- All right, good evening and welcome to UW Space Place. We have a guest speaker tonight, and our speaker is Ben Tofflemire, who is a very advanced graduate student in the UW Madison Astronomy Department doing research on, as you can see, binary star systems, which is an interesting topic. I think maybe this is the first time we've had a talk here at Space Place on binary star systems. Ben comes from the northwest originally,  working on the Sloan Plates at University of Washington, right? The Sloan Digital Sky Survey Plates. He was just telling me about that, as an undergrad. And then came here just about the time that UW became a Sloan partner. So that was a nice coincidence there. But that doesn't figure greatly into his talk tonight. He's going to talk about binary star systems formation  and the implications that has for our thinking about planets and things like that in such systems. So, let's welcome Ben.  [applause] - Okay, well, thanks for the introduction, Jim. And thanks for inviting me to come give a talk, and thanks to you guys for being here. I know it's a special day, so hopefully you've all had a chance to vote. If you haven't, there's about an hour until the polls close, so if you run out, I won't be offended, don't worry. So, hopefully, you know, the next hour can be a nice reprieve from any election worries that you may have. And we'll talk about something a little lighter. We'll talk about binary stars, how they form, and what that means for planets and for star formation. Okay, so why should we care about stars and star formation in general? Well, stars, just in general, are really important for astronomy. You know, in astronomy, you know, what we have from space is photons, is light. And most of that light, at least in the optical and the near infrared, is coming from stars. So basically everything we know about astronomy is informed by having an understanding of how stars work. Stars are also drivers of galactic evolution. They form galaxies, help galaxies evolve. But this birth of stars, star formation,  is really the least well understood phase of a star's life. And we'll kind of get into why that is in a little bit. And then of course planets, a little more clear. We want to know is there Earth beyond, sorry, is there life beyond the Earth? And we've done a really great job in the last couple years to find planets, and we're finding them in these weird architectures where they're very different than the architecture of our solar system. So how can, you know, studying how planets form help us describe, explain these planetary systems that we find around other stars. Okay, so why is it difficult to study stars? Well, star formation happens fast, of course. I put fast in quotes because I mean fast on, you know, astronomical time scales. So we're talking tens to hundreds of millions of years, which is a long time for us, but over the course of a star's life, over the course of the universe, these are blinks of an eye. So it's very hard to catch stars during this formation process. It also occurs over a wide range of scales. We're talking parsecs, hundreds of parsecs down to AU scale. So an AU is the distance between the Earth and the sun. so we have important things happening on that small scale, as well as large scales. And then all of this is happening within these enshrouded regions covered by dust and gas that makes it hard to look into there and see what's actually going on. And then, of course, we've had a few surprises along the way. Binary stars were definitely one of them. Okay, so I'll break the talk up into five main parts. I'll just initially just kind of overview how single stars form. This is a formation scenario that's been pretty well established over the years, and we think does a pretty good job describing how single stars form. Then I'll talk about how planets form around those single stars. Then I'll talk about binaries. Basically, what binary stars are, their prevalence in our galaxy. And then talk about kind of the wrench that binarity throws into the star formation scenario  Okay, so if we decide to kind of pick out one little spot on this image here and call that a cloud,  here's some kind of characteristics for how much material is in that cloud. So it's really enormous. We're talking about tens to hundreds of thousands of solar masses worth of gas. So there's a lot of material that's just hanging out in these clouds. They're enormous, so tens to hundreds of parsecs. To give you some idea of scale, our nearest star is four parsecs away, and that's pretty far. So these things are really, really large objects on the sky and in physical space, they have densities of about 1000 particles per cubic centimeter. So if you think of like a small little, like a dice, there's about a thousand particles in there. To give you some idea of what, you know, what that means, the air in this room, there's about 10 to the 19th particles in one cubic centimeter. So, you know, we call these things dense in astronomy, but they're actually much less or much more diffuse than even the best vacuum we can create on Earth. Okay? And that's the dense part of our galaxy. And they're very cold. So 10 degrees Kelvin. This air is about 300 degrees Kelvin.  