All right, I'm gonna go ahead and get us started here today. So welcome to everybody online and of course, physically in the room. It's my pleasure today to introduce our colloquium seminar speaker. This is Dr. Nevin Weinberg. So he comes to us from UT Arlington and he earned his bachelor's degree from the University of Chicago and his PhD in astrophysics from Caltech. He was a postdoctoral fellow at the Cavalry Institute for Theoretical Physics at Santa Barbara. If you've never gotten a chance to visit there, find an excuse, participate in one of their programs and go. That place is amazing. And also at the University of California at Berkeley. He joined the MIT physics department as an assistant professor in 2011 and became an associate professor in 2016. He then joined the faculty at UT Arlington in 2020 where he is currently an associate professor of physics. His research interests include stellar fluid dynamics, tidal physics, gravitational wave sources and thermonuclear explosion but they just get more dramatic as you go up the list. Thermonuclear explosions on a creating neutron stars or X-ray bursts as they're politely called. So we're very pleased to have Dr. Weinberg here today to lecture on when stars go non-linear, large amplitude tides and stellar oscillations. Please welcome our speaker today. All right. Definitely audience online. Okay, great. Thank you. Thank you very much for the invitation and for the introduction. So let's see the picture you're looking at here which maybe some of you have been looking at now for a few minutes is a picture of photograph really of Jupiter's moon Io taken by the Voyager 1 mission in 1979 as it passed near Jupiter. And so Io is on a slightly eccentric orbit which means that it experiences a time-dependent compression and expansion as it passes closer and further from Jupiter and that compression and expansion heats up Io's interior. And so Io is actually the most geologically active body in the solar system decided small size and age. And a nice illustration of that geological activity is this volcanic plume. You can see spewing out the top of Io here. And so in this talk, I'm gonna be describing tides in completely fluid bodies, not rocky bodies like Io. But I like this picture and this idea because I think it nicely illustrates an important theme of the work I'll be talking about which is that sometimes tides can have a really dramatic influence on a binary and its components as I'll describe. And so before I get going, I just wanted to acknowledge my collaborators who have been working with me on this problem for a number of years now especially the students that have worked with me. So Reed Essek who's now a postdoc at the Perimeter Institute, Mohamed Morbit who's now a graduate student at Youth Yarlington working with me. Deborah DJ Promenade who's a graduate student at Princeton and Hong Yu who is a student who worked with me at MIT and is now a postdoc at Caltech. And also of course the funding resources which have supported this work. Let's see. Oh, that's right. Oh, let's see. Well, I can always just click with my hand, that's fine. Okay, so this talk sort of can be broken up into two parts. In the first part, I'll be focusing on tides in stellar binaries and in exoplanet systems. So systems where you have two sun-like stars orbiting each other with short period orbits and orbital periods of days. So those are called solar binaries. I'll talk just very briefly actually about neutron star binaries which are important gravitational wave sources and probably spend the most time on short period exoplanets systems called hot Jupiters. And then in the second part of the talk I'll switch gears a little bit and talk about seismology. Sometimes referred to as asterose seismology. And these are stars that are isolated but have waves excited within them. And by studying those waves, observing those waves with telescopes and then analyzing those observations you can learn about the interior of the star. So basically these waves are providing a window into the stellar interior that you wouldn't get from just the photons which of course are just coming from the outermost layers of the star. It's not working. Oops. I see there's a delay. So there we go. So yeah, tides. So I think a nice place to start when you're talking about tides is the classic tide system, the one that Newton studied, the Earth and the Moon. So obviously this is very exaggerated but the idea is that the Moon of course raises a tidal bulge on the Earth in the Earth's ocean. And that tidal bulge leads the Moon's orbit, right? The Moon is orbiting in this counterclockwise direction and the Earth is spinning in this counterclockwise direction and the tidal bulge or this angle delta leads the Moon's orbit. And the reason it leads is because the Earth is spinning faster than the Moon orbits, right? The Earth is spinning on a time scale of a day and the Moon is orbiting on a time scale of 28 days. And so you can sort of think of this as the Earth is dragging the ocean at the base of the ocean in the crust. It's dragging the water with it and the Moon is pulling it back. And the net effect is that this bulge slightly leads the Moon. And if you now decompose the forces acting on the Moon, there's a component of the force that's pointing towards the tidal bulge. And if you now think about it, there's an R cross F, there's a torque acting on the system. And that torque leads to an exchange of angular momentum. So the Earth's spin is slowing down, is losing angular momentum and the Moon is gaining that angular momentum. And so as a result, the Earth's spin is slowing down by something like two milliseconds per century. And the Moon is moving away at something like four meters per century. And we can actually measure that motion. Small as it is, we can actually measure that motion because the Apollo astronauts left mirrors on the Moon and we can shine laser lights from Earth at those mirrors and time how long it takes for that light to reflect. And that time allows us to measure the distance of the Moon to a centimeter accuracy. In fact, we need to account for where on the mirror the laser light hits, right? Because we're measuring it so accurately. And so this four meters per century is roughly a nanometer per second, which is roughly the rate at which your fingernails grow. And so this guy showing how far the Moon has moved away over the last 10 years. I think that used to lag. Okay, good. So another interesting system where tides are important is hot Jupiters. So these are Jupiter mass planets with orbital periods of just a few days. In 2019, the Nobel Prize in physics, half the Nobel Prize in physics was awarded to two astronomers, Mayor and Kalos for their discovery of the first exoplanet orbiting a sun-like star. And that planet was a hot Jupiter. So these are, Nobel Prize physics worthy systems. The other half of the Nobel Prize went to a cosmologist, Jim Peebles. And so if you now analyze the tides in these systems, you can show that the torque is in the opposite direction from the Earth and the Moon. So the star is spinning more slowly than the planet orbits. The planet orbits with a time of maybe days, whereas the star spins if it's a star like our sun with periods of tens of days a month. And so the bulge that the planet raises on the star lags the planet's orbit, it points behind it. And so if you now analyze the torques acting on the system, the planet is spinning up the star. It's transferring the orbital angular momentum to the spin of the star. The planet is losing angular momentum. And that means the planet is falling into the star at some rate, it's inspiring into the star. And the question is, and that, this was something that people noticed or realized right away, back in the early 90s when they first detected these systems. And there were big surprise when they first found them and they quickly realized that the tides would be dramatic in the system. But the question for all these years has been, what's the rate at which that in spiral occurs, that infall occurs? And that depends on the efficiency of tidal dissipation in the star. Essentially, what's the effective viscosity of the star? And so I'll be describing work with my students that have addressed exactly that question. What's the rate of infall? Okay, so how do you go about studying these problems? So you can do something, what you usually do is something that I like to call tidal perturbation theory. So the idea is you take this spherical object, just gonna make sure I have a timer so I can see what time it is. So you have this spherical object, a star, and you put a companion near it and the spherical object becomes ellipsoidal. It takes on this kind of football-like shape. And the amplitude of that distortion, delta R over R, depends on the ratio of the masses of the companion, say the planet to the star, little m over big M, times the ratio of the radius of the star to the separation of the system cubed, right? And so if you now think about the fluid forces in the star, the fluid response of the star, the fluid equations are inherently non-linear. So there's restoring forces due to pressure, due to buoyancy within the star, and you're perturbing those forces with this delta R over R. And so just like in a Taylor series expansion of a non-linear equation, you get terms that are linear, non-linear, and so on. Same is true of the fluid forces. There's a linear term. There's a term that's quadratic in delta R over R, cubic in delta R over R. So there's this full expansion in terms of delta R over R that you can express the fluid response in terms of. And so what most studies of tides, dating back decades have assumed is that you can ignore these non-linear terms. They've basically said for the systems that we're interested in, we're going to assume that we can ignore those non-linear terms and just do what you might call linear title theory. And really the motivation was one of simplicity. It's a lot simpler to just keep the linear terms. The non-linear terms, as I'll give you a feel for, are complicated and in an ideal world, we can ignore them. But the question, of course, is that true for the systems that we're studying? Is that a good description of nature? And so there's both, I think, observational motivations and theory motivations for not dropping those non-linear terms in many of these systems. So from the observational side, some of the best measurements we have of title dissipation in binary systems comes from these observations of solar binaries, sun-like stars. And so we see these systems in sometimes eccentric orbits. And you can show that over time, tides will circularize in orbit. And so you can use this collection of solar binaries that astronomers have observed in clusters of stars and place constraints on how efficient tides will circularize a system. And when you look at the numbers, you find that linear theory predicts what are called quality factors. So if you strike a bell and you ask how many times does a ring before the amplitude falls off by one e-folding, you say the Q of the bell is a hundred or a thousand. Linear theory predicts that the Q of the star is 10 to the nine. So it's a measure of the viscosity of the star, the title dissipation efficiency. And so the larger the number, the less efficient. And so linear theory says 10 to the nine, but to fit the observations, to fit the circularization of these binaries, you