can do in stars that are far away. So what's shown here schematically are waves which have different amounts of what we call, if you think of the trajectory towards the center. So a wave that is nearly radial basically gets bent, but very little. A wave with a high tangential direction gets bent at this coordinate. So this is the reflections I was talking about. So a wave which is trapped and goes all the way around the surface cannot get to the interior. Waves with what we would call lower L for those who are physicists in the crowd get to get to higher depths. But in this case, when we look at distant stars, there's some things we're not going to be able to see. We're not going to be able to see a wave like this red one because of the cancellation of the intensity around the surface of the star. Okay. So I'm now cutting out 20 years of work by others to give you the punchline of what you could say for the sun. So if I go back, I see waves, some of which get near the interior, some of which don't, but you can use that to then dissect the sound speed as a function of radius in the sun. Right? You use the properties of the different waves to do that, and this is the result. So on the x-axis is showing the radial coordinate relative to the surface. So here's the surface of the sun to the far right. Here's the interior. And they chose to write this as the square of the sound speed. So this is roughly the square of the sound speed. So as you go into the sun, as I said, there's heat that's transporting. So this is equivalent to temperature. So the temperature is rising as you go in, but then you see this interesting thing at the center. The sound speed goes down. Now this is a quiz for those who want to be so brave. The temperature, I will tell you, is uniformly rising as I go to the center. Why would the sound speed drop? Yes. Yes, please. No. As you go into the star, the density is rising, but the sound speed does not know about the density of the material. What does the sound speed know about? It's an ideal gas. Yes. That's correct. So the answer is that it all starts as mostly hydrogen, but at the center it's been fusing, and there's more helium, and helium is a heavier atom than hydrogen, and therefore the sound speed drops. For those of you who inhaled a helium balloon recently, you know that the pitch goes up, right? Nobody's done this? Ever? I'm probably in trouble now. But that's because you're replacing air, right? Air is mostly nitrogen and oxygen, so its atomic weight is 28, and helium is 4. So that's evidence of the fact that we were pretty confident of, which is that at the center, the abundance of helium is risen because of fusion over time. And then if Wick is here, he can tell you how this impacted the solenoid trino problem, but that's another talk. But the point is this was quite profound. You can do a lot of things. You can measure the rotation rate within the Sun. So this is showing, as a function of the radius of where you are on the Sun, its rate of rotation. It's roughly rotating as a rigid body at the center. This dashed line is the place above which you have this vigorous convection, and you see that the rotation varies. It's faster at the equator than the pole. You see this in sunspots, but you can now measure as you go deep in that it becomes uniformly rotating. Again, this is from Helios seismology. I'm not going to show you this evening, but for other stars, we're doing this, but not at this level of detail. But we are able to now infer rotation both surfaces and interiors. So what I want you to think about is that when you look at the sky, anybody know any astronomers in the crowd? Pleiades, very good. That was an easy one. Gabor got that just like that. This is for you, Gabor. This one is for the Pleiades. But this is really a movie. This is what I really want you to take away. It's unfortunate that the amplitudes of the variability are comparable to the naked eye, but if it were, you'd go out every night. The brightest star tonight is the faintest star, and you'll discover that it's oscillating every five hours, the period's changing. I'm sorry, the brightness is changing. And another star suddenly is doing something different. It would be super exciting. And unfortunately, that's just not available to us because our eyes are not that great. But again, to go back to the sun, you don't get to see everything. So if you just ask, you put a disturbance on a star, disturbances that have small amounts, have long wavelengths that are of order the size of the star, would give you a change in brightness. Everything I'm going to talk about from now on is a measurement of just the brightness of a star. For the sun, we were using Doppler measurements to get velocities, but for distant stars, we just get the brightness. So the data I'm going to show you and the results this evening with theoretical understanding is really just based on measuring how bright a star is as often as you can. That's it. And things like this, which have a lot of plus, minus, plus, minus, all cancel out. And so you don't get to see these types of waves in distant stars. You can only see what we call the lowest possible L. You could see a radial oscillation, a breathing mode, and you could see some of these, but that's it. Okay, so what would the sun look like if I put it far away and only allowed myself to make these sort of cruder measurements? Right? So the sun, you know, it's fantastic because there's millions of frequencies. But what if you only could do it? Well, this was done. And this is what we call the power spectrum, which I'll explain. This is the frequency of the oscillation that we're seeing. And this is basically the change in brightness, the amplitude of the change in brightness and what you might notice here is a sort of fine-tooth comb and you probably can see from the back of the room a very characteristic frequency shift, a frequency spacing directly. Right? You can see there's a characteristic frequency spacing between each of these. And there's a force. There's three different modes here for the physicist. There's L of zero, one, and two. But what you can see is that there's a characteristic frequency spacing. How many nodes there are? If I add another node, the frequency goes up. If