Okay, so most of this material is not going to form a star. Okay? The only part of this cloud that could potentially form a star is going to be a molecular cloud core. Okay? So a core is going to be just a very small, overdense region within that cloud. So it might only have about five solar masses of material, be about a tenth of a parsec, and more dense than the ambient cloud  but still kind of not that dense compared to the air, and a much colder temperature. And these, you know, you can kind of see some in the depiction of that image there. These clouds are turbulent. There's all these flows that are kind of passing through the cloud. And so they're not this kind of calm, quiescent environment. There are, you know, there's turbulence, there's chaotic motion within the cloud. Okay, so let's take our cloud, let's zoom in on it, and let's talk about how we're going to get this cloud to collapse to form a star. So I've drawn eight arrows, four pointing in and four pointing out. The blue arrows are depicting the force of gravity. So gravity is trying to make this cloud collapse, and gas pressure, depicted in the red arrows, is trying to keep this cloud from collapsing. And so a cloud core by itself is naturally  in what we call hydrostatic equilibrium, which is basically just a fancy word for saying that gravity and gas pressure are balancing and that this cloud is not going to collapse on its own. If you compress gas, it heats up, the pressure goes up, and so it's going to want to push back. So to get this cloud to collapse, we're going to need to give it a kick, we're going to need to give it some stimulus to push it over the edge. So the main ways that we think this happens is from spiral arms and galaxies. So you've seen pictures with these beautiful spiral arms within galaxies that are traced out by stars. We think that those spiral arms are actually density waves that are passing through the disk that locally make the density in the galactic disk higher. So that increase in density might be enough to send this cloud over the edge and make it collapse. Other ideas are blast ways from nearby supernova that make a little of that pile up material that make it dense enough to collapse. Or from potentially colliding turbulent flows within a cloud that collide and just make a momentarily overdense region that could possibly collapse. But this process has to be fast because you have to collapse the cloud faster than the gas can react, because if the gas has time to react, it's going to heat up and it's going to push back. So this has to happen really fast. And fast in astronomy means hundreds of thousands of years or a million years. Okay? So while to us that's pretty mind-blowing, but it's so fast that we've actually never been able to observe this happening. This is just something that we think must happen to form a star. The reason is because, of course, it's hard to observe, it's embedded within a cloud, but also, you know, these are things that just happen quickly and are not a commonplace in the galaxy at large.  Okay, so let's say that this thing does happen to become overdense, it starts to collapse. The main thing that's going to govern the collapse of this cloud is angular momentum. Okay? So what's angular momentum? Angular momentum is one of the like... Sorry, one of the physical descriptions  of material that's conserved. So the conserved quantities are usually mass, energy, linear momentum, and angular momentum. So these are conserved quantities. They're special physical properties that describe a system. So when you think of angular momentum, you can think of like a top. It's spinning. It has some angular momentum, and that's what prevents it from tipping over. Okay? That's one description of how you can think of angular momentum. But when we're talking about this cloud, it's not that easy to describe. The cloud is not, it doesn't have any net rotation, let's say. So the way that we have to describe angular momentum is go around to each point in the cloud and takes its mass,  multiply it by the velocity of the cloud and multiply it by the radius within the cloud. So that's like, you know, the radius from the center here is what you would use as the radius. So, because velocity has a direction,  angular momentum also has a direction. So you make that measurement for every point in the cloud, you add them all up, and a lot of them are going to cancel because we have these turbulent flows. There's not an organized coherent rotation. They're just kind of flows happening everywhere. But they're not all going to cancel out exactly to zero. There's going to be some minuscule leftover net angular momentum when you add it up from all this cloud.  