 All right, welcome back. I guess everybody in this room knows about LIGO and the discovery of gravitational waves. So it's a pleasure to introduce Michele Valisneri and his first lecture about gravitational waves. Since we begin, thank you so much for your introduction and for inviting me here. I'm very, very happy to be at this school. I think there's a wonderful atmosphere, a wonderful vibe. And so I think I'm going to have fun over the next few days. And I hope you can learn a little bit also. I must say that I pitched this lessons more or less at the level at which I know cosmology. So I know cosmology very little. And I have assumed that most of you are cosmologists, so will be cosmologists. And so you don't know very much about gravitational waves. And you do need something. You do know something about general relativity. So this first lecture is going to be not blackboard. We'll keep that for later. It's going to be mostly slides and a little bit at a more qualitative level. So my affiliation with NASA, with the Jet Propulsion Laboratory in Pasadena, but over my career, I've worked on pretty much every experiment to detect gravitational waves from the Earth, from space, using radio telescopes. Not cosmological observations, but I know you heard about that last week, about BISEP. So I'll start with what gravitational waves in a nutshell, let's say. So this could be an elevator pitch. And when you're going home, you need to tell somebody on your airplane about this discovery. They ask you about how it is that Einstein's was proved right in February. You can tell them these kind of things. And you may not have the images, but you can wave your hands or roll something. So what are gravitational waves? Gaitesha always are ripples in space-time. So this kind of image, in addition to being somewhat hypnotic, if you look at it, you feel inspired, gets most of the facts right. So there are waves. They're propagating perturbations. In space-time, I think that's what the lattice there, all the lines, is supposed to tell you that space-time is a metric, there's a geometry, and that's what's changing. And they're emitted by the accelerated motion of massive bodies, sorry. And the way to get massive bodies in the universe pretty much is to take a binary of any kind, of black holes, of stars. That's your prototypical source of gravitational waves. So this is the platitude. This is the commonplace that everybody is saying, new window, new window. We've been saying this for 20 years. I got very tired of it, actually, at some point, because when you open windows, sometimes you don't see much. Sometimes you just get noise, and that's what we were doing for almost 30 years. We were opening the window and just hearing instrument noise, detector noise of many kinds. But now I can put it back again, because it is true, in addition to being a proof of principle and a very interesting test of general relativity, gravitational wave is also a new kind of astronomy, so a new way to learn things about the universe. This is Asher, of course, this image. This was also on the cover of a book by Italo Calvino, Cosmic Comic and Cosmic Comics, where if you read the book, it's apparent that he read quite a bit of general relativity, or he knew what science was about. And that book is about strange walls, and it's a good parallel to learning about general relativity, which is about, in many ways, how strange our world and our time and space are. So, window what, okay? On some of the most energetic events and systems in the universe, some of the conditions that gravity being weak compared to other interactions, you really need to do a lot of work, and you need to get some very special conditions in order to get gravitational waves strong enough that we can see them. Now, this is the comparison slide with the electromagnetic. The idea is that many people, maybe not those that you'll meet on your plane, but many people will be more aware of electromagnetic radiation and radio waves and whatnot. So, the comparison is that, whereas light from an astrophysical system will be emitted mostly by the surface, or by the environment, the nearby environment of the system, gravitational waves are emitted by bulk motion of masses. Okay, so it's kind of like the collective gross scale excitation of the system that you'll see. The typical strength are very small on the order of a part in 10 to the 21. This doesn't mean that these are not energetic, and it's not an energetic phenomenon. If you take the 10 to the minus 21, and you look at it in just in terms of energy that's contained in such radiation, you get something like, I don't know, one watt per square meter, something definitely, that would be really measurable by eye very well if it was photons. But it's not photons, it's gravitons. The spacetime is incredibly stiff, so it really takes lots of energy to get a measurable effect in creating ripples in changing distances. Because of this reason, spacetime is very stiff. However, gravitational waves also pass through and impede it through pretty much anything. You cannot screen them, you can lens them because they are, after all, a light-like particle, light-like photons, but you cannot screen them. It's very hard to absorb them. They are phase coherent, so again, you don't see just the sum of many photons doing their thing on the surface of a star. You see the phase coherent motion of a binary. So very interesting because it maps directly into the equation of motion of the system. Detectors tend to be almost omnidirectional. They have some kind of pattern of sensitivity, but it's usually very broad, which means that you don't make images, right, with gravitational waves. You're basically detecting one or two times series, and that's the analogy with sound. That's why the other platitude, in addition to the windows, is that you're here in the symphony of the universe. And you add that, maybe you have two detectors, so you say stereo. And you add that, maybe, let's go here. You throw it on, okay. Probably heard that already on some website early in February if you went to the news, but that's pretty much taking the instrument data in the one second around the event that was detected and turning it into sound, okay. Most of the woo that you hear is actually the tactile noise. You've done something to it. You've equalized the bit, the bands. Otherwise, you'd just be hearing the lowest frequencies where the noise is higher. The signal itself is just a little whoop at the end, okay, that you heard. And in this video, you hear it twice. The second time is pushed up in frequency. Since, after all, we're turning gravitational waves into sound and may as well change the frequencies a bit and to hear it better. It's all, you know, in good, okay. Black. You know, it doesn't sound too impressive, actually. There's a radio show on American Radio called Prayer Home Companion that's about the Midwest and good old values and so on. And one of the things they were saying, oh, this great, incredible discovery. Einstein confirmed and so on. And it sounds like whoop. And that's underwhelming. But however, this slide is, is a beginning or something, right? It's also the end of something, which is 20 years in which, in giving these lectures, it was all about the prospects and the promise and how people were trying to do things. So finally, it can be how something was seen and all about all the other, all the physics that we can draw out of, you know, those wave, those waveforms and those plots. And about many more like this that are going to come soon. Okay, rest of these lectures today is to go through quickly sources or some of the source highlights for me at least in gravitational waves and also to tell you about the three leading detection experiments that are operating today. One of which, LIGO, has reached this milestone of actually seeing something. Please, let's be socratic, okay? Let's do ask questions and comments and I think those would be actually the most interesting part of these lectures. I think the questions that you might have and that I couldn't imagine in advance, we should really try to get to those. And if I don't know the answer, I'll try to find it out, you know, tonight I'll go and look up either my colleagues