need Qs more like a million, which tells you that linear theory is underpredicting the efficiency of title dissipation by factors of a thousand or more. Question. They're out of contact, they're separated. Yeah, so they're orbital periods of a few days to tens of days. And so they're not Rho-Slob overflow, or anything like that. They're pretty close. Yeah, and the title effects are strong, but there's no mass transfer between them. So another system, another type of system where there's indications that linear theory is getting things wrong are these hot Jupiters. So when you look at the orbital distribution of hot Jupiters, how many planets there are as a function of orbital period, you find that there's evidence of orbital decay in these systems. There's measurements you can place on, or constraints anyways that you can place on the Q of the star that is orders of magnitude smaller than the linear theory estimates. Again, just like with the solar binaries. And then finally, there's stars that some people call heartbeat stars. These are binaries that the Kepler Space Telescope saw that you see individual modes of oscillation, waves in the star are excited. And there's pairs of waves that they see in any given in some of these stars that whose frequencies add up to the frequency of a third wave, which is exactly what you expect from non-linear interactions of waves, triplets of waves interacting with each other. And so you can only explain those observations if you account for the non-linear effects I'll be talking about. So those are all the sort of observational motivations. On the theory side, you can do calculations of tides and stars and show that the waves are gonna reach such large amplitudes in portions of the star and regions of the star that they're gonna become unstable to various non-linear interactions and excite secondary waves. So the primary wave reaches a large amplitude and excites secondary waves. And I'll be talking more about this in a moment, but you can do these calculations that basically can convince you you need to account for these non-linear effects that the linear title theory is not enough in many of these systems. And then when you account for those non-linear effects you can show that they significantly enhance the rate of tidal dissipation exactly in the direction that the observations are pointing that the efficiency is greater than the linear theory predictions. So these sort of considerations motivated us about 10 years ago to develop some of the formalism and computational techniques to study this problem of non-linear tides. And so over the last few years we've kind of been systematically applying these tools to a range of problems, including hot Jupiters, compact object binaries, binary neutron stars and white dwarfs, which are important gravitational wave sources and also isolated stars in which waves are excited through internal motions within the star, astro-sizing measurements of red giants and other types of variable stars. And so there's this range of examples. In all of these cases, the question is that we're interested in is when are non-linear effects important in which systems? And when they are important, how does it impact the system? How does it impact the evolution of the binary, for example? And so an important component of the story that I'll be telling you is that when the tide perturbs the star it excites oscillations within the star, waves in the star, modes of oscillation. This is sometimes referred to as the dynamical tide. And so I just wanted to give a very brief primer on modes of stars and the types of oscillations they can support. So there's something known as P modes. The P stands for pressure. So pressure is the restoring force. So basically these are sound waves in the star. They tend to have short periods in the sun periods of order minutes. There's what are called G modes where G stands for gravity. So there the restoring force is buoyancy or it's sort of like gravity waves that you see when you throw a rock in a pond. These are internal gravity waves within the star and they attempt to have long periods, orbital periods of hours to days. An important property of these G modes is that they only propagate in radiative regions of the star. So this is supposed to be like a sunlight star and this sort of granular region is supposed to represent the convection zone. So the outer third of the sun is convective. So these G modes can only propagate in the interior of a sunlight star. And then finally another class of modes that's important if the star is rotating rapidly enough are inertial modes where the restoring force is the Coriolis force. And those tend to have periods of order the spin period of the star. And so a particularly important class of modes for tides are the G modes. And that's because they can have these long periods, periods of days, which means they can be resonantly excited by the planet or the companion star, which also has a period of days. So you get into a situation where you have basically a driven damped harmonic oscillator that you're driving resonantly, you're driving these modes resonantly. So there's a really neat terrestrial example of this resonant dynamical tide here on earth, the Bay of Fundy in Nova Scotia, Canada. So this is a Bay that's about 300 kilometers in length. And the natural oscillation frequency of this Bay is about 12.4 hours. If you think of the oscillation frequency of a bathtub, it's maybe a second, right? This is because it's so big, it's 12.4 hours. And that just so happens to be the tidal forcing period due to the moon. So the moon is resonantly exciting the water in this Bay. And as a result, you get this huge tidal range, 15 meters between high tide and low tide, vertical difference between high tide and low tide, twice a day. So twice a day, you get this and twice a day, you get that, right? All this water comes in and out of the Bay due to this resonant dynamical tide here on earth. And so in getting back to stars, the tide can excite many waves in a star, but in linear theory, those waves all pass through each other and don't interact. They sort of obey the principle of superposition, but pass right through each other like ships in the night. Whereas when you start accounting for non-linear effects, these second order and third order terms in your fluid forces, you start getting wave-wave interactions. And so at second order, an important type of wave-wave interaction is something known as a parametric instability in which you have a, we can call a parent wave that's directly excited by the tide, by the forcing of the companion. And if it reaches large enough amplitude, it can excite daughter waves of half its frequency. And whether that happens or not depends on the amplitude of the parent wave, the strength of the coupling and the vertex of this Feynman-like diagram. I know there's some high energy physicists here. So a shout out to them, right? And then there's the frequency of the daughter waves whether there's really pairs of daughter waves that can add up to the parent wave frequency. But the important thing is that if this happens, if this instability occurs in the star, you have a new source of dissipation in the system, right? Because suddenly this parent wave can lose energy to these daughter waves. And those daughter waves themselves can have very short wavelength, much shorter than the parent. And so they can be much more efficient at thermalizing the wave energy and just depositing it as heat within the star. And so this is a new source of dissipation that you have in nonlinear theory that's not there in linear theory and could potentially lead to a faster rate of tight induced orbital evolution. So in a moment, I'll describe where you have many, tens of thousands of interacting waves but as a sort of toy example, a toy model of the problem, I thought I'd start by just showing you what happens if you have just a three wave system. And so this plot here shows the energy of a parent wave as a function of time. And I initialize the parent to have basically zero energy, turned on the tide, and the parent starts growing in energy due to the tidal driving. And if I didn't have three wave interactions, the parent would follow this blue line here and reach some linear equilibrium. Basically it's the solution to the driven damped harmonic oscillator problem that probably you've seen in your undergraduate physics classes. But when you now allow for three wave interactions, when you now allow the parent to couple to other modes or a pair of other modes in the star, what happens is the parent can reach a critical energy sort of shown by this dashed line here, horizontal line. And rather than reach the linear energy, it starts to undergo this kind of sort of complicated limit cycle interaction with a daughter pair, which initially has zero energy, but then grows exponentially, right? And so the non-linear solution to this system is very different from the linear one. You have a parent that doesn't quite reach the same energy and a daughter pair that in linear theory would have effectively zero energy, excited to large energies. And so this can obviously then affect the efficiency or rate of dissipation in your system. Okay, and so in terms of the parameters of a binary, you can ask the question, which systems are unstable to these three wave interactions, to this parametric instability? And the sort of relevant parameter space of the binary is the mass ratio of the binary shown on the vertical scale. So the mass of the planet or companion star to the main star as a function of the orbital period. And this jagged black line here is the threshold for the parametric instability. So anything below that line is stable to the parametric instability, and anything above it is unstable. And so as a point of reference, I put a hot Jupiter on this diagram. So Jupiter has a mass of about 10 to the minus three, the mass of the sun. And if it's a hot Jupiter, it has an orbital period of a few days. And so you can see that a hot Jupiter is well inside the unstable region, well above that jagged line. If you think about a solar binary, those have mass ratios of order unity, right? There's two stars, maybe two sun-like stars orbiting each other. So they're sort of off the scale of this diagram. They'd be up here, but they'd be unstable out to tens of days to this parametric instability. So nonlinear effects are extremely important in both these hot Jupiters and solar binaries. And you can do the same kind of analysis in different types of systems, white dwarf binaries, neutral star binaries, and show that in many cases, for the short period systems, the nonlinear effects are important. The linear approximation fails, that you can't just ignore those nonlinear terms because it's simpler, right? You have to account for them if you really want to understand what's going on in your system, right? And so the question then is, if you're unstable to these wave interactions, what are the implications? How does it impact the evolution of these systems? And so now I'm gonna sort of starting getting into the specific systems that we've studied and applied some of these ideas to. And so this is a problem that my former student, Reed Essek, investigated the orbital decay of hot Jupiters. So as I mentioned, these planets are falling into, inspiring into their host star, but the question is at what rate, right? Are they sitting out