So, because angular momentum is conserved as this cloud starts to collapse, the mass will remain the same. Angular momentum is conserved, so that's going to remain the same. Your radius is decreasing because the cloud is collapsing. And so the velocity is going to increase. The rate at which you're spinning is going to increase. So you can think of an ice skater spinning on the ice. As he or she pulls her arms in, he or she is going to spin faster. So that's the analogy to kind of give you an idea of what this cloud is going to do. So as it starts to collapse, it's going to want to collapse in all directions in towards the center, but because it's rotating, it can't go in in this direction perpendicular to, whoops, perpendicular to the spin axis. It's like if you're on a merry-go-round and you're spinning around, it's hard to walk in towards the merry-go-round. So if you think of a bunch of merry-go-rounds nested on top of each other, you can go in this direction, but it's hard to go this direction So as the thing collapses, it doesn't collapse into just a ball. It collapses into a disk. And eventually, within that disk, you're going to, basically a protostar is going to turn on, it's going to be born, and it's going to be very luminous and it's going to start to blow out this cavity. So this is the end of our first phase of star formation once this core collapse phase is over. So, to put this onto a timeline,  if this is our star formation timeline, this happens in about one percent of the total star formation process. And that's why it's hard to observe. Imagine every star that could possibly be forming, only one percent of them are going to be in this phase. Okay, so there's very few of these things to look at. Okay, so our next phase is dominated by this interaction between a protostar and its disk. Okay, so as this cloud collapses, our protostar is going to return to hydrostatic equilibrium. Basically, it's going to collapse enough that it's going to find the balance where the gas pressure becomes high enough, it's hot enough they can push back against gravity, and we have some sphere that is at the center with this disk of material left over. This is a very luminous object, and so it's able to blow out all the gas that's not in the disk and leave us with something like the top right corner there.  At the same time, the star is also developing a strong magnetic field. Okay? Which you can see in these field lines here around the star. So the star, these field lines actually look very similar to what you'd see if you put iron filings on a magnet. Okay? So the distribution of the magnetic field is very similar between the two. And the way the star develops this magnetic field is that as the star collapses, it tangles up all the magnetic field that's in the cloud and it basically makes it stronger and reorganizes it into this global field. So basically you're taking the whole magnetic field of the cloud, collapsing it into this star, and reorganizing it into this nice shape that you see here.  And so the remainder of this step of evolution  takes place as the disk material slowly accretes or gets transferred onto the star.  The way that happens is disk material is all rotating, but an inner part of the disk is going to rotate faster. So that's going to make it drag as the material goes around. So the drag is going to slow down the inner part. If any material orbiting the star starts to slow down, it will not longer be able to maintain its orbit. So it's going to start to decay in. So that's what's bringing the material in. It's going to follow this kind of slow path in towards the star. It's going to then become truncated by the star's magnetic field. And then it's going to be confined to flow along these magnetic fields and impact the star at the top. Okay? So that's how the material gets from the disk, across this gap, and onto the star. And you can observe this by looking at brightening events. So this makes a hot spot on the star. It makes the star brighter. So you can actually see a star get brighter as these accretion events happen. And we'll tie back into that in a little bit later. Okay, so what are the implications? Well, this is a reservoir for continued mass growth onto the star. And this interaction between the star and the disk actually works to regulate the star's rotation rate. So, as we said before, as things collapse they start to spin faster. But if you have this connection between the star and the disk through this magnetic field, the magnetic field can actually lock the star to the disk's rotation, slow it down so that the star is not, you know, at this extremely high spin rate. It actually slows it down. Okay, so that takes about 10 percent of the full star formation lifetime. So we've made it 10 percent so far. Don't worry, the last step is pretty quick. Slowly, we just accrete onto the star. The star is very bright, and it blows out the remaining material. And we're left with just a star and a planetary system.  So if we put that up on a timeline, that takes the last roughly 90 percent of star formation. So we really, you know, w e have a really good understanding of this phase here, where the star is just slowly contracting from gravity, it's giving off energy, making it contract more, and eventually that core becomes hot enough to start fusion. That fusion is the new energy source that prevents the star from collapsing from gravity. So this is just a smooth,  very gentle path towards starting fusion  that takes most of the star formation lifetime.  To give you a further idea of how short this whole process is, a star in the main sequence will last, will stay on the main sequence for one to 10 billion years. 