or papers and so on and I'll tell you over this week and so on. And also please come find me during coffee breaks or lunch or whatnot, if you have something that you think is more, that is better discussed privately. I don't know, it's about your research or something that you want to know. So sources, there's a spectrum of gravitational waves just like there is a spectrum of photons and there's a spectrum of light and you get different sources and in different bands and you get different experiments to detect them. Very roughly, since geometrical units are the best way to do general relativity, the frequency, the typical frequency of emission of a source scales roughly as the inverse mass, okay? So at the highest frequencies, sound like frequencies of 10s, 200s, 2000s of hertz, where the ground-based experiments like LIGO and Virgo are looking, you have systems that are of stellar mass about the mass of our sun, like Newton stars or maybe several masses, several, up to several tens of our stars like the black holes that were observed in back in September. If you go lower, if you go from 10 hertz down to, 10 to the minus three hertz, so things that are changing with periods of one hour, you get to see heavier systems, typically supermassive black holes, massive and supermassive black holes. A million, 10 million, maybe 100 million solar masses, the black holes that we expect at the center of galaxies. So a lot of the sources you see are binaries, which is the easiest way in the universe to get some time-dependent quadruple. We'll talk tomorrow about the generation of gravitational waves and all that. But certainly, you know, you expect gravitational waves from early universe fluctuations, from exotic even phenomena in the early universe. You can look for waves in anything that goes boom or bang in supernovae, in neutron stars that are rotating rapidly and are somewhat non-homogeneous. And really, you want to look at every window in this spectrum. So you want to push all experiments and you want eventually to detect gravitational waves in all of them. So black holes, I think you know about black holes, but when people say that the discovery of gravitational waves confirmed Einstein's theory, they're saying the truth, but what they're saying is also somewhat limited. In 1916, Einstein had some equations. They predicted black holes. They predicted gravitational waves. But he didn't really believe in either. So he went back and forth on gravitational waves, whether they were actually physical events or just mathematical curiosities. He could only imagine that black holes existed back then. So it took 100 years not just to understand the theoretical implications of Einstein's relativity. Well, let's say 50 years. After 50 years, we had a pretty good idea of that, but also to realize that these objects, these predictions actually existed in the universe. So a black hole is something very impressive. It's perhaps one of the things that, you know, when I first studied general relativity, it led me to say I want to work on these things. I want to find these things because it's kind of like, you know, an elementary particle in space almost. It's a perfect mathematical solution. It's described only by two numbers, right? Mass and spin. There's no hair. That's all it is. And it's pure gravity. There's even no mass in there, no matter in there. And yet it's something that we've seen in, you know, low mass x-ray binaries, for instance, which are binaries where you have a star or a stellar remnant, you know, giving donating mass into a black hole that accretes it, gets it very hard, you get x-rays from it, a very high luminosity. You get it with time scales and we get it with inferred masses for this object that can pretty much only be explained by a black hole. Okay, so Cygnus x1, right, was the first system that was really considered a black hole. We also see the big black holes. At the center of galaxies, we infer the presence of big black holes from the orbits of, well, from the typical, there are many ways to see black holes at the center of galaxies, but perhaps the most striking is in our own galaxy, this detection there on the right, is measurements of stars in very tight orbits around an object at the center with an inferred mass of, you know, million four, 10 to the seven solar masses, and which you can just read off of just the Keplerian motion of the stars. And that object is very, very dense. And again, it begins, it's very hard for it to be anything else than a black hole, right? It's hard to make a cluster of stars that with this mass that's stable, it's hard to, you can make some exotic things, boson stars for instance, but even those are probably too large to be that object. So black holes are in the universe, black holes are massive, black holes can move very fast in a binary because they're so compact, okay? And so they can reach a velocities of maybe a third or half of the speed of light. Perfect, they are the perfect gravitational wave source, a binary or two black holes. And that's what was the first thing that was seen. So maybe you've seen this movie already. This is a, I can play it again. This is based on an actual simulation of the solution, a binary black hole solution of Einstein equations that was run on supercomputers taken months or years of CPU time. And it's the last maybe 15 cycle of an inspiral and the virtual merger of those two black holes. So this is all pure gravity, right? That's evolving here, nothing else. What you're seeing is actually the lensing of the, the lensing of the light from the background stars behind it. So this again got, this movie got me a little curious because it was played in the media lot, it's very pretty. So it will inform what the public thinks black holes are. And to some extent it's correct, right? It's two holes, it's two black things that deform space around them. But then if you look into it, there's something, there are some things that are missing, for instance. So that you could be wondering about. So let's start the socratic thing. So what's wrong or what's a little fishy about that movie? Yes? Yeah, so that assumes you have a very good telescope. So those I think in a sense are right, but one thing that's true in the, so one question that is how close do you have to be? Okay, to see that, to see that you have to be at 50 solar, at a distance, geometric distance of 50 solar mass from the binary. So that's pretty close. It's a question already whether you really have, you could really see gravitational waves there or you're in the near field zone where things are a little strange. But sure, where else? Yeah, so magnification. So the shapes are correct in fact, because that's a ray tracing simulation of just take the image at the back, send all the rays across the right geodesic, light light geodesics around the geometry and that's what you see. But magnification, you expect also to have an amplification of luminosity, right? So in particular, and not just that, red shifting, right? The big thing in curved backgrounds. So the light that gets really close to the edge would expect it to be really red shifted and not just the same color as everything else. So they didn't do that because that would get it pretty messy and not as pretty. You wouldn't see the edges as well, you'd be a little blinded where you have a convergence of light rays and so on. So it was fun to think that that's what the public now is thinking black holes are. Yes. Of the two black holes? Yeah. That's true, but there is angular momentum, right? And you don't lose that even at the very end. In fact, the final endpoint of the merger is a spinning black hole and most of the spin comes from the orbital spin. So it's true that it gets, the inspire gets to be lesser of an inspiring orbit and the radial accelerations are certainly stronger, but there still is some. So that's correct actually because that's a true solution of Einstein's equations. The other thing, the other small systems you can make gravitational waves with are Newton stars. So in particular here we're seeing a pulsar. Okay, one of the two Newton stars emitting radio emission along its axis and it appears to be pulsed to us because there's this lighthouse effect that we see the