 Awesome. We are live. Welcome everybody. Thank you for joining us today to today's webinar. My name is Alejandra and I'm going to be today's most physics coordinator. Today we are presenting a first look at the supermassive black hole by Leah Medeiros. Leah got her PhD this spring from the University of California, Santa Barbara, and she will start a post-acquisition at the Institute for Advanced Study in Princeton combining it with an NSF fellowship. She got also a master's from the University of California, Santa Barbara, and she did her bachelor's in physics and astrophysics at the University of California at Berkeley. She's part of the Event Horizon Telescope Collaboration and performed both theoretical simulations and also she was part of one of the four groups that reconstructed the image that the beautiful image we saw a couple of weeks ago. And today she will talk about the image of M87, how they estimate parameters, and she's going to talk about this cool project and science and remember that if you have questions you can do them over email through our YouTube channel or Twitter and then the questions will be read at the end of Leah's webinar. So without further ado we'll turn the time to over to Leah. Thank you. Thank you so much for that introduction Alejandra. I'm trying to share my screen. Just give me one second. Okay can you see my title slide now? Yes. Okay wonderful. So as Alejandra just told you I'll be telling you about the recent EHT results, specifically the image that I'm showing you here on my title slide. So the Event Horizon Telescope is a very long baseline interferometer with telescopes spread all over the world. So this includes the IRM telescope, the Alma and the Apex telescopes in Chile, the large millimeter telescope in Mexico, the submillimeter telescope in Arizona, the JCMT and the SMA on Hawaii, and the South Pole Telescope. And so as the air rotates different telescopes come into view and different telescopes can observe the source. And so we are essentially creating a virtual earth-sized telescope by combining all of these different telescopes that I showed you. So obviously telescopes are not enough to do this project. We also need a very large number of people that have been working very, very hard on this for a very long time. So this is a picture from our recent collaboration meeting in the Netherlands. This was November of 2018. At this point we had all seen the image already. We were all very excited. You can see all of our smiling faces. This is obviously not the entire collaboration that everybody could make this collaboration meeting. But it's a pretty good sample of the people that have been working on this project. So these are the EHT board institutions. I'm contractually obligated to show you these slides. These are the EHT affiliate institutions. And of course we have a lot of funding agencies that have been supporting this work as well. And this just really goes to show you that it really is a global effort to try to get the first image of a black hole. So the primary goals for the Event Horizon Telescope are first to observe black hole shadows. We'd also like to be able to probe accretion and jet physics. And finally we would like to connect a variability study specifically trying to understand the cause of the flaring events that have been seen for several H&N and also the galactic center black hole. So the black hole shadow was first discussed in 1973 by James Bardeen. And in that original paper Bardeen calculated what an observer would see if that observer was looking at a black hole. And there was somebody behind that black hole shining a flashlight on it. And what Bardeen calculated is that the observer would see a bright ring which would encircle a dark region. That dark region is what we now call the black hole shadow. So I also have an animation to try to illustrate this a little bit better. And so in this animation the green circle is the Event Horizon. The black dashed lines that is the photon orbit. And all of these red and blue lines that you see here on the edge, these are photons. And when I play this all of these photons will be evolved as they move towards the black hole. All of the red photons will escape the black hole and will fly off to infinity. But all of the blue photons will actually fall into the black hole and be lost forever. And so the black hole shadow is created by all of these blue photons. And the point that I wanted to make here is that the black, the size of the black hole shadow is essentially equal to the lensed photon orbit. Or I've also added here the size scale so that you can compare. So the the radius of the black hole shadow is about 5 GM over C squared. I've set G and C to 1 here. And so it's about 2 and a half times bigger than the actual event horizon of the black hole. And this is a really important point because there's a lot of media out there that's saying that the dark region that we see is the event horizon of the black hole. And that's not actually true. The dark region that we see is the black hole shadow, which is significantly different than the actual event horizon. So the diagram that I just showed you was what the black hole shadow would look like for a short child black hole. But we do expect that astrophysical black holes might be spinning. And so I have here another animation. And when I play it, what will happen is that the spin of the black hole will increase. So right now you're looking at the boundary of the black hole shadow for a short child black hole. But as we increase the spin, you'll see how the spin of the black hole affects the actual shape and size of the black hole shadow. And the other thing I want to point out is that you're looking at the equator of the black hole right now. And that is the orientation, which you'll see the largest possible deviation from the short child black hole. So I'm going to play that and you'll see that this shadow moves over to the side. So far nothing's really happened to either the size or the shape of the shadow. It's just moved over. And only when you get above about 0.8 do you get a significant change in the actual shape of this shadow where you get this little dent that you see here. It is obviously very clear that this is not a circle. But if you were to actually mathematically define how far from the circle you are, this is actually very close to