 And this process takes place over 100 million years. So if you think, just statistically, how many stars there are in the galaxy and how many could possibly be in this phase of evolution that takes roughly one percent of the star's total lifetime, there's just not that many targets that we can go after to try and understand this process Okay, so that's roughly how star formation goes, as best we understand it, for single stars. Okay, so now let's talk about how planets form within single stars. Okay, so looking at our star formation timeline, the window of time that's really important is this little yellow region right here, where the star and the disk are interacting. So if we zoom in on just that one little region, we have roughly one to 10 million years to form a planet. So how are we going to do it? The first step is that we have those dust grains that we talked about in the cloud. They are shielded from the star. They're out in the middle of the disk, and they can coagulate. Basically, they'll bump into each other and they'll stick. So you can take grains that are roughly a micron in size and build them up to be about a meter in size. But then we've run into a problem. This is called the meter sized barrier. Once you make large enough objects, when they hit into each other they no longer stick, but they break apart. They fragment. And so this is a problem. How do we get objects to get past this barrier? How do we get them to be big enough to where they can collect gas around them and get really big before something busts them up? Okay? So that's a problem that we really don't know the answer to as a community.  But assuming we can get... Oh, well, sorry, let me back up. One way we think we might be able to get around this fragmentation problem is with ice. So if we look at a schematic of the disk here, we've got the star at the center. As we go out in the disk, we've got a little thermometer. You can see it's quite hot. As you go further out in the disk, things are getting cooler. You're further from the star. You're being less heated. And eventually you cross what's called a frost or ice line where things like water or methane can form ice. So if you perhaps take one of these meter-sized dust grains,  cover it in ice, maybe that acts as a little buffer that can allow these meter-sized things to hit into each other and stick or form larger clumps rather than totally fragment. So that's one way around it. But another problem that we really don't have the answer to is planetary migration. So when planets are small, or dust grains are small, they are coupled to the gas.  So they rotate with the gas. They have the same velocity as the gas. As they become larger, though, they'll decouple from the gas, and as they orbit, they'll feel a drag from the ambient gas around them. So that's going to slow them down. Any time you're going to slow down an orbit, you're going to start to decay in. And so a lot of simulations that study planetary migration  have shown that you can make a ton of planets but then you just fling them all into the sun because this is a really effective process. So either your planet has to clear a gap in the disk or in some way shield itself from this process because it seems to be very effective. So that's one thing we don't completely understand, but it does explain things like hot Jupiters. So perhaps you've heard of a hot Jupiter. It is a Jupiter-sized star very near the sun. So imagine Jupiter at Mercury's radius. So these things are weird because we think you can only form a hot Jupiter way out here past the frost line because you need all of that gas to be in an ice phase so you can accrete it into a planetary core. So we definitely don't think you can form a hot Jupiter or a Jupiter-sized planet right next to the star, so probably what happens is it forms further out and gets migrated in. Okay? So why that didn't happen in our solar system is a good question that I don't have the answer to. But these are the types of things that, you know, planet formation is up against right now. But there's good hope that we're going to start to really unravel what's happening with planet formation due to the ALMA Telescope. This is a radio telescope in Chile that took this image  in the past year. It's called... This is a protoplanetary disk called HL Tau. The protostar is right in the center here, and you can see that in the disk we have all these gaps. And the interpretation is that these are planets forming within the disk. Okay, so this is, you know, an amazing image that is really kind of driving where planet formation is going, and hopefully in the future we'll be able to have more objects like this so we can kind of start to untangle what's happening. The good news is this is a really young planet, really young system. Only 100,000 years old. So if they already have these gaps, that could mean that planet formation is more efficient than we think, and we could have like planets forming very easily, and just then the problem becomes having them stick around. Okay, so that's planet formation in a nutshell.  Okay, so now we're going to talk about binary stars. So, binary stars...  