beam passing us. So that's a representation, a movie of the system that gave the original indirect confirmation of the existence of gravitational waves. Okay, the Hall-Stahler pulsars, this discovery in 1974, a pulsar in a binary, close enough that you have a loss of energy to gravitational waves and that the period of the binary period decreases over years with just the shape and with just the time-dependent that's expected by Einstein's quadruple formula. So by the leading order loss of energy to gravitational waves. So dual Newton stars, very good for that reason, already told us and showed us that gravitational waves exist. The other advantage that they had in the mind of LIGO analysts and LIGO physicists so far was that we knew that such systems existed. Okay, we knew in the galaxies at least five to seven double Newton star systems, all of which sometime in the future would be proper LIGO sources in the right band. And so that's, what's my next slide? This is an actual simulation as opposed to just an artist's rendition of a merger of two Newton stars. So Newton stars you think are definitely messier than black holes because they do well, matter. Okay, as nuclear matter. So you expect to have some very complicated interaction, hydrodynamic interaction even between the stars once they reach, they get close enough to break each other apart and then eventually merge. That's true and the systems are very challenging to simulate, but it's true also that for the band that the frequency band that's accessible to ground-based experiments, they're still pretty far. So treating them as point masses was sufficient to get a pretty good idea of what the waveform would look like. So that's both a blessing and a curse, a blessing because you could say we have Newton stars, they exist in binaries in our galaxies. One day they're going to merge. If we take a million galaxies, we're going to have one Newton star that merges every year on the average, close enough for us to see and we know how it's going to look like because it's just two point masses going around each other. The first approximation they are, they will be just the simplest Newtonian in spiral plus Einstein's energy emission that we're going to derive tomorrow, in fact. We can be actually more sophisticated and use post-Newtonian corrections to the orbits and do better with that, but it'll be a great first thing to detect. Then as we get more sensitive, maybe we'll also access this high frequency range of its emission, where the fact that they're not just point masses, but they're balls of nuclear matter and of matter as super nuclear densities is evidence and we'll learn things about the equation of state. The other attraction is that, you know, there are gamma-ray bursts, these very somewhat mysterious events and very energetic events, and Newton star mergers are expected to be the engine to produce short, hard gamma-ray bursts. So when you see a Newton star binary with LIGO, let's say, and if you're lucky enough to see also a gamma-ray burst in the same direction in the sky at the same time, you can get the final association of this. There's in fact a big industry of working out what the electromagnetic counterparts would be to such an event, a Newton star merger. Black holes are dark, so you don't expect to see anything, any light from a merger is just, gravitational waves is pretty much how you learn about it, but for emerging Newton stars, you could see a gamma-ray burst, you expect to see perhaps afterglows, you see radio emission, you have something called a kilonova, which is somewhat less than a supernova, and in, you know, with different timescales, so definitely enough to get astronomers excited about following up this event. And I was telling you, you get access to the hydrodynamics, to the structure of Newton stars, so that tells you about the equation of state of matter in Newton star, just the structure, and how matter behaves at the super nuclear densities, a regime that's not achieved or realized anywhere else in nature. So again, a big industry in theory in working out what the equation of stars are, that the equation of state is for Newton stars, and equation of state is mapped by this, you know, open-heimer-Volkov equation that you probably learned about in general activity courses, is mapped into a mass-radius relation, and you have stiff and soft equation of state, a stiff equation of state is where the matter pushes back against gravity more strongly, and so those are those that give you the largest radii, so the largest Newton star for the same mass. And you can certainly try to see this effect if you can see gravitational waves at high enough frequencies, and people have run simulations of merging Newton stars with, you know, some assumption about what the matter does and some simplifications, but definitely you can see that if you have a soft equation of state, smaller, smaller Newton stars, they can last longer in inspiring on each other before they break up and create a single merged object. It's kind of cute, I think, that the standard scale for the softness of Newton stars goes from 4B to 4H, to 4B, 3B, HB, 4H, which you may recognize as pencils, right? It's what you get graphite for, so that's become somewhat shorthand for that. And there's really one parameter, which is this tidal love number, so the tidal deformability of the Newton star, that's the parameter, that's the first one you would see having effects in the spiral. Because it's in addition to losing energy to gravitational waves, you're also dumping energy into the tidal excitation of the stars. A similar system that also can get you insight into Newton star equation of state and the structure of Newton stars is a mixed binary, where you have a black hole in a Newton star. So there you expect to tidally disrupt the Newton star when it gets close enough, right? Just the tidal field, so the fact that the black hole is pulling in slightly different directions in different places in the Newton star, breaks it apart, and how soon it breaks it apart depends on how big the Newton star is. So the first-order effect or something like this is that you have a sudden drop-off of a gravitational wave amplitude. So the wave form ends sooner because you've broken apart your Newton star into this cloud of matter. So I'm talking a lot about binaries because as I was saying, that the prototypical source of guidance are ways that the easiest way to get enough accelerated mass around to generate something that you can see. But in fact, there's really a lot that you can learn about it. About nature, about gravity, and about astrophysics from just these binary systems. And all that information is all encoded in the wave form, okay? The signal that you observe. So just quickly in this table, from stellar mass binaries, you learn about the populations of the systems, of the stars, stellar remnant that generated them. You may learn about the Equational State of Newton stars. You may learn about processes in that emit visible light or infrared radio whatnot around the system after it emerges from the inspirals of massive black holes at the center of galaxies. You learn about those populations. You expect massive black holes to merge because after galaxies merge, they each carry their big central black hole at the center. They find each other. They form a binary and some of them inspire quickly enough that they eventually get where they can be seen. To see those, you'll need something like Lisa, a space-based experiment. But they will tell you a lot about the co-evolution of galaxies and binaries across the universe. And of course, there's also GR. You can do all this business, but you're assuming that Einstein was right. That's our reference theory. That's what we're using. But you can also challenge it and try to test whether the waveforms that you observe are really those predicted by general relativity or whether the some alternative theory of gravity that's a better explanation from them. The other assumption is black holes. So we say, so you can look at astrophysics, you can look at fundamental physics in terms of whether Einstein was right, really whether GR has any alterations at this level. You can also try to test whether these black holes