I add another node, the frequency goes up. And I'll show you this for the distant stars where we can say that that means there's 10 node crossings within the star. Well, this you can measure in distant stars and that's why I want to highlight this. This frequency spacing is really just completely equivalent to the time it takes a sound wave to go through the star. And because the star is holding itself up, that's the intensity. If I measure this frequency spacing delta nu, I actually get to infer the mean density of the star. Because of the fact that it's holding itself up, that's the inference I get. So it's really an integral. It takes the amount of time. It takes a sound wave to get through. But because it's holding itself up, I get to infer the mass and the radius, cubed. Now for the sun, that's not exciting. I know how big the sun is so this is not exciting. For a star halfway across the galaxy we have no other way of doing this. So that's profound and it's literally just from reading off the spacing. You might also notice so let me just say it let's say that this is 10 nodes, 11, 12, 13, 14 but for some reason as you go to high frequencies you see this is really tailing off. So if I take the log of that plot y-axis to show the same thing here's that dense spectrum and you can see in power it really tails off dramatically. And so for some reason a star can allow for a wave to get to very large amplitude when it has 10 nodes but when it gets to let's say 20, it depends on the star suddenly the amplitude cannot stay large. The waves get damped and you don't need to really read the slide but for some reasons very simply is as the wave gets nearer to the surface of the star the temperature is low temperature at the surface of the sun is much less than the center and because it's fixed frequency that means the wavelength has to change and if the wavelength is getting of order the size of the last e-folding of the density what we would call the atmosphere think of the atmosphere here which is about 30,000 feet a 16 boundary or a leaky boundary so if the wavelength is very short at high frequencies it leaks out if the wavelength is long when it gets to that place relative to the thickness of the atmosphere it's reflective. This is called the acoustic cutoff because we've measured the temperature of the star distance stars this allows us to measure little g gravity how strong is gravity at the surface so just measuring that this frequency above which there's no power or power declines gives us a direct measure of little g ok so this is now two measurements a frequency spacing and a maximum power or maximum frequency this gives me gm over r squared well I have two variables and two unknowns so now I can get the mass and the radius ok again for the sun not exciting but this is a good time to pause because now we're going to go off and do the rest of the galaxy so before we leave this is the toughest sledding for those of you so I've got two measurements I have to make and I'm going to get the mass and the radius of all these stars if they happen to cooperate ok so let's get away from the sun let me show you other stars so this diagram is what in astronomy we call the Hertzsprung-Russell diagram it's on the x-axis the temperature of the surface of the object in kelvin and log and the luminosity of course in the units of the solar luminosity and each of these is for a different mass so here's the sun one solar mass and what happens to all of these stars is as they burn out a fuel and leave the main sequence this core as I mentioned in the sun the object will expand in radius that's this and it will brighten and it will get very large and most importantly for us it becomes the brightness means the convection becomes even more vigorous and it's a much larger volume of the stars what we call a red giant is undergoing vigorous convection because it's getting bigger the period should get much longer and the hope was that because it's the convection is more vigorous that the amplitudes of these waves would be large this is not a place where theory does a good job at predicting amplitudes is hard but thankfully in astrophysics we often don't need to calculate everything because you the taxpayers are happy to put something into orbit so what I want to show you for the rest of this evening are results from multiple satellites but these were the two that really opened up the field to us satellites put into space the Corot satellite which is a French satellite and then Kepler which many of you are more familiar with for its ability to find planets around nearby stars by looking for the transit the planet going in front of the star I highlight here that these are modest telescopes 27 centimeter diameter 95 centimeter diameter they're in space to their pricey but they're still very modest the key thing is that they're up above the Earth's atmosphere and because of that they can measure the brightness to extremely high accuracy and that's what we needed to actually make these measurements of how stars are changing their brightness because the amplitude was very low people had tried this from the ground again many people tried for many years it's very hard so here's what these stars look like there's a large envelope that we call the red giant envelope here's this core of helium which is the burned ashes of the of the it's wiggling now it's not me you're giving me an oscillation the helium ash of the of the fuel that was burned during the main sequence and so here we go so Karo when it's a space and basically immediately every red giant it looked at was oscillating so each of these panels is a different star with a name you don't need to it doesn't matter what's shown on this axis is the frequency on the x-axis and the y-axis is just the amplitude how much brightness variations are there at that amplitude and they've ordered them in order of frequency so it's easier just to look at the bottom one so here's one again you see the frequency spacing like I showed you for the sun and you can see above some frequency there's no power this is just noise and you know that's noise because you go up and find another star and look this one again there's frequencies that are spaced and then there's nothing above it so