Let me move my mouse over here. Okay. So binary stars are just two stars that are gravitationally bound to each other. They orbit a common... And they orbit a common center of mass. So I'm showing you two stars here, where one is very small, that's this one going around like here, and one is very large. The one in the middle doesn't look like it's moving. It is but its motions are very small. So you can imagine this being like the sun and Jupiter. If we make Jupiter more massive...  Oops. Let's see if we can do this here.  So if we make Jupiter more massive, closer to the mass of the sun, you'll see that both stars are now moving, and they're orbiting around this common center of mass. So these are very stable orbits, and a star is happy to do this dance for its entire evolution. One thing you can also change... Let's see if...  I can't quite get down there, so I'll just say that one of the things you can change is the eccentricity of the orbit. So these are circular orbits. But you can elongate an orbit as well, make them overlap in some cases, and those are just as stable. Okay? So just because all of the orbits in our solar system are nice and circular doesn't mean that an elliptical orbit is unstable. They're just as common as circular ones. Okay, so we can go back to our presentation now.  Okay, even in the same spot, look at that. Okay, so just to recap, there are four main characteristics  of a binary star. So it's semi-major axis, the distance between two stars. Their mass ratio, the mass of the smaller one divided by the mass of the larger one. This is usually or has to be less than one by definition. The eccentricity. So zero is for a circular orbit, one is for a very elliptical orbit, and then inclination is the angle at which we observe the system. Okay, so 90 degrees is right edge on and zero degrees is face on. Okay, so those are the four ways that we describe binary stars, and these are the ways that we detect them. So you can... Actually, if the separation is large enough, you can actually spatially resolve it on the sky, and you can observe the smaller star move around a larger one. This is hard work, though, because you can see this goes from 1970 to 2000. So this is a lot of observing. It takes a long time, and you can really only do this for close stars because the closer the star is, the easier it is to actually view the separation. Another way is to find eclipses. So if you have this sweet spot and inclination where stars are perfectly lined up in the orbit, they'll pass in front of each other as we view them and we'll have a drop in brightness. As one star passes in front of another, you'll have this dip in the brightness. So you can't actually see the separation between these two stars, it just looks like one, but you can see this drop in brightness as a function of time as one star passes in front of another. This one's great, but it requires that inclination to be right edge on, which is hard to do, you know, hard to actually find in practice. And the last one is a spectroscopic binary. So, again, the stars are too close for us to actually spatially resolve, but as they go around we can see Doppler shifts in their lines. So this is also a way that we find planets around stars. The stars' motion towards us and away from us shifts their spectrum back and forth, which we can measure. And so if you measure that rate of velocity pattern, you can create an orbital solution out of that. So this one is really great, but spectroscopy is an expensive observation to make so usually you're limited to only the brightest stars where you can do this. But each one is kind of complementary when you add them all together. Okay, so they're everywhere. Binary stars are extremely common. So one you probably all know about is the one that's in the Big Dipper. So the middle of the handle there you have Mizar and Alcor,  which, if you have good vision or binoculars, you can actually pick out these two stars with your eyes. Now, you know, this is, you know, a really well known pair of stars,  but as we studied them further, we found that Mizar, the brighter of the two, is actually four stars. It's two stars in a binary and two other stars in a binary that are all gravitationally bound to each other. Okay, so there's four stars there. And Alcor, it turns out, is also two stars. So, you know, if you have poor vision, that's one star, but it's actually six if you can characterize all that's happening within that system. So it's kind of... Just recently we began to think that Mizar and Alcor are actually gravitationally bound to each other as well. That's kind of a recent discovery in kind of 2009.  So definitely an interesting system that you can see yourself. But it's not just that particular system. They're extremely prevalent in our galaxy. So 30 percent of low mass stars, so stars less massive than the sun, roughly 60 percent of solar mass stars, and as high as 90 percent for the high mass stars. So the sun is actually kind of not the most common outcome of star formation in that it's a single star. But there's definitely something happening. You know, there's definitely something intriguing here where we're seeing that as you go to higher masses, binarity is more common. You know, so that's like a clue that we don't have the answer to yet, but there's definitely something there. And then, of course, we found binaries or we found planets orbiting around one star within a binary as well as planets orbiting around a very close binary. So we know things like Tatooine exist in our galaxy. 