are really black holes. Are really the simple, short-should or cur solutions that you get from your equation or is there something different about them? You can do those with binaries also, especially with a very asymmetric binary where you have a small black hole or a small neutron star spiraling into a very big one. A system like that takes a very long time to spiral because the slowing down of the loss of energy of the small body is proportional to the ratio of the masses between them. So you expect to be able to follow those if you have a space-based experiment for hundreds of thousands of cycles. If you do something like that, that's a very, very high precision measurement of motion of quasi-geodesic motion in a background geometry, a black hole geometry, and that would be a very good test of the nature of the centrologic by way of its multiples, for instance, by the gross structure of geometry around it. Okay, so lots of binaries. There are other sources that I know less about because I think, I always thought there were more speculative and a little bit more high-risk bets, in a sense, to see. So let's see. So for instance, supernova, which is there at the bottom, well, definitely you expect to have some non-spherical asymmetric acceleration of mass in a supernova. The problem is that it's relatively little mass, little enough that you hope to see, you can probably hope to see one if it's in our galaxy only. And supernova in our galaxy, they come once a century. Okay, so worth looking for, and worth doing the analysis for, but probably not a very good bet in terms of making money. So think there at the bottom left are cosmic strings. Okay, so this hypothesized fundamental object generated in the early universe, which should give off gravitational waves very nicely, thanks to this very pretty kinks and also string recombination and so on. But speculative object, also one for which we don't really, we almost have no clue about what its typical parameters would be. So worth looking for, and so we write in papers about where we don't find it, but not the mainstream source. At top left, that would be an isolated pulsar. So a single Newton star, that's rotating very rapidly. How do you make gravitational waves from that? Not just from the rotation. You either need to put it tumbling, to have some kind of tumbling and possessing motion that gives you a time-dependent quadruple, which is what you want. Or you can put little mountains on it. If you just stick things to it and make it rotate very fast, that's your dumbbell, that's your time-dependent quadruple again. Problem is, those are such strong gravity. They're so small so then it's very hard to make mountains on Newton stars. So some of the papers in the LIGO collaboration that were in the last 10 years were claimed to be to have astrophysical significance, were put in limits on the non-ellipsoidal deformations of pulsars in our galaxy, such as the crab. Okay, but those limits were probably still a few orders of magnitude away from the kind of deformations that you may expect to have. And then relic, gravitational wave radiation, things from cosmology, things from the early universe. Very interesting for what they could tell you about the early universe, but pretty hard to come up with a scenario that makes them strong enough that you would see them with current experiments. They tend to be really suppressed for ground-based, for Lisa, for pulsar timing, which is the third technique I'll tell you about in a little bit. See my time, okay. There was an experiment called the Big Bang Explorer, which was kind of like a high-powered super Lisa in the sky, super expensive and super future, which was supposed to reach the standard inflation level for gravitational waves in a desihertz or hundreds of a hertz. So if you live to be a hundred, some of you may see such an experiment. Okay, let's move on to the main ways to look for gravitational waves at different frequencies, but let me take a quick break to see if there's a question about this, or comments or sources. Yes, the abundance, okay. So the question is about the relative abundance of different sources. That's usually taken experiment by experiment because there are people, say, doing LIGO, they want to know what they're going to look for. So if you look at LIGO, so sources between 10 and 1000 hertz, as I was saying, the mainstream Bona Fide system was a dual Newton star, a double Newton star, because we knew that these things existed. Okay, and with rates of about maybe once per year at a good sensitivity a little more if you're lucky. Okay, so black holes, black holes would be more rare, but they would be stronger signals. So you could actually see more with the same experiment per year. The problem being we didn't know that they existed. We actually didn't know that black hole binaries existed until one was seen back in September. So with that observation, I think now those black hole binaries are probably considered more abundant and to have higher rates for the same moving volume in the universe than Newton stars. Mixed system, we don't know at this point. So all that we know are from population dynamic simulation, but those have lots of uncertainties. So the way you come up with something like that, you start with your typical stars, with an initial mass function, put them in binaries, and then evolve those binaries through simulations and through lots of theoretical assumptions. From two stars, you have to do two supernovae, okay, to get the Newton star and a black hole. And you have a common envelope phases, very, very complicated physics, so that the final results had the orders of magnitude uncertainty. So really very little is still known about those rates other than what we can tell from observations, which will be the driver going forward. If you look, I'll talk a little bit later about sources in the low frequency band. So, but there, supermassive black holes certainly assumed to be the most dominant source, but there's something else. There are binaries of white dwarfs, typically, in our galaxy. Okay, so there are probably 100 million such binaries in our galaxy, and all of those would be sources for space-based detector, some below the threshold of individual detection, so just making up some kind of stochastic noise together, and some above it, maybe thousands. Okay, so detection. Since people are getting prizes for gravitational wave detection, and you know who those people are, okay, so I thought it was worth going a little bit back to the person who probably started the whole thing. So Joseph Weber, who in the 60s, started doing experiments with resonant bars to detect gravitational waves, and actually for a few years was convinced, actually throughout his life, he remained convinced that he had seen them. He couldn't, however, convince the scientific community, and also replications of that experiment couldn't find them again. But still, this early excitement in the 60s of some detection of pretty strong events, things that were challenging to explain in energetic terms in our galaxies, those got all the excitement started and got all the movement going that eventually led to the big interferometric detectors, and to the ideas to do things in space. So that's, in the 60s, Joe Weber, University of Maryland, the first bars, that's where everything started. These kind of detectors actually are not, are also outside the standard paradigm of gravitational wave detection that I'm going to discuss in the next slide, because they're actual physical resonant things where what you're observing is the shaking, is the ringing of a big physical object, okay, a bar of metal. And in that sense, a gravitational wave going by is pretty much a tidal force that excites the fundamental mode of resonance of this mass. But for modern detection, it's easier to think of it in this way. So you have the gravitational wave, that's actually the particle physics view of gravitational waves, where you have a graviton emitted by a binary, and all that you need to make it, to look for a gravitational wave is a good clock. Why? Well, because actually you need two clocks, maybe. If you compare two clocks that are displaced by space, you can get an idea of the time that it takes