there for essentially eternity, right? Much longer to say than the main sequence lifetime of the star, or are they falling in relatively rapidly? And we're only catching them in a moment before they basically merge with their star. And so if you go back and look at this diagram again, right? These hot Jupiters are well inside this unstable region. So it's not as if there's just a single daughter pair that gets excited by the parent wave. You have hundreds of daughter pairs that are unstable. Those daughter pairs reach such large energies that they excite granddaughters. And those granddaughters reach such large energies that they excite great granddaughters. And you get this kind of cascade of modes of waves excited in the star. And so what we did is simulate the resonant excitation of tens of thousands of these interacting modes by solving a large set of non-linear coupled amplitude equations for these systems. And so here's just one example of one of his simulations. So this is showing mode energy versus time for some of the modes in one of his mode networks. We're not, I think it's one out of every hundred modes. If we showed all of them, it would just be a blur and you wouldn't see anything. So we just picked out one out of every hundred randomly. And what you see is that the energies fluctuate in kind of this chaotic way. At any given moment, there's the different colors of different modes. So some of the modes are excited some of the time and then they die off and another mode is excited. So there's kind of this randomness to the energy of the modes. But if you then ask what's the dissipation in the system and the way you can calculate that is by calculating the damping rate through to each mode times this energy and summing all those up, right? And so each mode contributes a small amount. You sum up each of the modes contributions and you get this plot on the right. This is showing the total dissipation as a function of time. And after a kind of burn-in period for our run, you sort of, you get a saturation of the dissipation. You basically reach a non-linear equilibrium that you can turn into a measurement of the total dissipation in your system, which in turn tells you how much energy is being pulled out of the orbit and thermalized inside the star, which then tells you the rate of the orbital decay of the planet, how quickly its period is decreasing with time. And so this is what we found. So in terms of, again, this quality factor, which is again a measurement of how efficient the dissipation is in the star, we found that for a Jupiter mass planet in a one-day orbit, the Q of the star is around 10 to the five, 10 to the six, right? Which is orders of magnitude smaller than linear theory prediction. Linear theory, if you did the same kind of analysis, but ignored the non-linear terms, would give you Qs of 10 to the nine, 10 to the 10, which would say that the planet should basically sit there for all time, the decay so slow that you shouldn't have to worry about it or think that it's gonna happen on a time scale of the star's evolution at all. Whereas when you account for these non-linear effects and account for the fact that Q is this small, you find that the orbital decay time is less than a billion years for planets on orbital periods less than about two days. Meaning that the orbit is gonna decay in a significant way on less than the time scale of the age of the star. And then the question of course is there observational evidence for such orbital decay? And so there is some indirect evidence. So you can do a statistical analysis of the number distribution of hot Jupiters. How many hot Jupiters there are as a function of orbital period. And there's indications that there's fewer very short period planets than you would expect if only linear theory was at play. And so there's the evidence of a clearing out of the shortest period systems. But there's not that many hot Jupiters with orbital periods less than two days. There's maybe a dozen or so. And so you're sort of in the small number statistics regime. So you can't do a really precise measurement of Q in this way. There's some hope that the test space mission, I know some of you take observational data with tests. So not in the context of exoplanets, but obviously one of the goals of tests is to find exoplanets and to find hot Jupiters. And so it's finding many more hot Jupiters. And so there's some hope that we'll have better statistics in the coming years and be able to do this kind of analysis more definitively. That said, there is a really interesting hot Jupiters system called WASP 12B, which shows direct evidence of orbit decay. So this is a planet on an especially short orbital period or just a little over a day. And what astronomers have been able to do, so they detected this planet in something like 15 years ago and measured its orbital period really well through the transit timing. Basically the planet eclipses its host star. And what these transit timing observations do is they come back 10 years later, 15 years later and look at where the planet is. And they can say if the period was perfectly constant, the planet should be exactly at this spot 15 years later. It'll have orbited the star thousands of times in that time scale, but if the period is really constant, you can be able to say exactly where it should be. And instead what they find for this system is that it's a little bit ahead of where it ought to have been if the period were constant. It's consistent with the period decreasing at a rate of something like 30 milliseconds per year. Not much, but look at the precision at which they can measure them. Again, because they're sort of integrating over this long time scale.  So much less than a billion years, much less than the lifetime of a star. And so then the natural question asked is, can you understand this as being the result of tidal dissipation of orbital decay? And so we studied this problem because it seemed like this is the ideal system for the kind of problems, kind of questions we're interested in. And so we analyzed the system specifically and found that if the star is a sub-giant, then what can happen is you excite a wave, internal gravity wave in the outer parts of the star at the radius of convective interface for subtle reasons. If you ask me, I can tell you them. And what happens is that internal gravity starts propagating towards the center of the star. And as it propagates, its amplitude deep increases due to geometric focusing. So basically you're trying to put the same amount of wave luminosity in a smaller and smaller volume of the star. And so the amplitude increases. And what we found is that the amplitude gets so large as it approaches the center of the star that the amplitude becomes larger than the wavelength of the wave. Delta R becomes larger than lambda. And that's the condition for what's called wave breaking. So we've all seen this when we go to the beach and the waves come to the shore and they turn over and crash. So these waves propagated thousands of kilometers in the open ocean and then deposit all their energy right at the shoreline. Just like this wave propagates throughout the whole star and then deposits all of its energy in angular momentum right in the center or very close to the center of the star. So this is sort of maximally efficient tidal dissipation. This is an example of strongly nonlinear, not even weakly nonlinear, like the parametric instability that I was talking about, strongly nonlinear wave breaking. And so you can do a calculation of this and what we found is that the implied dissipation is very close to the one that you observe, that there's a good agreement between the theory estimate and the observation of period change. And so I think this is a really nice example of nonlinear tidal dissipation. The one sort of outstanding question that remains is is this star truly a sub giant? So from the parameters of the system, we can't quite rule out the possibility that it's not a main sequence star, right? There's sort of an open question whether the star is on the main sequence or has just evolved off the main sequence in a sub giant and that matters because it changes the structure of the star and therefore the efficiency of tidal dissipation. And so really to answer that question, we need more precise measurements of its stellar parameters. People have tried to do that with Gaia and seismic measurements. There isn't, I don't think great prospects of doing much better than they've done, but it sort of again is an open question that remains to be answered. Okay, so another aspect of Hot Jupiters that I think is interesting and of course important is how they form, right? How do you form a planet so massive, so close to its host star? So you can show that in the protoplanetary disk, that close to the proto star, the temperatures are so high that you don't expect gravitational instabilities in the disk to form a Hot Jupiter. You don't expect the direct formation of a Jupiter mass planet that close to a star. So the preferred explanation for how you form these systems is that they form somewhere further out, maybe where our Jupiter forms. And then somehow some mechanism brings them into this very short period orbit close to the star. And so one mechanism that people consider is something known as high eccentricity migration. The idea is you have this planet on initially a circular orbit far out. It gets kicked into a very eccentric orbit by another planet in the system. There's a third planet or second planet system, a third body in a system that perturbs the Jupiter and puts it on in a very eccentric orbit, eccentricities of 0.99. And as a result, the planet passes really close to the host star. The paracenter passage is only maybe 10 stellar radii or even less. And as a result, the tides are really strong. The tides not just in the star, I've been focusing on tides in the star, but the tides also in the planet become really strong. And the idea is that those tides will circularize the system, tides remove, tend to circularize systems, and you end up with a Hot Jupiters we see, these nice circular short period systems that we see. The problem with this high eccentricity migration scenario is that if you assume the tidal dissipation in the planet is like our own Jupiters corresponding to queues of around 100,000, the prediction before Kepler went up was that there should be several high eccentricity systems in the Kepler sample, whereas Kepler didn't see any. And so, well, what does that tell you? Well, one possibility is that maybe the high eccentricity migration scenario isn't responsible for the formation of most Hot Jupiters.  