a circle. So the deviation is relatively small. And so the main point that we're trying to make here is that because the size and the shape of the black hole shadow depends only weekly on spin, if we were to measure the size and the shape of the shadow for a black hole where we knew the mass of that black hole, we'd essentially be able to perform a null hypothesis test for the current metric. We have a very precise prediction for what the black hole shadow should be if this is a curve black hole. And if it is anything different than what we expect, then it can bring the current metric into question. And maybe black holes really aren't described by the current metric in real, you know, actual space. And the only other thing I wanted to point out here is kind of try to explain very loosely why this shadow is moving over to the side and why it ends up still being very close to a circle. So what's going on as you increase the spin is that the quadruple moment would increase and that would tend to make the shadow more oblate. However, because of the frame dragging effect, as you increase the spin, you also increase the frame dragging effect. By the way, the black hole spin axis is pointing up. So the frame dragging would tend to push photons towards the right of this image. And so what happens is just from the quadruple moment, the shadow would become more oblate. But because you have the frame dragging effect, these two effects almost perfectly cancel out. And so you end up with a shadow that just kind of moves over to the side instead of the shape changing significantly. So I also just wanted to give you a little bit of a taste for one of the other projects I've been working on recently. I'm not going to have enough time to actually talk about this project, but I just wanted to give you a little bit of an idea of what else is possible. If you were to take the ker-metric and if you were to perturb away from the ker-metric slightly, these are a few examples of what the black hole shadow might look like for a non-ker-black hole. And the point here is that hopefully you can see how much the size of the black hole shadow is changing on the left panel. And on the right panel you can see that by adding perturbations to Kerr, you can make the the perturbation to the black hole shadow much more significant than it was for the Kerr black holes that I just showed you. Okay, so the Event Horizon Telescope has two primary targets. The two targets are the black hole at the center of our galaxy, SAJ-STAR, as well as the black hole at the center of M87. And so the black hole at the center of the galaxy is about a thousand times smaller than M87, but it's also about a thousand times closer to us. So those two things cancel out almost perfectly, and we expect that the image of SAJ-STAR will be a little bit bigger than the image that we've already published from M87. And so the plot that I'm showing on the right here, this is trying to give you a summary of how different black holes might appear if you were to image them with the EHT. And the idea here is that on the y-axis I'm showing you the flux of each of these black holes at 1.3 millimeters, which is the wavelength that the EHT observes at, which I will explain on the next slide. And the x-axis is showing you the resolution that the EHT, at least in this current configuration, would be able to obtain. And the point here is that as you go towards the left on this x-axis you get higher and higher resolution. So SAJ-STAR and M87 are very clearly the two best candidates for us to get a horizon, sorry, an image that is resolved to horizon scales. But all of the sources in this purple triangle here on the side, these are sources that are bright enough for the EHT to observe. We just won't be able to do a horizon scale science with them. And so all of these sources in this purple triangle are sources that we have already observed. And we hope that there will be a lot of really exciting science that comes out of our observations of those sources again, sorry, as well. But the main point here is just that there are two sources where we hope to actually be able to resolve the black hole shadow itself. So why are we using 1.3 millimeters? There's a few main reasons for that. So first, the peak of the millimeter and infrared emission for the galactic center black hole SAJ-STAR peaks around 1.3 millimeters. Second, the atmosphere is transparent at this wavelength so that we can actually observe from the earth. Third, the interstellar medium effects are sub-dominant so we can actually see through the galaxy to the center of our galaxy. And finally, the accretion flow is expected to become optically thin at this wavelength. And so what I'm showing you right now is the result of a general relativistic magneto hydrodynamic simulation. What you're looking at right now is what a black hole like the black hole at the center of the galaxy or the black hole in M87 might look like if you were to look at it at 1 centimeter. And of course, the main point here is that you have all of this orange material that you see that is the accretion disk. And at this wavelength, the accretion disk is optically fixed so we can't actually see the black hole shadow. But when I play this animation, what will happen is that the wavelength that you're looking at will decrease. And so we'll get to see how this accretion disk becomes transparent as we go to shorter wavelengths. So there we go. And hopefully you can see now the black hole shadow. We're going to zoom in a little bit as well. And the point that I wanted to make here is that it'll start playing as a function of time. There we go. The point I want to make here is that there's a lot of variability that you see in this structure. But hopefully you can see that there is this relatively constant ring shape that remains stable despite all of the variability that you see in this image. And of course, this variability comes from the turbulence and the accretion flow and how that gets lensed by the black hole itself. So let's dive a little bit deeper into how interferometry works. So each pair of telescopes on Earth can observe one specific location in for a space. So interferometers don't observe in the image domain, but they observe in the for a domain. So we get a few complex for a components of the image. And then we use those for a components to try to reconstruct