for light to travel between them. And a gravitational wave will alter the distance of two freely falling clocks or test masses in a way that's periodic, okay? So it will apply a modulation on that distance. And that's what you look for in all the experiments to detect gravitational waves. If you're using pulsars, as I'll show you a little bit later, you basically are doing a one-way measurement. You have a very good clock out there. You're comparing the time that you see from that clock with your own local reference, and suddenly you see a difference between the times because, which you don't care about, but what you're looking for is kind of like a modulation on the difference of the two clocks, of the rates of the two clocks. In something like LIGO or LISA or Doppler tracking, whereas when you look at spacecraft going, say to Saturn or to Jupiter, you send a signal and you get it back. And again, you compare with your local reference, you look for some modulation. You're doing two-way measurements, okay? You have something like a mirror back there. So maybe there's only one clock that really matters, is the clock that you start with. So you're measuring. So measuring time is really how you see changes and periodic changes in distances between test masses. So that's the principle of the technical waves. And now different ways to realize this for different frequency bands, but as in all physical measurements, there's noise, okay? No measurement is perfect. In practice, you're limited by how well you can make things and buy basic limits of nature. And all the noise curves, noise curves are a big thing because they tell you where you're sensitive, which are your frequencies, and they tell you how strong you're going to, how well you're going to see a signal. They all look like that, okay? So they're good in the middle, then they go bad on the sides, which I like to describe as must get better before it gets worse, just the opposite of what happens in life, hopefully when you have some traumatic events, it gets worse and better. Here, it's the other way around. And the reason that happens is in very general terms, is that so we're measuring the distance, perhaps as measured by light, between two freely falling objects. That's the basic measurement. So then there are two big things here. One is how well you can measure that distance, just in metrologic terms, okay? So to what fraction of a wavelength of light. So that's imprecise measurement, and that's what eventually worsens, gets you to be less and less sensitive at high frequencies. Okay, there's another effect there, which is also that your experiment needs to be commensurate with the waves that you're looking for, so that if the wavelength, coagulation wave get to be much smaller than the reference distance that you're measuring, then the effect basically cancels out. Okay, so that's also built into this imprecise measurement. On the other side, at low frequency, what happens is that these freely falling test bodies, well, they're not really freely falling. On the ground-based experiments, you have masses suspended on pendulum that are supposed to be freely falling in that direction, right, in the directional measurement. Well, there are residual noises of them, so they're shaking a little bit, and that, to you, looks like a gravitational wave, but it's not, in space, same thing. And for pulsars, for pulsars, you have that, the reference clock that you have, your, the rotation of the pulsar is not quite stable as you expect. So then, you know, you map that into the actual experiments, and so for instance, the measurement noise for ground-based is photon shot noise, effectively, just your limitation in measuring a distance based on how many photons you have. There's thermal noise at low frequencies, space-based, similar story, shot noise and acceleration noise. So there is actual acceleration on the test masses at low frequency. And pulsar timing, again, timing noise, so measurement noise and at low frequency, stability noise, the stability of your basic reference. So these are the three leading techniques to detect gravitational waves, each maps to a different frequency band, high frequency for LIGO, for ground-based, LIGO and Virgo, ground-based experiments, low frequencies, 10 to the minus 3 hertz, or around that for space-based, and even lower frequency in nanohurts, so 10 to the 9 hertz for measurements that you do by looking at Newton stars as a reference. So I'll go through each of these in turn, and I have a few movies for that, but we're also going to do a simple computation on the blackboard. So the basics of a ground-based interferometer are the fact that, you know, if you make a simple Michelson scheme where you split light at the beam splitter, you send it to distant mirrors, then you get it back. Okay, if you arrange everything so that the arms of the interferometer are perfectly equal, then you have a perfect destructive interference at the output port of the interferometer so you don't see any light. On the other hand, if now the arms are changing a little bit because the gravitational wave is going by, you get a little bit of constructive interference or not as perfectly destructive, and you get some power on the output port of the interferometer. This is the basic of interferometric detectors, and they're sensitive at in the tens to thousands of hertz. And they're incredibly precise tools, incredibly precise experiments, so because you need it. Okay, so I'm going to show you tomorrow that the typical, and we said already, that the typical amplitude of a gravitational wave on Earth for something that you expect to see about once per year is a part in 10 to the 21. Okay, so let's see how we can, what we need to measure something like that using interferometry. Let's see, first of all, this is a strain. Okay, so this is a fractional change in length. So how big an effect we see depends on how big we can make the interferometer. The biggest we make it, the more we amplify this effect. So what can we make on Earth? People started in their lab, so it was five meters, then they took over a building in a university so it got to be maybe 40 meters, and then you start saying, okay, what's the biggest that I can make such a thing? And it's around, it's something like four kilometers. If you go beyond that, it's a problem to find a place that's flat enough, and also you start to have a problem because the photons are falling in the gravitational field of the Earth. Okay, so we have four kilometers, so that means that the effect that we're going to see is going to be something like five, give me a five, 10 to the minus 18 meters. Okay, so that's pretty small. You may worry that you'll actually have, that you get into a small fraction on the size of a proton, so how do you measure this small fraction on the size of a proton? Well, you're not measuring that, okay? You're measuring something that's macroscopic, a heavy mirror, something at the end, so that's fine. The wave length, the quantum wave length of that is way smaller than this. That's not a problem, but how do you measure it? Okay, with interferometry. Interferometry with a laser, that's the most stable light we can get. Typically use infrared lasers, so the wavelength of an infrared laser is going to be something like a micron. Okay, so 10 to the minus six meters. So that means that we have to go down to something like, we have to resolve a difference in phase in a wavelength of the order of 10 to the minus 12. Actually five, 10 to the minus 12 cycles. So that's, by contrast, I think the original Michelson measurement, which established that the speed of light is constant in every, no matter what your state of motion is, okay, was on the order maybe of a 20th or a 100th of a wavelength of light. So, although we still call that a Michelson interferometry, there's a very different Michelson interferometry. So how do you resolve such a small, such a small wavelength? Well, the idea is that use lots of light. Okay, so typically you can resolve interferometically a distance to something like the wavelength divided by the square root of the number of photons that you have. Okay, so let's see. A decent laser, something that is going to burn your retina if you're