And there are others, people talk about disk migration where the planet in spirals in a disk as opposed to high eccentricity migration. But the other possible solution is that maybe this assumption that our planet, that these Hot Jupiters have the same quality factor as our own Jupiters is incorrect. Maybe their queues are much less than 10 to the five and they circularize so fast that it's not surprising that Kepler didn't see them because they spend so short a time in that phase of their evolution that you just wouldn't have expected Kepler to see any question. So how many Hot Jupiters? Oh, and I forgot to repeat the question. So how many, the question was how many Hot Jupiters there are in the Kepler sample? I think there's, on the order of dozens, tens of, yeah. So what do you say separately? Yeah, three or four or five, yeah. So the error bars are actually big enough that you can say, well, maybe we just got unlucky because you're sort of small numbers in six. That was for linear title. That's for linear title theory where you assume that queue is 10 to the five. That's correct. So there's an important class or type of title and interaction that takes place in very eccentric systems. This is something that goes by the name of Diffusive Tide. It was first discovered in the mid-90s in the context of stellar binaries but more recently has been applied in the context of these highly eccentric Hot Jupiters and the high eccentricity migration scenario. The idea is to follow them. As the planet passes through Paris Center and gets really close to the host star, the title kick of the planet, the title perturbation of the planet excites the F mode of the planet. And F mode is the fundamental, F stands for fundamental mode of the planet. And that title kick is so strong that it excites the F mode to a large amplitude that F mode can back react on the orbit. Basically, the energy of the F mode is so large it takes so much energy out of the orbit that it changes the orbital period enough that the next time the planet comes around, the phase of the F mode is slightly different from the phase it was in the previous Paris Center passage. And so you get this kind of random feedback interaction between the phase of the mode, each Paris Center passage. And you get, you can show it's, you can show that the energy of the F mode undergoes a kind of random walk, diffusive walk so that the energy increases linearly with orbital cycle. And then the question, you know, this is something that people appreciated a few years ago and we got to think about this problem and realize that the mode energy can become so large that again, you start wondering about nonlinear effects and how important those might be and understanding what's going on. And so with my former student who's again now a postdoc at Caltech, he and Phil Harris and I studied this problem and found that indeed nonlinear mode coupling can be important in these systems and lead to a very efficient dissipation of mode energy. So efficient that you would expect the cue of the planet during this high eccentricity phase to be only around 10 or 100. So, so small, the efficiency so great that it very rapidly circularizes orbit on timescales of tens of thousands of years. And that timescale is short enough that it's then not surprising that Kepler didn't see any high eccentricity systems. The phase that they're in lasts for such a brief time given the sufficient dissipation that it's not surprising Kepler didn't detect any of these systems. Okay, so I'm not gonna have time here to go into tides in binary neutrosaur as I still wanna leave time for the seismology of red giants. I'll just briefly mention some of the key things that we've thought about and why tides might be important in these very interesting systems. So these are of course systems that the LIGO gravitational wave detector has observed. There's been two binary neutrosaur systems that the LIGO saw and to a first approximation you can treat these neutrosaur as point masses but since they're actually merging at some point in the in spiral tides are gonna be important. And the question is how does that impact the gravitational wave signal? So tides will speed up the rate of in spiral by some amount. They remove energy and angular momentum from the orbit on top of the loss of energy and angular momentum associated with the gravitational waves. And so that is a signal that in principle you can hope to see with gravitational waves. And if you can detect it, you can use it as a constraint on the properties of the neutron star and say something perhaps interesting about the equation of state in the core of the neutron star, which is significant unknown because the densities are several times the nucleus of terrestrial matter and we can't probe such high densities in the lab. And if we can use astrophysics of neutron stars to do it we learn something not just interesting astrophysically but about fundamental physics about the strong force and QCD. And so people have of course wondered about this problem but just like with the stellar and binaries and hot Jupiters that I talked about they've in large part ignored nonlinear effects. They've said, well, let's just do the linear problem. Let's also treat the neutron star as a normal fluid as opposed to a super fluid which we think they are because they're old and cold. And so in some studies that we've been doing we showed that both effects can be potentially important that super fluid effects might impact the tidal signature and the gravitational wave signal as well as nonlinear effects. But as I said, I'm not gonna have time here to go into those details but I'm happy to talk to anyone afterwards if they have questions. Instead, yeah, what I'd like to do for my remaining 10 minutes here so is to switch gears a little bit and talk about waves in isolated stars stars that are not in a binary so the waves are not excited because of tides but instead are excited due to internal motions within the star. For example, convective motions within the star. And so in the 1960s, astronomers made the unexpected discovery that our own sun is awash in sound waves. The photosphere of the sun is just oscillating in sound waves. This is an actual image of a small patch of their sun taken by the Stanford Solar Telescope. And those variations are basically sound waves that are excited by turbulent motions in the convective zone of the star. So again, the outer third of the sun is convective and these sort of bubbling eddies excite sound waves that we see at the surface. The characteristic time scale of those oscillations is minutes. There's what's the famous five minute oscillation of the sun which is the characteristic period of these oscillations. So this movie that I just showed is sped up significantly time would be kind of boring to watch a movie of something very on a five minute time scale but the idea is the same. But what you can then do is do a Fourier transform of those fluctuations and get a power spectrum. And this is what you find. So this is power as a function of frequency and you see individual spikes at specific frequencies in the power spectrum. And those frequencies correspond to oscillation modes of the sun. So you're seeing the ringing of the sun much like an instrument has a characteristic modes of oscillation. You're seeing the characteristic modes of oscillation of our sun. And what's interesting about that by analyzing where those spikes occur and their frequency spacings, you can learn about the internal properties of the sun. So even though you're seeing the only the surface aspect of the waves, those waves propagate throughout the sun and their internal and the spectrum depends on how the material they're propagating through the internal properties of the sun. Very much like you can use earthquakes and the seismic measurements of earthquakes to learn about the crust of the earth, the mantle, the inner and outer core. You can do the same with the sun. You can basically see inside the star. And so for 50 years or so, the sun was really the only star where you can do such a measurement with significant precision. But about a decade ago, 15 years ago, this field really underwent a revolution. And that was in large part due to the Kepler space telescope. So Kepler was designed to see detected exoplanets by looking at for transits of these planets in front of the host star. And it needed really good photometry to do that. And one of the sort of secondary pieces of science that came out of that was that it could, it was really good at looking for luminosity fluctuations in isolated stars. So we can measure fluctuations of like a part per million in the stars, enough to see the waves, the impact of the waves on the brightness of the star. And so it made such astro-sizing measurements for tens of thousands of stars, including tens of thousands of red giants. So of course, a red giant is a star that has evolved off the main sequence. It's no longer burning hydrogen, it's core. And it's gotten really big and puffy. And it has a convection zone that excites these waves. And so just like with the sun, you can take a Fourier transform of the light curve of the stars and you see something similar. You see these spikes at specific frequencies corresponding to oscillation modes of the red giant. And so these kind of measurements for again, tens of thousands of red giants has allowed astronomers to probe the evolutionary state of these red giants, measure the rotation profile, which has interesting implications for the angular momentum evolution of these stars and also provided really powerful scaling relations that tell you from just any one star, it's mass, radius, and age with significant accuracy. I mean, if you think about it, when you look at a star, you really have no idea what its mass and radius is, right? But suddenly we have this way of measuring those properties for tens of thousands of stars across our galaxy. So this has impacted not just stellar physics, but also galactic physics. There's a field called galactic archeology that sort of underwent a revolution too because of these measurements. Because suddenly now you can age and measure the mass and composition of stars all across our galaxy with great precision. And so one of the things that Kepler saw, noticed, is that the amplitude of the oscillations of the red giants increases significantly the more evolved the red giant is. The more evolved the red giant is, the larger it is, it gets bigger and puffier, the older it gets. And the larger the observed amplitude of the oscillations more. So that's sort of shown schematically in the plot at the top, more quantitatively in the plot at the bottom, this is showing oscillation amplitude delta L over L, luminosity fluctuations in parts per million as a function of the luminosity to mass ratio of the star. And so as a reference point, here's the sun. So it has luminosity fluctuations of about a part per million. Whereas the red giants have luminosity fluctuations of tens to hundreds of parts per million. So the energy is that squared. So the energies of the modes in these red giants is thousands of times larger, tens of thousands of times larger than in the sun. And so people have wondered whether nonlinear effects are important in the sun and they're sort of maybe marginally important. But given that the energies are so much larger in these red giants, the question is that we were interested in is are nonlinear effects important in these systems? And do we need to account for them if we wanna fully understand what's going on in these stars? These are just red, so what I'm gonna be talking about is just red giants. But of course Kepler saw made astrocytes measurements for a wide variety of class of variables including AGM stars. Right, and so one of the sort of observational motivations for considering these nonlinear effects in these red giants is a mystery sometimes referred to as the suppressed dipole modes. So here are the power spectra of two red giants. They're both very similar in mass and radius and age. But what you can see, and so the color coding is a different degree of the oscillation mode. So black is L equals zero. So if you remember