an image. So as the Earth rotates, what happens is that each pair of telescopes will probe a slightly different location in for a space. And of course, as we're seeing here, different telescopes come into view and you can probe yet more regions of for a space. And so over about 12 hours or so, we perform these observations and we can probe the areas of the furrier space that are shown by these red dots on the right side here. And so as I just promised that is in fact what we did, the plot on the left here, these are the actual real baseline tracks for the observations that were performed in April of 2017. So these are the areas of the for a domain that the event horizon telescope actually observed. And on the right, I'm showing you the amplitude of the for a components as a function of the distance from the center of the for a domain. And so hopefully you can see how the colors here are matched. Oh, I lost my cursor for some reason. Okay. Well, hopefully you can see how the colors on the two panels are matched. And the point here is that as you go farther towards the right on the right panel. So as you get to higher spatial frequency or higher baseline length, you'll be able to probe finer scale structure. So just wanted to point out that we are also showing a light gray dashed line. Hopefully that is clear on your screen. And that light gray dashed line is really just to kind of guide your eye a little bit and give you a little bit of intuition for how this data might look. And that dashed gray line is the result that you would get if you were to take the for a transform and take the amplitude of a symmetric thin ring of about the size that you might expect for the black hole shadow. So there are a few different possibilities for what this black hole could have looked like. And so I'm showing you four different possibilities. And then I'm also showing you what the amplitude of those images might look like. So hopefully this can give you a little bit of intuition for how we can use the data that we get to actually be able to distinguish between these different images. So the first like the top left image here, this is the result of a GRMHD simulation. And this black hole is based on the black hole spin axis is either pointing towards you or against you, but it's parallel to your line of sight give or take 20 degrees. The one below that is also a result from a GRMHD simulation. But this black hole is inclined with an inclination angle of about 60 degrees towards the observer. The next one on the top right here. This is again a result of a GRMHD simulation. But the difference between this one and the one I just talked about is just the geometry of the initial magnetic field, the seed magnetic field that you put into your original starting point for the simulation. And so you can see even if the actual black hole was the same, it is possible to get an image that looks significantly different just based on the geometry, at least for these particular parameters that I'm showing you here. The last example is kind of the worst case scenario. If we had done something wrong and if the accretion flow actually wasn't optically thin, what would the data from that look like? And so again, the the two lines that I'm showing you in the visibility amplitude plots here, these are the vertical and the horizontal cross sections of the visibility amplitude map for these images. And the vertical and horizontal cross section is very frequently kind of the two limiting points. And so I will frequently show you those two cross sections and just know that most of the data points would be contained between these two boundaries if we were to actually observe a source like this with the event horizon telescope. So I wanted to go again a little bit deeper into what different images look like in the Fourier domain and specifically trying to really understand what this data is showing you without even using an imaging algorithm. Before we try to use imaging algorithms, just looking at the data, what can we tell about this image? So what I'm showing you right now is a very, very overly simplified model. It's literally just a disc. And that disc, the visibility amplitude or the amplitude of the Fourier transform of that image is shown as the yellow line on the right panel here. And all of the red points are the real M87 data points for the EHT. And so as I change the size of this disc, you can see how the location of this first minimum changes. And so we can change the size of this disc to match the first minimum that we see in the EHT data. However, as you can see the location of the second minimum as well as the actual height of that second little bump that you see there is completely wrong. So just changing the size of a simple disc is not enough to fit our data. But the next thing we tried was putting in a hole. So if you were to add in a hole, you can actually change the size of the central black disc and the size of the larger orange disc. You can change those two sizes such that you can actually match the location of both of the minima that we see in our data. But again, hopefully it's clear that if you compare the data right here, you're still a little bit off from the data. So if you blur your image just slightly, you can lower that second hump a little bit better. And of course, even though we're doing great with most of the data, you do still have some data points right here that are not well matched by this model. And this is because the model that we have right now is a symmetric ring. And if you were to introduce an asymmetry, you'd be able to have different regions of the for a space look a little bit different. And that's how you would be able to match the data points that you see here. So obviously what I just showed you is overly simplified by a very large amount. But I also just wanted to go through in detail how these imaging methods work to try to demystify the process a little bit. And so the way that most of the imaging methods that we use for this data work is that we start with essentially a grid of pixels. And it's a pixel dependent model. So you try to change the intensity in different pixels to better fit your data. And so the idea here is you're trying to iterate to minimize the chi-squared. And this is essentially the very first iteration that I tried back in June of 2018 when I was trying to image this the M87 