 You know, understanding formation tells us how is the formation of a planet in these environments different, and what does that mean for the evolution of the planet and things like that. Okay, so that's binary stars. Let's talk about how binary stars form. Okay, so there's two main theories for how you get a binary star to form. The first is that a cloud during this collapse phase will fragment. Okay? So perhaps the star or the cloud core  has some underlying structure that gets enhanced as it starts to collapse, and those two things break apart but remain gravitationally bound to each other. The other one is that as this disk starts to flatten out, if the cloud has too much angular momentum, if it starts to spin too fast, it'll start to fragment that disk and spread it out. Okay? So these are the two main scenarios we have to try and understand how binary stars form, and the key ingredients here are the total angular momentum of the cloud before it starts to collapse as well as the structure within the cloud. But there's some exciting new things that actually just came out this month. This is another ALMA image where you can see a triple system forming. Okay? So we have a very tight binary right here as well as a larger mass tertiary, or like a triple star, forming further out. And so this is good evidence that perhaps both core fragmentation and disk fragmentation are at play. Disk fragmentation could potentially be responsible for this closer binary while core fragmentation may have led to this triple companion. Okay, so these are really interesting results that have just come out. ALMA is going to do a lot of great things for helping us understand star formation by lights that peer through that dust. So you can never take and optical image like this. You're limited to radio observations.  Okay, so you form a star and there's kind of  three regimes where binarity has a different effect.  You've got really wide binaries, kind of medium range binaries, and very close binaries. We think it's probably safe to assume that the really wide ones are from core fragmentation and some spill over into this medium range, and then disk fragmentation is responsible for the closer period binaries. Okay? So I'm going to go through each one of these different steps and talk about how... Or each of these different separation regimes and talk about how stellar formation might be different. Okay? So the first, very little impact.  These stars are very far apart, they got fragmented during the collapse of the cloud, and so both will undergo, you know, formation and evolution in the same way as a single star would, relatively ambivalent as to whether it has a companion or not. If we put these stars a little bit closer together, the orbit of the binary is going to truncate the disks.  So that means that you're going to have less disk material that can fall into the star,  the disk is going to get exhausted more quickly, and because that interaction between the star and the disk through magnetic fields is so important for regulating rotation, these stars are going to have a different rotational evolution than a single star. And then, if we make, you know, go to the last extreme, you can have binary systems that have up to three disks of material. A small disk around each star, which my little cartoon doesn't quite depict, a small disk around each star as well as this gap, and then a larger circumbinary disk. So this gap is cleared out by binary orbital motion, and then you're left with this material like around it.  So the differences here is that we're going to have a very dynamic disk environment. So it's going to be a lot more churning up the disk from the binary orbit. You're going to have bursty accretion events and, again, a different rotational evolution. The disk in this case, there's maybe some hints that the disk could last longer around the close binary because there's this gap that the material kind of has to cross in...  I guess it kind of dams the flow of material into the binary. So that could slow things down and potentially leave you with a longer lived disk. So this is actually the area of my research. And we're going to go on a brief little foray into what I do my research on. So hopefully, you know, we've got a broad overview to kind of motivate where we're going to go, and you can get a glimpse into how ultra specific and esoteric a PhD thesis in astronomy is. Okay, so here we go.  Here is a simulation of exactly what you just saw, but now from the top. You can see there's two stars. They're orbiting each other. They're clearing out this gap in the disk. So the darker black and purple means that there's less material. The bright colors means that there's denser material. So as these stars orbit, they clear out this gap, but there are these streams of material that connect the two stars in the middle with the circumbinary disk. Now, the prediction of this simulation is that material is going to be brought in at every orbital period, and you're going to have this burst of accretion, a burst of mass falling onto the stars every orbital period occurring right when the stars are closest to each other. So if we just look at the, like a plot of what this simulation predicts, I'm plotting the mass accretion rate. So the amount of material that's falling onto the star, in units that aren't really important, as a function of time. As you can see in the blue here, you have these bright bursts of accretion, which, remember, accretion makes a hot spot on the star that you can measure by measuring the brightness of it. So the prediction is that you're going to have a brightening event every orbital period right when the stars are closest to each other. So that's the prediction, and that's one of the things that I've been trying to test with my research. So the way that I've done it is with this new network of telescopes called the Las Cumbres Observatory's Global Telescope Network. That's a mouthful, but all it is is a network of small telescopes located across the globe. So we've got them in Australia, South Africa, Chile, and in Texas.  