pretty fast, if you look at it, it's something like one watt. So, how many photons in one watt? An infrared photon of one micron is about one electron volt, maybe it's 1.2. So that gives you something like, and also that's power, but we are going to effectively integrate our measurement. So, you need to turn power to energy before you count photons. We want to observe things that run around the 100 hertz. So that gives us 10 milliseconds to integrate the one watt power. So that gives, if you work it out, it gives you something like five, 10 to the 16 photons. The square root of this is something like, you know, okay, two, 10 to the eight. So, the gain that we can get in addition to this is something like four, 10 to the minus nine. Okay, so, four, 10 to the minus nine. And we need five, 10 to the minus 12. Okay, so we're still a little off. So what can you do? You know, the answer already you can still tell us. Let's say you don't have to solve it on the spot. Yes? Ah, of course. Put an amplifier in front of the laser and keep it stable enough. So in advanced LIGO, in fact, you're working with something like 200 watts. Okay, so, you know, which is pretty powerful, but it still won't burn things down. So, however, that only gives you a factor of, again, a square root of that. Okay, because number of photons, you gain with the square root of the number of photons. But that's good. It gives us a factor of what square root of 200? Okay, 12, 13. So, 14, actually. So we need another factor of 100, roughly. So, where am I going to get that? Yes? Yes, yeah. So, since the most we can do is four kilometers, but how about we do multiple bounces? Okay, so, one way you could arrange it is actually to put your mirrors in just a way that you do some complicated scheme and bounce back, but you can only do that two or three times before you get to, you start confusing the beams and getting stray light into one another. So, what you do instead is that you turn your microphone into what's known as a fabric pearl interferometer by making cavities along both arms. So, you have a mirror here that's going to be only partially reflective so that once you put light inside the cavity, you will tend to, on average, to do something like 100 bounces back and forth, and then it filters back. So, that's true on the average, right? Because some, if you look at the individual photon, you can say, okay, this photon went back after doing one trip and some other when did 100 and so on. On the average, let's say 100. So, that's the fact of 100 that you need to get something like 10 to the minus 21. You can do other tricks, you know, you can typically put a mirror here also. This would be a power recycle mirror so that all of the power that would, you know, in a microphone will go back to the laser is actually reflected back in. You could put a mirror here also to do what's known as signal recycling, which is modifying the optical state of the layers in such a way that you get a little factor again. Of course, if you put a factor of 100 here, that means that your circulating power is going to be 100 times that inside the cavities. So, it starts to be on the order of kilowatts and you start to warm up things significantly. And so, in fact, cooling down the mirrors when you have a kilowatt of light that's impinging on them is one of the challenges. I go. Okay, so I did my little blackboard thing, so I'm happy. Three big gum-based interferometers, the two LIGOs and Virgo, which is a French-Italian interferometer in Tuscany, in fact, in Cascina in Tuscany. So, initial ideas in the 70s, built in the 90s. Science runs in initial configuration for both LIGO and Virgo in the 2000s. Didn't see anything. But finally, upgrades that got them down to this final factor of 10. So, initial LIGO didn't quite have that 200 watts and had some other reasons to have reduced sensitivity. So now they're both advanced. Virgo is not quite online yet at this final sensitivity. So, it's hoped to be taking data together with the LIGO interferometers maybe at the beginning of the next year. And these are very complicated instruments because that's the basic measurement I gave you, but of course, there's all kinds of noise on top of it. So, for instance, you can't afford to have any gas you can't have your lasers propagating through any significant gas because you get dispersion or have any gas around the test masses because they get buffeted and get shaken by it. So, you have high vacuum in a kilometer-scale environment. You have a very complicated seismic isolation because everything on the earth shakes. So, you have kind of like four stages of pendulum attached to four stages of the other way around of active suspension. You need to have high power lasers and your mirrors, they have to be very ideal objects. They can be shaking themselves because they're warm or they will be because you're operating at room temperature, say, but you want to have them to be such perfect monolithic chunks of silica, in this case, that all the thermal noise will be concentrated at a perfect frequency. So, the Q, so the quality factor for these mirrors is something like 10 to the 7, which means that if their typical model oscillation is, say, at 10 Hertz, then the damping of an excitation will be 10 to the 6 seconds. So, they ring forever, pretty much. And that quality factor also tells you how concentrated noise is in the typical frequencies, the natural frequencies of oscillation. And that's what all those lines are, in fact. All the different thermal modes of oscillations that you have in the system, the masses, the pendulum, all that is concentrated onto little lines effectively you can just notch out, cancel out of your experiment. And that's what the improvement is between the faint lines and the solid ones is between the first generation, the initial light interferometers and the advanced ones. And that's the factor of 10. And it's the factor of 10 that made all the difference between seeing only noise and between getting finally the signal. You needed the factor of 10 to have enough galaxies within your range, that even something that happens only every million years for each typical galaxy, you get in a year shorter time than a year. There's a broader international network of ground-based interferometers that includes Virgo, but that also includes an interferometer in Japan and a coming one in India, which is actually a copy, a replica of one of the US interferometers. So, the reason you want to have many is that just the two or the three detectors don't tell you very well where a source is in the sky. I'll tell you more about that on Thursday, maybe. The position in the sky, you get pretty much from the time of flight of the signal between the instruments. And to do better triangulation, you need a more solid, as opposed to plain configuration. So, whereas with only the two LIGO, Hanford and Linnestone, you can probably position typical events to hundreds of degrees in the sky, which is very, very bad, right, compared to what the telescope would focus on. With the entire international network, you can probably do something like over the one degree in the sky. We'll need a few more years to have a full network online. Okay, science goals, a lot about binaries, but of course, supernovae, as I was telling you, deformed neutron stars, cosmological backgrounds. There's really lots of different sources that they're looking at. Let's go to space, okay? You replicate the idea of doing interferometer in space. In space, you have a lot more space, okay? Also, things move more slowly. You don't have to worry about seismic noise. So, the concept was Lisa, right? The triangle so that you could actually do three interferometric combinations, flying around the sun, a little bit beyond Earth, once per year, okay? So, an Earth-based orbit. And the interferometry you do there is a little simpler because let's say instead of four kilometers, you're going to have something like five, 10 to the 10 million kilometers, okay? So, that's a factor of a million that you gain there in your measurement. You lose on the number of photons because again, you have your one watt laser, something like that. Maybe a few watts that you can, something that you can build and put