black hole. This is the very first iteration of that resulted from this imaging algorithm. And you can see that it's a pretty horrible fit to the data. By the way, I did not mention this earlier, but these lines right here are the vertical and horizontal cross sections of the image that I'm showing you here. And this shaded region are essentially the two lines are the boundaries. And we expect that all of the data points that we would measure if we had observed this image would be contained within these two boundaries and would be in this shaded region that you see here. So I'm going to go ahead and iterate a little bit more and we'll see how each iteration changes the visibility amplitude of our model relative to the data and you're trying to converge to something that matches the data pretty well. And so this is how we get an image that looks like the little the rings that you saw in the press conference. So these are the results of the imaging algorithms. So I just wanted to explain very simply what these algorithms are. So the bottom two are similar to the algorithm that I just described. And actually the image that I was showing you that I was converging to an image that was done using the EHT imaging algorithm. The top row is very different. It's called DiffMap, but it actually is clean. Many of you might be familiar from clean with clean. Clean is a a algorithm that's been around for a very long time to reconstruct data from VLBI sorry reconstruct images from VLBI data. And so the main point here is that we observed in four different days and we used three different algorithms and they all show this ring structure. And so we are very confident that the actual black hole does in fact look like a ring and the flux depression in the center is actually real. And so we did a lot of kind of sanity checks to be completely sure that we understood what we were doing. And so what this is showing you are just five examples of very simplified models. Obviously the GRMHD one at the end is not super simplified, but the other four are. And what we did here was we simulated an observation of these five models and then used the same imaging algorithms that we just used for the images that I just showed you. We used not only the same algorithms but also the same parameters. And the goal here is to convince ourselves that if the actual image was a disc would our algorithms be preferring a ring instead of a disc. And so the results of these tests are shown now. And the main point here is that if you do have a disc you will not create a ring which is very reassuring. The other thing I wanted to point out though is that if you look at the very first example on your ring example on the top left here if you were to image a uniform ring with the EHT you would not get a uniform ring out. And what this means is that there is significant asymmetry that is created from the fact that we do not have a complete for a coverage. And so the point that we wanted to make here is that we do believe that the asymmetry that we see in the images that we published is real but we do not want to assign too much meaning to the knots that you see in that image. So those are not necessarily features that you can actually trust. So in addition to the very large imaging effort there's obviously the theoretical part of this project as well. And so the theory and simulation working group worked very hard to create a huge dataset of GRMHD simulations that are probing the allowed parameter space for the M87 black hole. This is just a very small sample of all of the simulations that were run. But from this sample you can already see how different parameters can create very different resulting black holes. And so one of the most exciting things that we were able to better understand about this black hole by performing all of these GRMHD simulations is the direction of the spin axis of the black hole. And so what these diagrams are showing you are how are different ways in which the accretion flow and the spin axis of the black hole could be oriented. So the blue arrows, both the circular arrow and the linear arrow, both of those that are in blue are showing you the direction of spin for the accretion flow for different models. And the black arrows are showing you the direction of spin for the black hole. And what we found is that for most of the models that actually fit the EHT data, the asymmetry that you see in the images in the four different images that are shown here, that asymmetry is coming from the direction of rotation of the jet. And so the jet is actually rotating with the spin axis of the black hole in all of these simulations. It does not rotate with the accretion disk but rotates with the black hole. And so the asymmetry that we are seeing in our images is a direct probe for the direction of spin of the black hole and is not necessarily going to be affected by the direction of spin of the accretion flow, even if the accretion flow is spinning in an opposite direction from the black hole. And so the result that we published is that we believe that the black hole spin axis is pointing away from us because the asymmetry that we see in the images is that the southernmost portion is brighter than the northern portion. So we obviously would like to do more than just measure the orientation. And so we performed a measurement of the mass of this black hole and we did this using pre-independent methods. And so first we're going to talk about the imaging method. And so the idea here is that you use the images that I just showed you and you perform a feature extraction algorithm on these images. And you're trying to measure the diameter of the black hole shadow. Now of course these images are significantly blurred because of the beam of the EHT. And so we were very concerned that we would have a systematic uncertainty between the diameter that we actually measure versus the diameter that would be the true diameter of the black hole shadow if we had, you know, infinite resolution. And the way that we kind of got around this is that we performed simulated observations of GRMHD simulations. And so we ran the GRMHD simulations, we observed these GRMHD simulations, and then we performed the same feature extraction algorithm on these GRMHD simulations as we would for the actual images that we get using the data. And then by using these GRMHD simulations we were