your spherical harmonics those are radial modes. L equals one is dipole modes. L equals two is quadruple. And so the one at the top shows power in the dipole modes and the L equals one modes. Whereas the one at the bottom shows very little power in the dipole modes. But otherwise these two stars are very similar. So it's kind of mysterious as to why one would show power in a dipole mode and the other one not. And so one of the explanations put forward is that maybe in the one that shows suppressed dipole modes there's significant, there's a large magnetic field. And that magnetic field through a process known as the magnetic greenhouse effect basically traps the energy of the dipole modes in the interior, scatters the mode, the waves and prevents them from having large amplitudes at their surface. And so if that's the right explanation that would be extremely interesting because it would be a way of measuring the magnetic fields in the cores of these red giants. We don't even know the magnetic field in the interior of the sun, right? And suddenly this is saying you can measure magnetic fields in these thousands of red giants across our galaxy. But one question we were wondering is, well, what if it's not some sort of magnetic effect but maybe it's nonlinear mode dampening, maybe nonlinear interactions are suppressing the modes in some of these stars and that's the true explanation for the suppressed dipole modes in these systems. And so we basically did an analysis very similar to the one we did for the hot Jupiter problem. We showed first that the modes in these red giants have such large energies that they would excite secondary modes. Parent waves have such large energies that they excite daughter waves which excite granddaughters. So this is again a plot of energy versus time. So the black line is a parent wave who's being directly driven by turbulent motions in the convective zone of the star. And it has such large energy that it excites daughter waves in red. Those daughter waves reach large energies, excite granddaughters waves. And again, you have this cascade of modes excited. And so we analyzed these systems, these mode networks for a range of red giant masses and a range of evolutionary states and just sort of to cut to the chase of what we found. So you can ask the question by how much is the energy of the modes suppressed due to the nonlinear interactions compared to the linear theory predictions? So you can talk in terms of the suppression factor of the energy of the modes due to nonlinear damping. And so the different colors here are for red giants all of a two solar mass but at different stages of their evolution. So the least evolved is in blue. And the suppression factor for the least evolved is pretty minimal, maybe 10% or so due to nonlinear damping. But as you consider more and more evolved red giants the suppression factor can be significant. And it could be as much as 80 or 90% for the most evolved red giants that Kepler sees. So the implication is that these nonlinear effects are significantly damping the modes in the star. The question then of course is does that explain the suppressed dipole modes? And so we found that it maybe can explain the suppressed dipole modes in the more evolved red giants but in the less evolved red giants where you do still see suppressed dipole modes it doesn't seem to work. It doesn't seem to explain the detection of suppressed dipole modes in less evolved red giants. That said, I think there's still outstanding questions that remain about the role of nonlinear effects in these systems. So we focused on this parametric instability that I talked about earlier. There's other types of nonlinear interactions. There's interactions in which you could have two parent waves exciting a daughter wave of twice the parent wave frequency what you might call direct nonlinear forcing. And so with my current graduate student at UTA, Mohamed Morabit, we're planning on studying exactly that problem and addressing whether maybe that effect can explain the suppressed dipole modes. Okay, so to conclude, I think one of the takeaway messages is that the linear approximation is often not a good one. It helps simplify the problem but is not a good enough motivation for assuming it. And that's true in a wide variety of binaries. And when you started counting for these nonlinear effects we're finding that they can significantly enhance the rate of tidal dissipation. So this has implications for the formal formation and evolution of hot Jupiters and also for compact object binaries like binary neutron stars. And then finally, towards the end, I mentioned the role of nonlinear effects on the amplitudes, line widths and frequencies in astro-sizing measurements of evolved stars like red giants. And so this is something that we've been studying now for almost 10 years and continue to study because I think there's a lot of open questions that remain about high X and 50 migration and different types of systems, not just planetary systems, the role of tides in binary white dwarfs which are important sources for future gravitational wave missions like the Lisa space mission and other types of pulsations. So not just red giants, but Cepheids are a Lyrae Delta study, all of which have been detected with Kepler are continuing to be detected with tests. And I think one of the really important takeaways too is that this is a field with an amazing set of data. There's just a wealth of really great data that exists from Kepler and Tess and in LIGO and has a great future. There's gonna be future missions like PLATO which is a future planetary detection but also astro seismic measurement mission and Lisa, this gravitational wave detector in space and future versions of ground-based gravitational wave detectors like the Cosmic Explorer. So I think this is gonna be a really exciting area for many years to come. So I will stop there and thank you for your attention and happy to take questions. Oh, yes, he put it here. I don't know if you know how to think. Oh, I think I may have to turn this off, right? Okay, oh, there we go, yeah. So this might be a bit of a basic question but you have all these nonlinear effects. I presume you calculate all these just numerically or is there analytical solutions and how many orders, I mean, what's sort of the largest order that you need to get to before you can start neglecting them? Question, so you can get analytic solutions as long as you restrict yourself to like three mode systems. You can't assume for these systems because there are so many modes excited. So you really have to just solve them numerically. So we solve a large set of coupled amplitude equations. Let's see, I may have a, so here's a backup slide showing an example of an amplitude equation. So A is the amplitude of the modes. And so the first three terms are, what you might identify as a damped oscillator. And then there's the driving term, which if you include that one, then you have a driven damped harmonic oscillator. And then the last term is this way of coupling. So you have many of these equations that we're solving those all simultaneously. Basically, it's just a large set of coupled ODEs that you're solving on a cluster. And then your next question was, I think, how many terms in the expansion of your perturbation theory do you need to go to? And that's also a great question. So you can construct arguments to show that the next term in the perturbation theory, the cubic term, is unlikely to be important in many cases, but that's not always the case. So for example, in the neutral star binary problem, it turns out that the next term in the perturbation expansion can also be significant. And so really, the only definitive way of showing that is to include the next nonlinear term and see how much is that contributing compared to the previous term, right? But for the most part, as long as you're not strongly nonlinear, you can truncate at a second or third one. Okay, can you go back to your last slide? So I was gonna ask this question anyways, but you sort of led into it. Do you, we have the students and are actually here that we just talked about some of these objects, the RLI res and the Delta Scooties. Do you have any sense for what the effects will be for those? They're very different, obviously, than neutron stars or the red giants. The densities are a lot higher. Delta Scooties have a lot of non-radial modes. Like what do you have a sense for what the impact might be? So we're actually, we're starting with the Delta Scooties because there's actually, there is observations, some groups from UT Austin that show evidence of nonlinear mode coupling systems. That show evidence of nonlinear mode coupling. So you get basically a wave and you have pairs of waves whose frequencies add up to that other wave. And so, and so there's sort of that motivation, observational motivation for Delta Scooties. For Cepheids and RLI, I think it's entirely plausible that nonlinear effects are born. In fact, we know that they're important. The, you know, the radial expansion of these stars is a significant fraction of their actual radius. And people who do, you know, the theory, the simulations of these systems have to account for the fully nonlinear fluid effects. But those are kind of large scale waves, sort of wavelengths of order the size of the star. I think there's interesting questions about whether those waves excite shorter wavelength waves and what role those play in the dissipation of wave energy. But yeah, we haven't gotten to those yet, but I hope to one day. Thank you.


The James River is a major source of commerce for the entire eastern part of Virginia. In the early colonial period Yorktown, Hampton and others became the major disembarking of enslaved Africans. They are brought to these given ports and then they're sold and they move west towards the Piedmont. So rivers are very important to the slave trade and the river was very important to those that were enslaved because it augmented their diet. I mean the fish, the crabs and so on that they took from the river provided subsidence from them when the plantation system may or may not have provided adequate food. Large numbers of the pilots of those rivers were African-Americans, whether enslaved or free. And matter of fact during the American Revolution and during the War of 1812 the first thing that the British would seek out is the knowledge of those particular individuals. Land that was close to the river was marshland, mosquito infested and had less value than it does today. Therefore blacks in certain instances lived closer to the water's edge because it was land that was not wanted in large measure by the larger white community or the white economic interest. The seafood industry primarily was a black industry at the end of the Civil War. So when you have black freedmen coming out of the Civil War it becomes a major source of economic opportunity. It provided them a means by which they could improve their condition. It provided them a means to educate their children. It was an important part of the lifestyle of my family in particular. My own father even after he retired from the shipyard went to the James River in Treads Oysters. My sister and I were educated from the monies that my father earned outside of his initial job at the shipyard from when he oystered. So you can see that the river offers a great source of possibilities to local populations.