on a spacecraft. It's hard to do 200 watts in space without significant solar panels and whatnot. So, and by the time you're sent a laser five million kilometers away, it's really broad, okay? Even a laser is the focus to maybe a mile in diameter. So, you're at the level of a pico-watt, maybe 10, maybe 100 actually, pico-watt at the distance spacecraft. So, the number of photons that you get is only something like six, 10 to the 11. It's low power, but the loss from this is more than made up for that. So, in fact, Lisa, although it's in space, it seems extremely difficult to do laser interferometry at millions of kilometers, is actually about a million times simpler than doing it on the ground, which is good because if things break in space, you can't really fine tune things in space when they're up there, you can do a little, but what the video is showing you in the meantime is the interferometric setup. And it should have shown you here, right, that you don't have hanging mirrors from pendulum space. What you have is these cubicle test masses that you have to put into an approximation to free fall. And the way you do it is what's called a drag-free configuration. So, you have this little cue that's a reference for your measurement at the center of your spacecraft, and you monitor it and you move the spacecraft around it so that all the stray forces from solar wind, from, I don't know, micrometer, right, it's a little dust and so on, you're protecting the test mass with the entire spacecraft from them and using little thrusters on the sides of the spacecraft to move around it. So, you're really protecting free fall at the center for your points of reference. And now, actually, let me skip this a bit for a second to tell you that it's recent news just from last week that this free fall in space, this drag-free configuration was tested in the Lisa Pathfinder mission, which was flown by the European Space Agency with also some NASA components. After a long time, it was a long time coming, okay? When I got into the Lisa business, Lisa Pathfinder was promised for 2005. And actually for a way smaller budget that they eventually got. But finally, it was launched last year. It just reported the initial results. Pathfinder is not a full Lisa. It's just basically, in a sense, it's just taking one of these 5 million kilometers and fitting it within a single spacecraft. So just to 50 centimeters. So what it tests, it's not the interferometric measurements. It tests that you can actually keep two test masses in free fall to sufficient approximation that eventually Lisa would be possible. And so that's what I think I have a zoom here. So that's the configuration. Two test masses and you're measuring the relative distances and you're still pushing on the spacecraft using thrusters to keep it in approximate centered. And the measurement was actually quite spectacular. So in space experiments, people like to be conservative so that they can claim a success when things are done. So the wedge at the top, that gray wedge was the required accuracy, the required precision of the, sorry, the required tolerance in free fall for Pathfinder. In fact, the experiment did much better. It reached something like 1.25 times the Lisa requirement. So you could take that system that flew on Lisa Pathfinder and you could use that very system on the Lisa spacecraft and you get effectively the promised Lisa performance. The residual noises that you see are at high frequencies sensing noise. So just limitation on your interferometry. At mid frequency, residual damping from the gas around the test mass and at low frequency a centrifugal force. So that piece of news where what was a June 7th, the release it was the second thing that make people very happy this year other than the live announcement. So it's hoped, it's really hoped that going back here, the Lisa mission, which was again promised to me as a grad student for 2011 and on which I did work for 10 years at NASA and then which was then canceled in 2011 because NASA had other more expensive things to see and is now a mission for the 2030s by the European Space Agency. Well, we hope we can maybe push that a little forward and doing it a little earlier on the wave of excitement for the detection of gravitational waves and on this confirmation that the basic technology for free fall that the Lisa will need is actually not just feasible is proven. Okay, how much time do I have? 15 minutes. So this little animation here was to to show you something amusing I would say which is in space you cannot make the arm sequel because you're limited to what trajectory is around the sun will give you. So typically your triangle is pretty unequal. If you do that, your basic microphone doesn't work, you're not canceling out light after you reflect it back. And if you're not canceling out light that means you're not canceling out the basic noise in your laser which is something you would easily confuse with gravitational waves. So there's actually a very pretty scheme in Lisa which is called a time delay interferometry where you create a basically double microphone where you're sending light along both paths before you recombine it. And you don't really have mirrors because as I was telling you by the time you get to the distance spacecraft you're at 100 picowatts. So if you just put a mirror there you're going to get 10, 20 minus 12 of that back and that's no photons at all. Okay, so what you do is instead of putting in a mirror you actually measure the laser between all the pairs of spacecraft. You take these measurements and then you sum them up with the right time delays and you reconstruct in a synthesized interferometer that's what time delay interferometry refers to. And since you're doing that you may as well doing as many bounces and complicated schemes as you like. So there are many complications on top of that you can send light around do what's called the Sanyak scheme. You can do quadruple bounces and so on. And that's the kind of things that I was doing working on Lisa about 10 years ago. So while I'm definitely not an experimentalist who can build a real interferometer it was fun to do it by just taking signals and summing them algebraically. Yes, yeah but that gives you an narrow band interferometer. So you only need one arm actually. You don't even need to do interferometry if you can do a measurement like that. But you want to be broadband because you want to see spirals, chirping signals like you want to see lots of things. Okay, so this was a slide with the classic Lisa science goals. So in spirals solve massive black hole binaries these extreme mass ratio systems, M-rays where you have a small body go around the big one, lots of cycles. All the light blue dots are binaries in a galaxy of white dwarfs typically and the yellow one assistants that are known optically as binaries to be binaries of white dwarfs. So things that you know are there and that they will be there once Lisa turns on. So those are guaranteed sources for Lisa. One thing that another reason for excitement is this blue lines on the right, LIGO binaries. Somebody calls them actually Cezana binaries for Alberto Cezana who pointed out that they exist. And the story behind those is that the system that was seen by LIGO earlier this year with black holes of 30 solar masses is actually heavy enough that if you go back in time a year or two it would be in the Lisa band or in a Lisa-like experiment band. So you might have the same system that you first see here with a space-based interferometer for a year because it's evolving slowly and you wait and then you see it with a ground-based interferometer. So it's a new source, it's also an exciting prospect to do things together with the two. If you have one year of advanced notice you can do some things. For Cezana you make sure you're taking data when it comes but also you'll know roughly where it is in the sky because Lisa in astronomical, in telescope terms has a very long baseline, it's going around the sun. So the parallax to the source is big that puts it in the sky with a reasonably small error. So positioning is much better in this low frequency band than in the big. So that's the same thing, it shows you the power of the signals from