able to calibrate how the measured diameter would be related to the actual true diameter that in these simulations we obviously knew what the true diameter was so we could compare the two. So in addition to the imaging we also performed a 4a domain model fitting. And so the idea here is that you create a fairly simple model and you can compare your model to the 4a domain data. And so this is just one example of this. This model is one of the models that best fit the data. And what you can see here is that you get this asymmetric ring, but you also have some extended structure as well. And so in the right panels, I know it's a little light, but I'm hoping that you can see these light gray dots. Those are the data points. And the red and blue squares are the fit to the data. And so the two different panels on the plot on the right, the panel that is only showing you some blue squares, that is the visibility amplitude. But the other panel on the right is the phase of that. So we do measure complex visibilities and so they do have amplitude and phase. I've been focusing mostly on amplitude in this talk just because it's a lot easier to gain some intuition for the amplitude. Closure phases are the observable that the event horizon telescope actually gets for phases. And the point here is just that everything I've been showing you does match both the phase and the amplitude of our data. So here is a summary of our several different methods of trying to measure the mass of the black hole. So all of the blue and green circles that I'm showing you here, these are results from the image domain. And so what we're plotting here is the fractional width versus the mean diameter. And so all of these images, all of the results that we get that we get from the image domain, you can see that they're all above this dashed line here. This dashed line corresponds to a 10 micro arc second beam. And the point here is that almost by construction, none of the images in the imaging domain will be able to get a ring width, which will be smaller than the 10 micro arc second beam. And the blue and red dots and squares that you see here, these are the results that you get if you were to use a simple analytic model like the one that I just showed you in the previous slide. And so, of course, we do not impose the 10 micro arc second beam resolution for these models. And so you can get fractional lifts that are significantly smaller. This gray, sorry, it's actually blue and pink shaded regions, these just correspond to the correlations that you get from these crescent analytic models that we see. And so the point here is that there is an intrinsic correlation between the fractional lift and the mean diameter just based on how the black holes look just based on the fact that we expect it to be a crescent. But even when you take this correlation into account, if you were to look at the full range of all of these dots on the x-axis, the range over which we measure like the allowed range of diameters is actually quite small. And so we measure a image diameter of 42 plus or minus three micro arc seconds. The ring width is less than 20 micro arc seconds. This parameter gm over dc squared, this is essentially a proxy for the mass. If you have a measurement of the distance, then you can use this parameter to measure the mass. And the mass that we measure is 6.5 times 10 to the 9 solar masses. So obviously we're not the first people to ever try to image this particular black hole. And what's kind of interesting though is that the two main measurements that were done before us didn't actually agree. So I'm showing you here in red. This is a measurement done by Walsh et al in 2013. And this measurement was done using gas dynamics. The blue curve is a measurement by Gephard et al from 2011. And this is a measurement using stellar dynamics. And so the point here is that these two measurements did not actually necessarily match each other. But if you compare them to the measurements that we got from the EHT, you get that the measurements that we have gotten from the EHT data. By the way, as I mentioned earlier, we did use three different methods. The blue region is the mass that you'd get if you were to use the image domain. The green region is the mass that you'd get if you were to use fits of the GRMHD simulations. And the kind of magenta curve is what you would get if you were to use the analytic crescent models that I showed you earlier. And so the point here is that all three of these methods not only agree with each other, but they also agree with the measured mass that was measured from the stellar dynamics. And so this is a really exciting result because it might actually indicate that mass measurements from gas dynamics might actually have some sort of uncertainty that we weren't aware of earlier. I'm also kind of summarizing these results on the right here. So at the beginning of this talk, I talked about a potential null hypothesis test of the Kerr metric. And so the idea here is that because we have a mass measurement of M87, we can compare the mass measurement of M87 to the size that we actually see of the black hole shadow. And the answer to the null hypothesis test is that so far, given our current uncertainties, we do believe that the black hole that we have observed is consistent with a Kerr black hole. And what this plot is showing you here on the right is essentially what the deviation away from Kerr would be. And the point is that the blue curve peaks at zero. And so so far, we have not measured a deviation away from the predictions of Kerr. But again, this measurement so far just tells us that the measurements between the dynamics of the stars and the actual size of the black hole shadow agree to within 20%. Obviously, as we get more telescopes and we perform more measurements, we can get our statistics a little bit better and actually make that error bar smaller. So we also considered how the shape compares to the predictions of Kerr. So this is a little bit of a complicated plot, but I'm going to try to walk you through it. So the green and pink histogram, these are images that result from the two imaging algorithms that are not the clean algorithm that are like the model fitting, the pixel based model fitting algorithms. And the blue histogram that you see here is the result that you would get from if you were to observe a GRMHD