Hello all of you, I welcome you to today's lecture. We discussed some aspect of silane based reducing agents last time. We saw how silane gas can be modified and different types of organic groups, functional groups could be attached to silicon and different silane reagents can be prepared which are relatively more stable than the silane gas. And these modified silane based reagents can reduce a number of functional groups and such as a carbonyl group or an ester group or even halides which are capable of forming a carbocation. So if we have a possibility of generating a carbocation then the silane based reagents where there is one or two silanes the hydrogens are present can lead to the formation of the corresponding reduced product. Then we also saw how the rhodium modified reducing agents can be prepared and they lead to 1, 2 or 1, 4 addition of hydrogen and to an enone system and we can get either from an enone we can get either a 1, 2 product at a reduced product or 1, 4 reduced product depending on the bulk of the corresponding groups attached to silicon. Then towards n we saw polymethyl hydrosilane as PMHS which is something that is like a polymer and therefore we can expect that such a polymeric molecule which is liquid to handle and it is stable, air stable and inexpensive and how it can be used in reducing various kinds of molecules similar to the silanes that we discussed. So off late if you see the literature many people prefer to use PMHS as a reducing agent rather than triethylsilane or other reducing agents of similar type. Now we see how these reactions occur. For example, if we take a carbonyl group then PMHS in the presence of T-buff, T-buff is nothing but tetra and butyl ammonium fluoride basically it has a fluoride ion and counter cation as an ammonium ion. So what is done it is this is the species that you have here and this is how the polymeric species of the PMHS is having a hydrogen in the middle and then the fluoride makes a kind of pentavalent silicate and then what you have is a possibility of transferring hydrogen from this species to the carbonyl group. So basically this is the modified species which is formed when the T-buff interacts with the PMHS. So the reduction occurs in a slightly different way than the normal reduction that we expect from normal silanes where we first make the compound under acidic conditions and then we carry out the reduction. In a similar fashion we can convert an ester to the corresponding alcohol if we use 2 equivalent of PMHS and T-buff and the anion which is going to be formed after the carbonyl group gets reduced. So even gets reduction and get the corresponding anion which then is protonated to form the corresponding OH. So you have to use a proton source later on during the next step. Now there is another reducing agent which is called as Stryker's reagent and which is having this copper hydride basically it is a hexameric copper hydride reagent ligated with triphenyl phosphine. So it is also called as Osborne complex. So this is a reducing agent now suddenly from silicon to this Osborne complex or hexameric copper hydride I am coming to mainly because this can also be prepared using a silane. First let us see what is the utility or what is the use of such copper based complex. It is a brick red air sensitive solid which is known as Stryker's reagent is mildly hydridic because you have here hydrogen there attached to copper and therefore it is useful because it is relatively soft because of the copper being present is this allows the conjugate reduction of enones, enoates and related substrates different types. So basically it allows conjugate addition of the hydrogen occurring. The compound is prepared now this is where the silicon based things come into picture. The compound is prepared by hydrogenation of copper tertiary butoxide generated in situ from copper chloride and sodium tertiary butoxide. That means this copper tertiary butoxide is then hydrogenated and of course triphenyl phosphine has to be put then we get the corresponding Osborne complex or the Stryker's reagent. The reagent can affect regio selective conjugate addition of various carbon derivatives including unsaturated aldehydes ketones and esters which we already seen that we can have of any kind of unsaturated system where the reduction occurs at this end of the double bond. This was declared as the reagent of the year in 1991 as it could tolerate different types of functional groups, tolerance, high overall efficiency, mild reaction conditions in the reduction reactions. So how it is very easy to carry out such a reduction. Therefore it is it tolerates various functional groups and therefore it is of great use. Now this is used in catalytic amount you can use the Stryker's reagent in a catalytic amount where it is regenerated in the reaction and you can use some other source of hydride in a stoichiometric way and in that respect either use molecular hydrogen or even silane. So that is where the silane part comes in. So this is very important that you can modify the Stryker's reagent by basically using in a catalytic amount and reusing along with that silanes or molecular hydrogen. So obviously when you have to have a choice between molecular hydrogen and silane you might want to have silanes over hydrogen. If it is stored under inert atmosphere for example argon nitrogen it has indefinite shelf life. Although brief exposure to the oxygen does not destroy its activity significantly but solvents used with Stryker should be rigorously degassed to remove oxygen. So oxygen has to be removed. Now how it is made is that you take this copper tertiary peroxide and use excess of triphenyl phosphine in the presence of hydrogen in the in benzene solvent it gives this hexameric Osborne complex or Stryker's reagent. When this Stryker's reagent reacts with an enone hydrogen is transferred onto this end of the double bond and as one can expect that we can have an intermediate of this type enol cuprate and this enol cuprate upon this reduction will break the oxygen copper bond and of course you regenerate the catalyst here and you have the enol and that enol gives the product ketone. So basically this is how the catalyst is used where now molecular hydrogen is used in a stoichiometric way essentially to cleave the oxygen copper bond here and regenerate the Osborne complex or the Stryker's reagent and the reduced product ketone is formed. Now unactivated carbon double bonds are not reduced. So if you have something like this here a molecule of this kind and you also have both the possibilities you have a simple double bond, unconjugated double bond and of course conjugated double bond with the carbon group only this will get reduced at this center. So it is a very useful reagent and since it can be used only catalytically if you one wants to use in stoichiometric way we can do that but also catalytic way and now there have been many studies in which different types of silence that have been utilized for the reduction of this particular complex in such a way to form the Stryker's reagent. So in order to form the Stryker's reagent when the copper chloride, potassium tachybutoxide, typhenyl, phosphine and the silane that is used. So this silane is used in 1.2 equivalent. So the ratio is shown here. So if you have 1 is to 1 is to 1 is to 1.2 that means silane is used as 1.2 then they kept on modifying and you see the effect of that on the yield. So we have a PMHS in this ratio of different reagents then you get 47% and you see the best one is if you have 1 is to 1 is to 2 is to 2 as ratios then you get 82% yield and one can also see that you can get 88% of this when you use this dimethyl phenyl silane. So there are several possibilities of this type where you can use different silane based reducing agents where instead of using molecular hydrogen one can use these and form the corresponding Stryker's reagent. So it is very clear that we can take a catalytic amount of this and also use anyone of these silanes as stoichiometric reagents and these reactions are generally performed in benzene or toluene and they allow reductions to take place in a conjugated fashion. Now we see how this silanes can act as reactions as in reactions where radicals are involved. In addition to their function as a hydride donor, silanes also may act as radical hydrogen donors. In this role they can substitute for the toxic reagent type n-butyltin hydride. Before we proceed further, various kinds of radical based reactions have been carried out particularly reduction. So if one wants to carry out a reduction say for example of Br here and if you want to carry out reduction to form H here what is used is is tributyl tin hydride as a reagent as a hydrogen source in the presence of something called as Aibn, Aibn which is azoisobuturonitrile which looks like this. So you have here Cn then you have this particular azo group and then you have here Cn. So this is how this is what is called as azoisobuturonitrile which we will discuss it later on. So these two combinations by hitting allow such a reduction to take place and there are many other reactions that occur using. But in these cases the hydrogen source is basically tributyl tin hydride and this is what is considered to be a toxic reagent. It is also when the reaction occurs with this tributyl tin hydride the byproduct which is formed is tributyl tin oxide or other tin based products which are very difficult to remove from the reaction and create problems in during the workup of the reaction. So in that respect people have tried to use Tris trimethylsilicilane of this type TTMS or tetrafinyl disilane of this type and tetrafinyl disilane of this type. So these two reagents have been used in many places where people want to carry out radical based reactions. Radical based reactions have their own utility not only reductions but they allow also CC bond formations to take place when radicals are invoked as intermediates. Now these hydrogen transfer agents in radical reactions need a low MH bond dissociation energy obviously because we need to do these reactions not at very high temperature. So compared with the tin hydrogen dissociation energy of tributyl tin hydride which requires 74 kcal per mole the silicon hydrogen dissociation energy of TTMS is approximately 79 so it is very close which together with that of TBDS which is significantly lower than that of triethylsilane. So if we compare the reducing ability of this versus say triethylsilane so the triethylsilane based reagent requires high energy that is the reason why this TTMS Tris trimethylsilane or TBDS that is tetrafinyl disilane is used. Now what does happen is that if you take an Rx where x is a halide for example and if you use TTMS in the presence of benzoyl peroxide then you generate R dot from here and basically what is happening is that benzoyl peroxide which is benzoyl peroxide or we can write it something like this you have O O CO phenyl when this is heated it eventually breaks to phenyl radical or phenyl CO O radical but eventually it forms this phenyl radical which can take the x from there so you have here Rx that leads to the formation of R dot plus Phx here. So this is how one possibility can be the other possibility is that here Ph dot takes the hydrogen from the silicon of the PMH of this TTMS and form Ph H and TTMS or TTMS dot. So and therefore this the TTMS dot can of course react with Rx to form R and then the R will react with the remaining TTMS to form Rh and TTM radical this TTM radical will take the x from here and regenerate R dot. So essentially what is happening is that benzoyl peroxide initiates the reaction to generate a TTMS radical or TTM radical that takes the x from there generate R dot and the remaining