heavy stellar mass black holes as it gets out of the Lisa band and into something like advanced LIGO. Okay, so last one, last technique. Oh, okay, I have more audio here. So that's a pulsar, okay? So a Newton star emitted in radio waves along the poles but the emission axis is misaligned with respect to the rotation axis and if you're lucky to be in the right direction you get this lighthouse effect, okay? And that's why it's a pulse and which you observe as a periodic signal with the periodicity of the rotation of the Newton star. So these were the systems that were discovered by Jocelyn Belburn Nile right in 1967 and the fastest of this ones, the millisecond pulsars that have periods of a few milliseconds are very, very good clocks. So those are what we think are the recycle pulsars, so pulsars which have been accelerated again by a creating mass from a donor. So they are the lowest end of the period scale on the x-axis and they also have the weakest magnetic fields. So these are precision clocks, of course just so you can just, if you have a very good clock on the other side of the galaxy, you can use that as your gravitational wave detector, okay? You just look for the change in the time of arrival of these pulses as a gravitational wave goes by your path of propagation. The typical precision on this clock is something like at best 10 nanoseconds over 10 years, okay? So you want to look for very slow signals with periods of once, the joke appears one over a grad student lifetime, okay, a grad student tenure. You want to observe them for 10 to 15 years and what you need to do, however, is to take out lots of physics still because these pulsars tend to be in binaries themselves. Of course the earth is moving around the sun, so there are lots of deterministic signals that give you apparent changes in the time of arrival of the pulses. These are, in fact, interesting. They tell you where the thing is in the sky to great precision. They also tell you the period of the binary. They tell you the change of the period in the binary as they did for the host tail of pulsar and thus proving the existence of gravitational waves indirectly 24. And they even tell you the fine details of the orbits so that you can test gravity with them. You can look for the precession of the peri-astron, for instance, in such a system. You can look for gravitational redshift of the signal as it goes around the companion in the pulsar. So you take all those effects, you parametrize all of those and you fit all of those from the times of arrival of these pulses and what remains is a gravitational wave signal. So this is extremely fun, I must say, to do for somebody like me because instead of doing very complicated optics and buying big lasers, you get to use radiotelescopes, point them at the pulsars and you can say one that you have the largest detector of them all because it's the size of the galaxy. And that's true, that's your baseline. And second, you can say that to understand my experiment, I don't need to understand just lasers and oscillators. I have to understand the Newton star physics and I have to understand the physics of propagation of signals across the galaxy. So that's a lot of fun and these pulses are really amazing objects. You may know this, some of you may have a shirt that looks like that. Maybe you're not old enough to have it because the Joy Division had a, was it unknown pleasures? I don't know, they had a record that had these iconic plots of pulses from the whole state of pulsar in the seven, maybe the early eighties. The thing is, these things are rotating very rapidly. You don't actually see the individual pulsars. They're too weak individually to be seen like that. But once you sum them up, you align them, you get an integrated profile. Say you do it for 10 minutes so you get 10,000 pulses or 100,000 pulses. And that integrated profile is extremely stable. So that's your clock, it's not the individual pulses. And this stability of the integrated profile is actually an empirical fact. It's not fully understood why it should be like that. It's probably due to the fact that the emission mechanism is stochastic for the radio emission, but the geometry and the geometry of the rotation is very precise, effectively. So you get your regularity from the geometric stability of the system and the fact that the emission is periodic just feels in this profile stochastically, but in a way that integrates back to a very constant term. This is not a great simulation, but it's not not a great video, but it shows you two supermassive black holes at the center of the galaxy. And then there's this strain of gravitational waves that comes to you, which, I don't know, reminds me of Disco more than Joy Division for some reason. And if you have a pulse, that's our galaxy. Okay, you have a pulse that are sending you pulses. And again, the fact is to slow them and to get them faster to you depending on the phase of the gravitational wave. It's also shown as being red and blue because you could also describe that as instantaneous redshift or blue shift of the signal. You don't want to do that with a single pulsar because you may understand it, but you won't trust it. It's not something that you built. It might have some changes, some noise in its rotation. So what you do is you do it for an array of pulses across the sky, maybe 40 of them. And then the fact of the gravitational waves at the moment when the signals are received on Earth is going to be common to all of them. Actually, better than common is going to be correlated with the geometric factor that depends on the angle between any two pulsars. So you can build, there's a curve known as the Hellings-Downs curve, which tells you how correlated the residuals due to gravitational waves are going to be for any pair of pulsars. And there's an international collaboration that tries to do this. Actually, there are three national or sovereign national consortia, European, American, and Australian that are competing to see gravitational waves. And the main signal is the stochastic signals from the black holes at the center of galaxies. So all of them out to a Z of maybe one. And so far we've only done upper limits. So we've only determined that the data taken over the last nine, 10 years cannot support the existence of a signal from all those binaries stronger than some level. But these upper limits are beginning to impinge, let's say, on the theoretical predictions. So we should, in effect, our projections are that we should be able to see the signal within the next 10 years. If the astrophysicists are right about how many binaries of massive black holes are at the centers of galaxies. Okay, so that's the end of it. And that's the other hypnotic thing, more Asher. I like this field because there's some geometric perfection to it, and there's Einstein theory, which is very pretty, but there's also lots of details. And lots of things you can learn about the dirtier physics and surprising things about the universe. There should be a lizard somewhere in there, if you can spot it. I don't know what it's supposed to represent, maybe some kind of exotic star that we don't know about. I can see a dinosaur, but there's also a lizard, yeah. And there's also a lonely observer somewhere sitting on some step. Okay, so my last slide, I checked out of it, but tomorrow we're actually going to work a bit through equations in general activity that give you gravitational waves and the point to see that they're natural, actually, that they're a natural prediction, and we're going to derive basic in spiral equations. On Wednesday, I don't have a lecture, but actually I have a talk where I'm going to tell you a lot more about the system of black holes that was seen back in September. On Thursday, I'm going to tell you about the data analysis and statistics technique that lets us extract information from these signals. And on Friday, it's a little bit miscellaneous kind of thing, so applications with cosmology and to testing GR. And if you have questions that you come up with in the meantime that you're going to need, for which I'm going to need to look up things, please tell me today or tomorrow, and then on Friday I'll try to tell you about them. So thanks a lot.