simulation with the EHT. And the point here is that we know in these GRMHD simulations that we have a Kerr black hole because we impose that. And so what we wanted to know is what essentially is the intrinsic uncertainty in this measurement. So this plot shows you the probability of you getting any particular fractional diameter spread. And so the point here is that we're comparing for each of these rings that we get, we're comparing the largest radius to the smallest radius. And we get a ratio of those two quantities. And so even if you were to observe a black hole that is Kerr, some of the images that you would measure using the EHT would have a fractional diameter difference that would be nonzero. And so based on our understanding from having applied this to GRMHD simulations, what we get is that the observations that we see are perfectly consistent with a Kerr black hole. And specifically the maximum deviation that we've been able to achieve with any of our different methods is about 10%. So we believe that these images are circular to within about 10%. And so again, so far our observations are consistent with GR, at least for now. But again, as we improve our observations, we might be able to get that error bar smaller as well. So I've been talking only about M87, but I promised you in the beginning that we were going to observe the galactic center black hole as well. And the galactic center black hole, at least for me, is the more exciting source, because we have a very precise measurement of the mass of this black hole, which means that if we were to measure the size and the shape of the black hole shadow, we'd be able to constrain whether or not this black hole is a Kerr black hole much more precisely because of the much smaller error bars on that mass measurement. And so most of my PhD was actually focused on the galactic center black hole, specifically focused on the variability that you see right here. So the black hole at the center of the galaxy is about a thousand times smaller than the black hole at the center of M87, as I already mentioned earlier. This doesn't matter for the actual size of the image that we expect to get, but it does matter for the time scale of variability for this black hole. So because it's so much smaller, we expect that the time scale over which the image structure might vary for the galactic center black hole will be about a thousand times faster than the black hole that we've already imaged. And so this is also supported by actual real measurements observations of side j star where we've actually seen flares on time scales of about an hour or two. And so because it takes us 12 hours to actually probe different regions of the foray domain, we expect that this black hole, the image of this black hole will be variable on time scales that are shorter than the time it takes us to get enough data to actually make an image. One of the fundamental assumptions of image synthesis is that the image structure remains stationary throughout the length of the observation. So this is really the first time that we have attempted a very long baseline interferometry observation of a source that is variable on time scales shorter than the observational time scale. So this is one of the main reasons why sad day star is so much more complicated. The other reason is of course that you're looking through the entire well half of the galaxy to actually get to sad day star. So you need to deal with a lot of interstellar medium effects as well. But the variability is a very, very big component to why sad day star is so much more complex. So let's look at what happens in the visibility domain when this image is variable. So here the leftmost panel is showing you the image. This is again a result of a GRMHD simulation. The middle panel is showing you the full map of the amplitude of the foray transform of that image. And then again I'm showing you two cross sections. And remember that if we were to observe this image we expect that our data points would lie between the two lines that I'm showing you here on the right panel. And so the point is that this black hole, the way that this black hole varies, affects very significantly the data that we might get using the EHT specifically the depth and the location of the minima that we see in this black curve here on the right changes very significantly. If you're wondering about the time scale this image right here, sorry this movie lasts about one minute and that one minute corresponds to about 60 hours of black hole time. So obviously this has sped up a lot but if you think about the fact that we're taking 12 hours to observe we expect that the visibility amplitude of the image of the black hole will vary very significantly during that time. And so the first thing that many people want to do when faced with something that is variable is take the average. It's kind of the obvious first step. And so does taking the average fix this problem? And the short answer is no but let's actually look at this a little closer. So I do apologize I labeled these two panels incorrectly and I'm so sorry for that but the panel on the left this is the panel this is the result that you would get if you were to take the visibility amplitude of each image throughout the whole simulation and then take the average of that visibility amplitude. So the the labels that are shown in these little blue squares at the top those labels are correct the labels that are actually shown on the panels of the figures are incorrect. The middle panel shows what you would get if you were to instead take the average image right so just take the average of all of the images in your simulation and then after taking that average then you take the visibility amplitude. And the point of course is that you have a very different structure in your visibility amplitude in both of these two examples. And so the the white curves that I'm showing you here these are the baseline tracks that you would get if you were to observe the galactic center black hole. And many of these longer baselines that you see here come from the fact that the that the south pole telescope can see the galactic center black hole but cannot see the black hole in the center of m87. And so again I'm showing you the two cross sections on the right panel here the solid curves correspond to the leftmost panel and the dashed curves correspond