TTMS then reacts with the R dot to get to the product which is Rh and then regenerate the TTM radical which re-reacts with the Rx to generate R dot this is how the reaction keeps on taking place. Now there is another reaction which is called biotin macombi reaction or biotin deoxygenation it is a method for the deoxygenation of alcohols. So if we have an alcohol of this type we can convert into a thio carbonyl derivative which is how it looks like and then that can be reacted with tributyltin hydride under conditions of similar type where we use tributyltin hydride and SAIBN which I discussed as of earlier and it allows the formation of the corresponding deoxygenated product. Once the radical chain has been initiated attack on the tributyltin carrier by Sulphur initiates decomposition yielding the alkyl radical for which this serves as hydrogen radical donor. We will see how the reaction takes place. This is what is azobis isobutonin nitrile where as you when you heat it it breaks homiletically from here to form this particular radical intermediate and the nitrogen goes off from the reaction. When this radical reacts with the tributyltin hydride in a similar fashion as we discussed earlier that the benzoal peroxide gives a phenyl radical that reacts with the TTMS to form the corresponding radical. So similarly this tributyltin hydride reacts to form this particular tributyltin radical and of course this radical will couple with the hydrogen dot and will go away. Now this tributyltin radical then reacts with the the thio carbonyl compound in this particular fashion in this way and generates an intermediate of this kind where R1 is O methyl if R1 is O methyl. Now this decomposes in this fashion here like this and forms this as a byproduct and then you generate a radical of this kind. This radical then reacts further with tributyltin hydride generating this reduced product and you generate the same tributyltin radical which was generated here. So it is exactly similar to what we saw where TTMS and benzoal peroxide was used instead of benzoal peroxide here we are using AIBN which is generating a radical like this. So the driving force of course here you take the radical form here and then you generate this tributyltin radical. The driving force for the reaction is the formation of the stable sulphur tin bond. The main disadvantage of this reaction the only problem that with this reaction is the as I earlier mentioned is the use of this tributyltin based molecules which is difficult to remove and toxic expensive and so there are problems and that is the reason why some modifications have been carried out. An alternative is to replace tin reagents with the silane based reagents. A few examples of reactions are shown here which exhibit similar reactivity as tributyltin hydride in a variety of radical reactions. An example of the Barton McCombie deoxygenation reaction using tetra phenyl disilane that is TPDS whose structure is here as shown. Now TPDS is a better reagent than tributyltin hydride not only in terms of toxicity but also it gives better yield. So if we take an example of this kind which is sugar derived xanthate then with TPDS AIBN combination in reflecting ethyl acetate that deoxygenation leads to the formation of this particular product. Now not only xanthates can be reduced to the corresponding deoxygenated product but it is also possible to generate a radical if we have a halide carbon halide bond can be cleaved to the corresponding radical as it is shown here. So if we start with a brominated molecule like this and react with TPDS AIBN combination in reflecting ethyl acetate what we first generate is of course this radical. If this double bond was not present then of course this radical would have taken hydrogen and then we could have got the correspondingly reduced product. However since there is a properly oriented double bond which is present in the molecule therefore this radical undergoes intramolecular cyclization to form this type of bicyclic molecule. So it is also possible not only that we can reduce the carbon halide bond but also we can allow the radical to undergo intramolecular cyclization. So these kind of cc bond formations are also possible and thus tetra phenyl disilane or similar types of silane reagents make a better alternative than the tributyltin hydride. We can also use this type of substrates where we have this particular reagent. This is TTMS and AIBN and of course here base this is like a different types of nucleic bases and we can then have two radicals that are going to form one here and one here they couple or they form the corresponding double bond. So radical based transformation of visceral diols to olefins this is this can come from the corresponding diol via thio oxo carbamate derivative and that leads to the formation of this. So you can start with the corresponding sugar based molecule and carry order reaction which has been published in 2003. Now another alternative is the use of catalytic amount of tributyltin oxide approximately 7.5 percent as the radical source and poly methyl hydroxyl oxane Pmhs as the hydrogen source. Now what is done is that the substrate which is a hydroxy compound can be converted to the corresponding thionocarbonate derivative like this by reacting with phenyl chlorothiono formate like this in the presence of pyridine and we can react them this particular thionocarbonate derivative with tributyltin oxide in the presence of Pmhs and of course AIBN but the solvent N butanol is a very important solvent and a mixture of N butanol and toluene is used and it is reflux in that particular medium to form this deoxygenated product. Now what happens is you get a side product as this carbonyl sulfide which is a gas which goes away and of course we get this phenoxy tributyltin derivative. So this tributyltin oxide actually reacts with Pmhs at 80 degrees in N butanol to release the tributyltin hydride and that is what is basically reacting here in this particular stage in the presence of AIBN to generate tributyltin radical which of course interacts with this thionocarbonate and leads to the deoxygenation. Now this byproduct which is phenoxy tributyltin derivative then reacts with Pmhs again at 80 degrees in N butanol and releases tributyltin hydride and of course there will be silane derivative here. So this is how the reaction is perceived and it gives an alternative to the use of stoichiometric amount of tin hydride based compound. So we will stop it at this stage and in the next class we will take the radical based reactions because they are very close to these and therefore how the radical based reactions can permit not only reduction but also C-C bond formation in many cases. We will take up that next time till then you can go over whatever I have discussed in today's class. Thank you and see you next time.


Guys, I have an idea for a challenge. The challenge is going to be between me and the two other content creators here at Artlist, Oneg and Talia. We're each going to be competing against each other to see who can make the best slow motion video. Okay, so now we've got to the point where we're going to figure out who's taking which camera. Rock, paper, scissors. Let's go. That's a three. Okay. One, two, three. One, two, three. One, two, three. Ha ha ha! I'm going fast. I think I'm just going to stick to classic iPhone with great camera. My prop is glitter. I'm wanting to take the phone, but I'll grab the GoPro. I got a water balloon. Okay, so I guess I'm choosing the black magic and I have Coca-Cola and Mentos. By the way, guys, if you want to sit to the end of the video, you guys have a chance to vote whose video is going to be the best one. You'll be entered into a raffle to win a prize. So stick around for that. So I've got my bag of props here and we need to find a dark place to film this. So let's go and see if there's a room upstairs we can film. What we need to do is use the flash of my phone camera to get the sparkle of the glitter. If I've got a brush, some green glitter, some colorful glitter, every iPhone obviously has a slow-mo mode and I can just go on to slow motion. Amazing. So I can make it 240. The way I'm going to do it is I'm going to turn my camera upside down, turn the flash on, I'm going to take some of my glitter and then pour it on or I can dip it into the glitter, hold it above and tap it onto the camera. Yeah, obviously you can see my face in it in a very unflattering angle. That's not what we wanted. So we need to do it again. All right, I got balloons, I got the GoPro. Let's go for green. Is that enough? I feel like it's going to explode. So I've got 240 FPS, I put it on the narrow lens, I nail. All right, let's see how it came out. I think it's the only thing working first time. Let's give it another try. God, please don't explode. It feels like high school. I'm trying not to have my hand show. Let's see how it went. I think this one went better. Well, I'm not sure about the background. I want to win. I want to have the best shot. I want a place that's not really in the way of anybody because it's going to be a big mess. It's going to be a little too bright. I think we can do it over here. But it's really cool about this location that there's a lot of leading lines. But I need a way to prop it up. Here's where a little bit of DIY comes in. My phone and my wallet. Yeah, that's good. So I just realized that maybe filming this way towards the street might not be such a good idea. Recently we're going to switch where the camera is and where the bottle is and we're going to see if it looks better going this way. So that was a fail, let's try again. With a darker color. Hold it further up so we get more of a draw up. Okay, I honestly think I got a great shot. Okay, it doesn't work with two hands. I brought Jonathan Barney, creative director here in our list and we're rolling. I think we have it. Not bad. I'm not used to working with GoPro. I'm going to go try and edit it. I'm going to add some music to it. The top of works is really janky. Let's make sure it's rolling. Boom. Okay, I'm going to cut my video. I quite like this. The green's quite nice. Maybe I can make it a secret of all different colors. I'm really excited to see my final product. I have a great shot at winning this. This was too wide of an angle by 230% of GoPro. Let's go video theme, slow motion and balloon explode. That's the song right here. First time I shot in GoPro, I think it's decent. Let's see how far we can slow it. We'll shot in 120%. Let's do it 50% of the other echoes and also don't forget to do optical flow. I think it's a little too choppy. Let's see if we can bring it back down. 70 is the sweet spot. So let's go and look for a song. First, you guys can actually see how I'm looking for the song. I'm using the waveform. That's where I know the drop is. What I like about this one is you can hear that little like gurgle. Sounds a little weird, but like listen for this. That could be like the fizz in the bottle. Looks good. I'm going to export this. Let's just go and watch the other videos. I don't know whose slow-mo video was the best. And the one with the least votes is going to get a cake in the face. One of you will win a free yearly R-List subscription. The full videos are going to be uploaded on our Instagram and TikTok, so go check them out. All right, peace out, everyone.


If women are getting what they want, why are women so unhappy? So apparently, since the 70s, women have become more and more unhappy. But that's funny because it seems to me that the rights of women, the feminists have won. So if the feminists have won, and we have all the freedoms and all the equalities, then why are women reporting lower happiness levels than men, or the same?