basically their phenomenology is pretty much identical to the sun but the numbers are all shifted because the star is bigger if you want to think of it very simply these modes are quite small in amplitude 3 to 200 part per million that's why you can only do this in space from the ground it's very hard to do anything better than about 1% apart in 100 Kepler launched a little bit later bigger telescope more data same exact phenomena plays out these are all different red giants again it doesn't matter these are just different names for them numbers in the catalog I wanted to show you which is you take the frequency and divide by the frequency spacing and this is now you can think of this as how many nodes are there there's 10, 11, 12, 13, 14 number of nodes in the radial coordinate so again if you're a musician you're familiar with this as you modify and add more nodes the frequency goes up and that's the same thing you're seeing in these stars and so if I go back to this plot it's a little bit easier to see I can measure a maximum frequency above which there's no power and I can measure a frequency spacing so those two measurements allow me to get the mass and radius for the star now at this point you would say Lars you've not told us anything about what a theorist could contribute which is embarrassing so how does theory play a role in this theory plays a role in this by actually checking and confirming that what you're seeing is true by doing the honest calculation and those calculations well let me have really been one project that I was intimately involved in called Mesa which is a modules for experiments in stellar astrophysics which is an open source code and then a code really highlighted by Rich Townsend at Wisconsin called gyre which does the pulsations so these are calculations that are spherical stars but then we do the perturbation analysis to understand what the waves are and confirm or deny or modify the sort of simple story I've been telling you this is what early Corot data looked like for many stars that they had using underlying theory the radius of the objects the radius of the objects, their masses and their ages so it's pretty remarkable to think about looking across the galaxy and saying that star is one and a half times the mass, the sun it's three times the radius and it's a billion years old we've never had that capability so the impact of this work is not only for the stellar astrophysics someone like myself but also for those who are trying to understand how the galaxy has been created what we call sort of galactic archaeology to really understand how the galaxy was formed and when were stars made within the galaxy Kepler of course had a lot more data this is the distribution of the masses of the objects they found as giants it doesn't really matter this is just the best plot I could find for them ignore the red versus the blue and these are the radii and interesting things so for those astronomers in the crowd you notice that there's a radius for which there's about twice as many stars as usual well this is because there's a phase in a star's evolution where it actually burns its helium and that phase and that phase means that the star gets to live there for a time it's sort of the main sequence for the helium burning that's called the red clump and again we've known about this but it's just sort of sitting here in your face you know there's no star that's small again these things we've known for stars to become red giants they have to evolve and basically that's why there's almost no low mass objects here if there are any here there must have lost some mass somehow so there's a very very rich data set that really allows us to understand better what's going on here's sort of what it looks like in terms of the amplitudes so the other bit of phenomenology is as the star gets bigger it gets brighter as it gets brighter the convection gets more vigorous and as the convection gets more vigorous the amplitude of the modulations gets stronger so this is the schematic showing that so here's an object that's quite large probably maybe 50 times the radius of the sun this is showing a real data from this but even here it's not quite yet even at 1% but these are data this gives you a sense from space how well you can do but when the star is much more compact you also can see that the amplitude is lower but you also can see it's higher frequency and you can see straight away this has longer time scales in it than this does and so that object that's smaller oscillates at a higher frequency now the last thing I want to do is sort of one extra bonus there's two topics I'm not going to talk about which you can ask me which is rotation and magnetism properties that we never really get our hands on for distant stars that we can also do for these stars but I want to close with how do we know anything I've told you is true this is the question you should always ask sorry how do we know it's true well you get one extra bonus in this exercise which is that the observers have measured via a spectrum the surface temperature of these objects so these are objects for which we have surface temperatures I've now given you the radius via this right if it's big it's a long time scale right I've given you the radius and therefore you can calculate the luminosity just 4 pi r squared times the Stefan-Boltzmann constant times t to the fourth and this t is known so that's great so now I've told you that star you're seeing has a certain luminosity certain intrinsic brightness it's 100 watt bulb but I'm measuring some flux at the earth in my telescope and obviously as the object is further away the flux I see goes down and that's just shown by this formula the luminosity divided by 4 pi r squared so if I've given you the radius and the effective temperature you can calculate how far away the star is how else can we get distances to stars parallax parallax is we can all do the experiment now I'm going to find out who's awake in the audience this is great put your finger out awesome have it cover me now you've just discovered which eye is your dominant eye now switch to the left what am I doing relative to your finger I'm moving so parallax is the same phenomena but when the earth goes around the sun you make