to the middle panel. And the point here is that if you take the average of several minimum and different locations with different depths by taking the average of those you'll essentially be left with a function that's almost monotonically decreasing and you'll erase all of the information that you could have gained by actually studying the location of that first minimum that you would see in the average image of the black hole. And so just taking the average of the data is not going to be enough for us to be able to reconstruct an image. So there are several different aspects to this right. So I've just talked about the variability that we see in the observations but there's also a different variability that we see in the actual simulations. So there are two main things that this collaboration is trying to accomplish. One is to image using our data but the other is to perform some model fitting using our data as I've already shown you with m87. And so not only do we need to worry about what happens with variability when you're trying to image something but you also need to worry about what happens with variability if you're trying to compare the variable data that we get to a simulation that is itself also variable. And so okay hopefully I've convinced you that you can't just take the average in the observational domain but what about in the simulation domain? Can you just use the average image of a simulation and compare the average image to your data or do you need to do something a little more sophisticated than that? And the answer again is that the average is not enough. So the top panel that I'm showing you here this is the average image from a simulation and the bottom three panels are three different example snapshots from that same simulation. And the point here is that if you were to use the EHT to observe one of the snapshots on the bottom row here and then if you were to compare the observations that you have to the average image of this simulation shown at the top here not only would you not get a very good fit for most of these images but the parameters that you might derive from performing such a fit would be very suspect and so we need to be very careful when doing that. And that's one of the reasons why in paper six the EHT papers are numbered there's six of them the six one. If you were to look at that one instead of just using the average most of the time we actually compare each and every snapshot in each of these simulations to the data which itself has some complications that I will also talk about now. So based on the results that I just showed you that you know variability is a very big concern for the galactic center black hole my collaborators and I decided to explore the possibility of using principle component analysis to both understand the variability that we see in the simulations but also as a means to try to actually resolve this problem so that we can actually try to create an image of the black hole despite this variability that we see. And so if you're not familiar with principle component analysis or PCA, PCA is just a algorithm that the diagonalizes the covariance matrix of the data to find an eigen basis that is ordered such that the first few principle components explain the majority of the variance. So I know that that's a lot of words but I also have a very simple example on the right here so let's say that you had data that looked like the data points in red here and they have the correlation that you can see on this plot. If you were to apply PCA to this the two PCA components that you would get are shown in blue. So the longer blue vector is aligned in the direction of the highest variance in your data set and the second blue vector is orthogonal to the first and is going to explain a much smaller percentage of the variance in your data set. And so obviously this is much simpler than what we're actually trying to do because we are applying PCA to images not just the simple data points that I just showed you. And so I have a very simple example that uses images instead of just simple data points. And so obviously this is not an actual simulation, this is just a Gaussian moving in a circle but I hope that it will build some intuition for how PCA behaves when you're dealing with images. And so the result that you get from applying PCA to this set of images is shown on the bottom here. These are the first four PCA components. Obviously there are more PCA components but these four are the ones that are the most important. And hopefully you can see that based on these PCA components if you were to create a linear combination of these PCA components you would only need a small number of PCA components to be able to arrive at a relatively good approximation of any of the snapshots in this original data set of images. And so the point here is that you're finding a new basis for your image space and you can use this new basis to reconstruct all of the original images in your data set. So obviously we have applied this to GRMHD simulations as well. This is just one example. Obviously I'm showing the actual movie of this simulation on the top here. This red circle is what you would get if you were to calculate the boundary of the black hole shadow analytically for this particular black hole. And you can see that the results from GRMHD do in fact match what we would get analytically. And so the bottom four panels here are showing you the first four components of this of the PCA of this simulation. And hopefully you can see how if you were to create a linear combination of these components you might be able to approximate several of the images that are shown in the animation at the top here. And so we of course did that. So this is just one example. The leftmost panel shows you the original snapshot. The second panel shows you that same snapshot reconstructed using only 10 PCA components. And the point here is that obviously if you are doing a reconstructed with only 10 PCA components you will tend to smooth over a lot of the fine scale structure that was in the original image. But if you were to compare the result that you get with the reconstruction using only 10 eigen images if you were to compare that to the EHT beam for example the result that we get is that only 10 eigen images should actually be more than enough for the purposes of the EHT at least in the current