1017 let's talk about I gotta ask you about inch and that's the elephant in the room when you look you up that that's a history that came be denied how important do you feel like you were to her career blossom in who she is how important yeah if I didn't exist she wouldn't exist yeah we on boss talk one-on-one you one of those guys man like I said we can't not talk about the elephant in the room you know I'm saying let's talk about your deal you being linked with 1017 let's talk about I gotta ask you about inch and that's the elephant in the room when you look you up that that's a history that came be denied how important do you feel like you were to her career blossom in who she is how important yeah if I didn't exist she wouldn't exist that's how much that's how if you didn't exist she wouldn't exist she wouldn't exist but how did what did you do to impact her so much that you felt like if it wasn't for me you wouldn't be here pretty much anything you can ever think of her artists are supposed to do for themselves I had to do for her I took it I took an image I took a face and I pretty much put everything together what I thought people would love the music that I thought people would attract to I posted the sexual content that people would attract to on Instagram just to build a page yeah but you said something you said everything that an artist should do for themselves yeah so you saying that she didn't actually do anything no you did it all no I mean she had what did she what part did she play and what part did you put the face in the voice that's how she played she was facing the voice with record labels do for artists is what I was doing by myself and all that everything I had ten jobs in one I was writing the song recording the songs and mixing the songs marketing the song so she didn't write her own songs no I mean she wrote her own songs I don't want to take credit away from what she did do she did write songs but there's a difference between a good song and great songs and okay so you critiqued her song I critiqued her style to where it was like when I met her she probably had a sound a song a EP on SoundCloud with like 25 plays but I seen the vision and I took what her vision was and I added to it and together we made motherfucking how did you how did that's what I was about to ask it was on Facebook she was just like known in Fort Worth Dallas Fort Worth is a pretty face on Facebook Snapchat shit like that and I just found her and I heard the music I told her to send me something she sent me a song she had a nice voice and then from there on I just hit her up and told her to come to the studio and that's how we met and at that time did you have any other artists you were working with yeah I was working with this artist at the time called Nana Kiana she had a song called beat up the pot that kind of got popular around that time and that's what really attracted Channing to what I had going on because she's seen Kiana you know and she knew Kiana and she's seen Kiana growing scale it so she was like I got to figure out what's going on over here so that's how she got in the mix with me so you like working with females it's just I seen the vision before Cardi B and everybody came out I seen that females are going to be the next wave so I was putting together strippers and making them rap and saying hey we don't talk about what y'all lifestyle is at the street club on album so before the city girls I was trying to create the city girls but it's like you can't get everybody to see the vision they understand it and they might think yeah this sounds good but you you really got to make people believe believe right and if you ain't at that time I had no accomplishment so it was hard to get people to believe that I can make it happen but Channing was one of those people who believed that I can make it happen over time so it happened so when you when you say it happened for you basically you guys were together you created a sound and you created a wave and then 1017 comes into play how long after how not only how long after but how did it all happen you know what I'm saying how the 1017 yeah how did they link up with you guys how did that happen I mean it was a couple more people that tried to reach out prior to who was it we had la re with hit cold tried to hit out or reach out a fucking uh hit cold fucking um um who else was it we had def jam in the beginning we had epic records we had a meeting with Sylvia wrong that was yeah I'm saying then why you didn't choose any of them crazy situation that happened and uh I guess it was a conflict of interest so can you tell what crazy situation I mean just people we dealt with prior to the situation and we got black ball this person tried to black ball us from having any type of accomplishments but you can't stop somebody from the Dallas Fort Worth area yeah somebody from Dallas forward really yeah they just tried to stop what was going on and and can I research and find out who this person is or how the hell I need to find out who this is you ain't gonna speak on it so I need to find out somebody somebody who the hell is somebody you know I'm talking about this boss talk nigga you know somebody yeah I'm gonna need to find out who this is that so-called tried to black ball somebody which it didn't work too much because you guys end up on 10-17 you see what god have for you nobody can stop that's right because it just wasn't meant for you to go where at first the other people that was reaching out to this is what it was meant for you to be yeah so yeah we on boss talk one on one


What is hell? I mean, I think the daily pictures out of Gaza, I think, illustrate that. We see Gaza, basically, to a large extent, flattened. You're seeing thousands, thousands of people killed, many of them deservingly so as supporters and members of Hamas, some not so children, many children have been killed, which is always a sad to see. But of course, from the perspective of Israel necessary, there is no real alternative for Israel to defend itself without this kind of bombing. But on Friday, I think we got a sense of how hellish war can be and how just the uncertainties, the fog of war, as it's described, in particular fighting an enemy like Hamas, who's fighters are in civilian clothes, who are regularly set booby traps and use Hebrew and use the sounds of children and regularly finding ways to lure Israeli soldiers into situations where they are killed. Well, on Friday, it turns out that three of the hostages, three male hostages, managed either to escape or were abandoned or somehow freed themselves from Hamas. They had been hiding in a particular home. They had been trying to send SOS and help signals out. I guess nobody saw these signals. And then when they thought Israeli soldiers might be approaching, they ventured out with a white flag trying to basically get the attention of the Israeli soldiers. Israeli soldiers saw people approaching, unidentified, and shot them. The first round of gunfire killed two of the hostages. A commanding officer then required that the soldiers stop firing, but one of the soldiers continued and killed the third. In other words, Israeli troops on Friday killed three of the hostages they were there to save. I mean, this is a massive tragedy on top of tragedy on top of tragedy that Israel has suffered really from October 7. And it's something that I think has resonated throughout Israeli society. Everybody has been traumatized over the weekend over. I think the soldiers who did the shooting will be traumatized really for life. I don't know. I think, no matter how much they are told that this is what happens in war, and this is kind of the consequence of war, they won't be able to forgive themselves or forget this completely. And it is going to hound them. I feel sorry for them in the future. Of course, the families of the three hostages that were killed. And this is a point worth emphasizing. The Israeli forces have now re-emphasized, so the three hostages were carrying a white flag, re-emphasized, don't shoot at a white flag, even if you're afraid of a booby trap. They spoke Hebrew, but sort of many of the terrorist speak Hebrew. This is what happens when you deal with an enemy like this. And these things will happen. And it's quite possible that some of Israel's bombing has killed some hostages. This is why I said early on Israel has to engage in this war under the assumption that the hostages are dead. Because you cannot fight a war against a group like Hamas on edge that anything you might do is going to cause damage to your hostages. You have to defeat them. That has to be priority number one. You have to defeat them, and you have to defeat them thoroughly, and you have to defeat them quickly. And again, the more time Israel takes, the greater the international pressure on it. And you have to thoroughly defeat them.  And you have to bring the Palestinian morale, the Palestinian view of the world to a low so that they reconsider the view of Israel, they reconsider their view of themselves. Sadly, I don't know that this could have been avoided given the conditions of battle. I don't think it's worth speculating about whether this could be avoided given the conditions of battle. The Israeli army will now be more alert to the possibility that there are hostages out there whether that can actually be implemented under the conditions of intense fighting. This was all in an area, by the way, where there was intense fighting going on between Hamas and the Israeli soldiers. Whether more lives of hostages can be saved, it is clear that the Hamas does not want to negotiate, is not interested in a ceasefire, does not want to release any more hostages. It's not clear how many they have. It's not clear how many are alive. It's not clear how many they have control over. I mean, hostages are being held in all kinds of places, and it's not clear that the Hamas even knows who they have. It's also clear that they don't want to release some of them because of the horrors they've inflicted on them, and they don't want those horrors to get out. Another female hostage over the weekend was announced that had been killed by Hamas. I think it was one of the women who were raped brutally before she was captured. Israel just has to get on, get on with the job, of capturing and killing the entire Hamas leadership and capturing as many of the Hamas fighters as possible, and demoralizing the Palestinian people as much as they can. One of the fines over the weekend was a large tunnel. I mean, this is quite a tunnel underneath Gaza, particularly in the north, reaching out all the way basically to the Israeli border. It is pretty obvious that this tunnel was part of the process of preparation, and from which the October 7th assault was made, the entry rate to the tunnel is just a few hundred yards from the actual crossing into Israel and a nearby military base. A military base that was overrun on October 7th, where a lot of soldiers died. It stretches over two and a half miles. It's linked with a sprawling tunnel network across Gaza. So it's linked to the other tunnels that are connected. But this one is wide enough for cars to pass through. And vehicles were brought to the mouth of this tunnel on October 7th to launch the attack that they initiated. It is made of materials that they haven't seen in other tunnels. It is more solid. And it also seems to be another Israeli intelligence failure in not knowing that the tunnel existed so close to the Israeli border. And not knowing of its size and capacity, it just shows the limitations, I guess, ultimately of intelligence. And one of the elements of this is, I mean, this tunnel, you can extrapolate on the rest of the 500 kilometers of tunnels, this tunnel must have cost tens of millions of dollars to build and tens of millions of dollars that could have gone to bettering the lives of Gazans. But this is the kind of, this is what Hamas did with the money that they got, including from the United States, but from Qatar and Saudi Arabia and Iran and everybody else. The tunnel has ventilation, electricity, and is 55 yards underground in some points. Millions and millions of dollars went into building this thing. All right, other than that, battles continue. It's very fierce. It's fierce, both in the North and in the South. Israel, I think in some sense, they keep thinking they've got control of the North. But Hamas still has men underground. They keep popping up. And re-establishing themselves, in particular neighborhoods, Israel goes in, destroys them, destroys some of the tunnels. They pop up somewhere else. Others pop up somewhere else. This is just going to take a long time because you're not fighting a final war. You're fighting a war where the enemy is really unseen for most of the time and can move from place to place without you noticing. So until Israel literally demolishes the entire tunnel system, which is going to take a long time, very, very difficult engineering task, it is going to still be dealing with these Hamas terrorists coming out of different holes in the ground and attacking. This is the kind of urban warfare. This is worse than normal urban warfare because of the tunnel system. But this is the kind of urban warfare that is so difficult and is so deadly and is so hellish. And think about a soldier who is in this for weeks upon weeks. It's not surprising the mistakes are made. I also told you, I think the other day, that over 20% of all Israel's casualties in Gaza have been a result of Fendi fire. That, again, is tragic and horrific. But pretty standard, particularly in an urban warfare like this. But even in Gulf War I, well over 20% of the US's casualties in that war were caused by Fendi fire.  It's just a disaster. It should be avoided. And when you cannot avoid it, it needs to be done with massive force as quickly and as thoroughly as possible to get it over with quickly because of how hellish it ultimately is.