And the nice thing is that all these telescopes are networked together, and it's always dark in one of those places. So you can observe a star continuously. You know, you don't have to wait for the sun to go down as you do in a traditional site. You can observe constantly, and you can observe at weird times. Like if you want to observe a binary every other day, or, sorry, every day-and-a-half, you couldn't do that in one site because a day-and-a-half later from the night is noon the next day. So this allows us to observe things continuously and at weird cadences. So, what I've done is measure mass accretion rates as a function of orbital period. So as I play this, you're going to have, you're going to watch the mass accretion rate that we measure, and then on the right you're going to have the binary orbit evolve. So we already know the orbit of this system. Yeah, we know basically the orbital parameters of this system. So as we play this, remember we expect a burst at closest approach, which is marked with a dashed line. And what do you know, we've got a lot of activity happening. So the accretion rate goes up. When the stars go away from each other, it goes back down. The stars start to get closer together and, boom, another burst of accretion. So, you know, so that's what my has been trying to do, understand how binary stars interact with this disk when the stars are close together. So that's pretty exciting. We've kind of confirmed the results of this simulation. Hopefully we can understand this interaction better and how it relates to planets. Planets and their formation. Okay, so diversion over. Let's talk about binary stars form in planets and what that means for their evolution. And, excuse me, and at this point in the talk we're kind of in uncharted territory. We barely understand how stars interact with disks and now we're going to understand how a planet forms within them. So this is definitely, you know, we're kind of going to the realm where we don't have good observational evidence to back these claims up, but, you know, we'll take you there anyway. Okay, so we'll start with each of these different separation regimes, go through them, and talk about how planet formation might be different in these environments. So when the stars are very far apart, you know, the star's evolution is not going to be very different, and so the planet's probably not going to be very different either. A planet is probably not going to care that there's another disk and another star that's still gravitationally bound but very far away. So these guys are not going to care too much that they're in binaries. Okay, let's get a little bit closer now. In this case, you know, we talked about how there's less material in the disk and the disk is going to live for a shorter amount of time. So you have less fuel and less time to form your planets in. So one prediction is that it's going to be harder to form planets in these kind of medium range binaries because there's just less material, less disk material and less time to get a planet going. Okay?  The final regime that we saw earlier  is when you have these two stars very close together. So, as you saw in the video, each star has a very small circumstellar disk around it. And that disk is constantly being perturbed by the companion. It's having mass flow in. It's shooting material onto the star. So it's probably going to be very hard to form a planet very close to the star there. At the inner edge of this circumbinary disk, right here, as you saw in the movie, it's a very dynamic region that's constantly being churned up by the binary orbital motion, and so it's definitely not a very stable place to form a planet or have a planet reside in a nice kind of quiet orbit where it can grow. As you move further out from the stars, though, you're probably going to be in a much better place. Somewhere out here you're not going to care too much that there's a binary at the center, and so you can probably form a planet that's just, you know, very happy to, you know... You know, it's not going  So let me just kind of recap what we talked about today. So we started with just single star formation and the challenges that come along with trying to observe these systems. We got a huge range in spatial scales, it happens quick, and they're happening within these dusty clouds that's hard to see within. Binary stars are everywhere, our understanding of how that affects our formation is definitely still in its infancy, but understanding how binary stars interact with disks  actually gives us kind of a unique way to understand how disks evolve, how viscous disks are. 

 That can kind of give us a window into better understanding disks in general. And then, finally, we're really at this interesting stage in astronomy where, with things like ALMA, things like the James Webb Space Telescope, which is going to be like an infrared version of Hubble that's going up in 2018, we're going to have a really interesting view of these systems. We're going to be able to peer through this dust to really get a good idea of what's happening behind the screen and understand formation of stars and planets much better. And we're kind of at the point where our observations can start to constrain simulations of star formation in a way to really understand, basically, this disk-star interaction and how this kind of collapse phase takes place. So, with those up there, I'll just go ahead and leave those up there and say thanks and take any questions.  [applause]