a measurement six months later of a nearby star relative to some distant object that's called parallax so you can do that and you can get the check on this this is first the data so I haven't given you the answer for the check but the Kepler satellite has these are the distances for all these different stars how far away they are in kilopar sex the center of our galaxy is about 8 kilopar sex away TASS is another satellite that's very actively doing this it sees stars it's not as sensitive so it sees stars that are closer by but GAIA is making these parallax measurements so GAIA is a European mission that's been up for five, six, seven years at this point and it's measured this parallax for many many stars so you can check so there's a prediction from the astro seismology that's on the books it's written down you go make the measurement and this is what you see so this is the distance as inferred by GAIA do the parallax so this is geometry this is the distance inferred by the seismology in the way I showed you okay and then here's the scatter so basically it's 5-10% accurate and this is the best baseline we also have things in binaries where you can do the same but it's quite remarkable and sort of tells us the power of what we've done in terms of accumulated understanding of both the astro seismology of the stars as well as the underlying astrophysics related to their behavior so in conclusion I really want you to come away with this strong understanding that when you look at the sky these stars are varying I wish we could all see it it would have been much more exciting but I wouldn't be giving the talk because you all would have known it because you grow up asking the question theory really remains a key part of the story so I love to show this plot these are the data the observer has for some star and the beauty of doing physics theoretical physics experimental physics is taking some data stream like that and now telling you it's a star that weighs twice the mass of the sun it's five times as big it's a thousand light years away and it's a billion years old so thanks this evening and I'm eager to take more questions it would be possible to measure the spectrum for the lensed stars it's a great question stars that get gravitationally lensed the likelihood test would be the only satellite that would probably have enough coverage to have the coincidence be detectable but I think the sensitivity is not there and test has a very crowded it has a very large pixel so the images would be crowded as my guess I don't know looks like we have a question here sure thank you so you can think of it if you will if you take a glass and you hit it there's typically just one frequency you put some water in it and hit it you get a different frequency so in physics we would call those different we call them eigen modes that are available given that body so when we take a star and we ask what are its free oscillations we have a few different variables we can consider how many wavelengths I'm trying to get to go around it how many wavelengths to get to go through it but I have to close that it has to be a free oscillation and each of those is a new mode that we would say is available to the star I hope that answered do these distance measurements have anything to say about the Hubble tension so the Hubble tension for those of you who are unfamiliar with it is the debate going on in the astrophysics community about the value of the Hubble constant which to me has been going on since I was a kid it's just the level of disagreement has really gotten much tighter the only variable stars that are used right now for this are what are called Cepheids which are variable stars that are dramatically variable these are naked eye variable stars the size of the star is changing by a factor of 2 short answer is no we're not having any impact on that problem but there are variable stars used as part of the distance ladder I have two questions but I'll just pick one you can come back to you start with the best one and then work your way down really early on at the start of the talk you made a point that the reason that you can tell a star's temperature just from the varial theorem and it's not to do with fusion and I find that very confusing because I mean like the probably the wrong interpretation of that is then a star stops fusing but it maintains its temperature and that sounds incorrect I was wondering if you could clarify what that means okay so the way a star works is the first part I told you is the easy part if you give me a mass and a radius that's how hot it is at the center okay that's step one step two is what's the rate of heat that's leaving the object okay so it's hot at the center it's cold at the surface so there's a heat loss which we call luminosity but just think of it as a heat loss so that then would say if the star has no energy and no fusion available to it it has to make up that heat loss by undergoing gravitational contraction upon itself so what happens is the star contracts upon itself the temperature rises okay until and that process continues the star contracts contracts contracts until you get to a temperature where something else can supply the luminosity and that's fusion and so if you so if you ask why is the sun have the radius it has today it's because that's the radius it needs to have to have the fusion luminosity match the heat loss and so it lives there just burning away happily for 10 billion years so yeah so don't let anybody tell you that fusion has set the temperature I mean well I have a bias here about how to explain the physics so I have a question here hey stellar formation yeah so let me give you one example so the sun today is in the interior I showed you has a certain rotation rate so this is called a month okay what's going to happen to the interior of the sun as it runs out of fuel is that core is going to contract because it's run out of fuel it can't match so it's going to contract if we didn't have any loss of angular momentum and it contracts of course it will spin up so one challenge we have in stellar evolution is that that spin up could be so dramatic that you end up being such a fugly held up that there's a rate at which basically you're matched by gravity and so what we are starting to see with astro seismology is we take stars that probably were like the sun and we see them today as a giant we see evidence that those deep cores have lost about 90 to 95% of their angular momentum already it's a big mystery about how it happens but we're seeing evidence that rotation that we're losing angular momentum from the interior and that is helping us because that will allow it to continue to collapse so it's not quite addressing your question but that's one way in which we can start to infer what's going to happen going forward does metallicity affect things at all especially on like the really like extremely metal poor end of stars yeah so let me unpack your question a little bit so in astronomy so many of you are physicists and a metal is probably well defined right it's it's something that conducts electricity typically right can this matter physicists like I was raised initially to an astronomer a metal is anything heavier than helium okay and the reason we do that is because all of those elements heavier than helium are being made in stellar evolution and so so when you have the first generation of stars there's no metals it's just hydrogen and helium but as you've gone through life cycles and made heavy elements then what we call the metallicity the amount of mass and elements heavy and helium grows that has a big that matters for the star because it ends up setting typically just how it radiates at its surface and so you can get different size stars due to metallicity so the answer to your question is unfortunately we don't have a lot of dynamic range of metallicity for these stars because they're all pretty much in the galactic disk so there's you know there's not a lot of metal poor stars but I mean there are some I'm sure in these samples but we're mostly studying red giants so the metal poor stars that are red giants are typically hotter than this but again they're fully convective so I wouldn't expect a big difference that's the technical answer I'll take questions all night you tell me when to be done okay our son has a well known solar cycle magnetic solar cycle does theory predict any other star stellar cycle one and does observation have any evidence of other stars magnetic cycle yeah so there's definitely other stars in our galaxy that undergoes cycles that are solar like in duration or period for sure the underlying theory for the cause of that is still actively debated it definitely has to do with the fact that in the sun there's a region between this fully convective region and the underlying material that's not convecting and you may have noticed that the solid sorry the interior rotates like a solid body but it's not solid it's a gas but the outer part doesn't and so there's areas where there's tremendous shear and the neutral point sort of at mid latitude and so the understanding is a lot of the magnetism and growth of magnetic fields that lead to sunspots has to do with that shearing layer and we think that condition is present in a lot of other stars set up but when you show the distribution of radii and masses of stars they didn't actually go down all the way to where stars and so you want to comment on that you mean this one yeah so right so this sample are the sample of pulsating stars via this method so these have to be red giants or sub giants or even barely on the main sequence so I think the board which you're asking is why not a 0.5 or 0.4 right so lower mass stars if you go to very low mass stars they are fully convective so everything I said is true they're bubbling and they're boiling but so far we've not seen any oscillations that are like this in those types of stars people have looked they keep looking the sense is probably because of the luminosity and the amplitude of the velocities it's not adequate to build up to be a detectable amplitude but because we can't really predict the amplitude we don't know so it would be really exciting we haven't found it yeah please yes is there a rendition earthly rendition of the music of the stars yeah I didn't do it because I think it's better if you imagine it personally but you have to decide what frequency you want to hear at so people have taken these Kepler objects and you shifted the frequency into the audio and I think if you probably look at I haven't googled it but I know you can find it Kepler music of the spheres you'll probably find it but yeah is there something like the sound barrier in other mediums and air so for example in water or in a star is there something like the sound barrier that could be broken that could create some interesting shock waves yeah yeah sure so so I think what you're asking about is sort of supersonic supersonic transport right so most of these stars the velocities I'm talking about of the motion are less than the sound speed so we're not causing shock waves there are other stars that are brighter more massive in particular more vigorous where we think the convective motion gets really close to the sound speed for these stars when it if it happens it's only in the very surface layers because the density is very low and so to carry the heat it has to move faster because it knows about the density so but we don't see anything here that tells us there's any shocks going on in these data but there's other data that many of us are actively pursuing other problems where we really care about the convection getting nearer to the sound speed yes for sure I may not have understood it properly but how in this theory do we account for the variance and viscosity of like the stars different layers so if you're a fluid dynamicist you definitely care about the viscosity of the fluid you're in and the measurement of does viscosity matter is compared to the velocity of the fluid and its link scale of the motion we compare that dimensionally to the viscosity these are in stars the product of those two quantities is so much larger than the physical viscosity that we ignore viscosity or to a fluid dynamicist it's that the Reynolds number is huge and so we don't worry about micro-physical viscosity like you would for molasses in any of these cases there's other ways of getting viscosity having to do with magnetic fields which is a very rich topic which I did not touch