configuration. Obviously if you were to use 40 as is shown in the third panel or 100 as is shown in the last panel PCA components you'd be able to reconstruct a lot more of the fine scale structure. But again we don't really think that will be necessary at least in the current orientation of the EHT. And so the point here is that not only have we been able to understand these simulations a little bit better in this particular paper but we're also proposing to use this to actually create a time series of images using the EHT data. So we're trying to not only create reconstruct a single image for the galactic center black hole but reconstruct a time series of images for the galactic center black hole. And the idea here is that you can use the PCA components that you derive from a particular set of GRMHD simulations to reconstruct images from a completely different set of simulations even if these two simulations are actually in two distinctly different classes of simulations. And so the idea here is that we can use the PCA components that we derive from these GRMHD simulations and we can actually fit these PCA components directly to the EHT data to be able to perform model fitting in a way that does not require that your image is represented in your original data set. So you can actually reconstruct images that were not included in your original data set by using these PCA components. And so this is you know future work looking to the future hopefully you have something to look forward to. But with that I will leave you with my summary and the main things I wanted you to take away from this talk are that we have detected the black hole shadow for the first time that the size and the shape of the shadow is consistent with the predictions for this black hole being a curve black hole. We've also shown that we can use this observation to measure the orientation of the spin axis of the black hole and the mass of this black hole. And finally the variability of SAJSTAR poses a significant challenge and that is what I am currently working on right now is trying to resolve that challenge so that we can get an image of SAJSTAR published soon. So thank you. Awesome. Hello, can you see me? Thank you Lea very much for this awesome webinar that we are very excited and I think the community not just like the black hole community but everybody on earth it's very exciting. So let me start with two questions I believe there is somebody from our youtube channel Lelver George sorry for the pronunciation say hi Lea I have an eighth question when you are in favor of using 1.3 millimeter band you showed a simulation of what we would see in the one centimeter range. So he has the question like we will see only a flat disk but I will expect the shadow to be there for any wavelength since we are dealing with a black hole what am I missing? Yeah so the shadow definitely does exist for all wavelengths the only difference is that when you look at one centimeter there's all this stuff between us and the shadow and that stuff is blocking the light from the actual shadow. So what you are seeing in that simulation was that the actual accretion disk that is between us and the black hole is blocking our view of the black hole shadow. Okay thank you Lelver for the question. Lea you can turn off your camera if you want to stop sharing your screen in case you want to if you are moving your hands or something. So do we have some question from our physics collaborators? I actually have a question can you guys hear me? Yes okay so can we scale observation to test GR? So that's a very good question so I try to be very careful with questions like this because what we are testing is specifically the metric for black holes which is obviously very related to our theory of gravity but it is possible to imagine that that GR could be right but black holes might not be cur right so black GR could be right but you might have a naked singularity instead of a cur black hole for example. It's also possible that GR could be wrong but that the black hole could still be a cur black hole or it could be that GR is wrong and the black hole is not a cur black hole right so there's like four different possibilities and so we try to be very careful to emphasize the fact that what we are actually measuring is the metric of the black hole and we're not actually sensitive to the dynamics of the theory itself. Okay so do we have any other question? Yes yeah from a totally known expert perspective I'm just wondering the variability of black holes depends only in the media or it has something by itself that makes one black hole more viable than the other one? So I'm not arguing that one black hole is intrinsically more variable than the other so essentially when we do these simulations the GRMHD simulations are scale independent so the point there is that you can run the simulation and then later you can scale your mass but what makes these two black holes different is that the mass is so different that the time scale over which anything varies is different and so the idea there is that even though the physics are the same when you change the scale that you're working with if you have something that's much smaller it can the dynamical time scale for this smaller object is shorter. Okay so both black holes do vary and if you were to put their variability time scales in terms of their mass their variability time scales would be similar in units of mass right but because the mass is so different it means that the black hole in the center of the galaxy can vary much faster than the other black hole. So to be sure about the geometry the black hole in our galaxy the shadow that you see in the left side is also because of the flux of the photons that are coming like this way or just like facing photons particles. Can I share my screen again because I have a I have an extra slide for this exact question. Thank you. Just for the other people this is not planned. Yeah it's not. Sorry this one I just personally I just really love this particular plot and I really was hoping that somebody would ask me about it but I knew I wasn't gonna have time to actually talk about it. Okay so what I'm showing here in the leftmost panel is the total image that you would get if you allowed all parts of a GRMHD simulation to emit light the same way that you always do right. So this is like the total that you would see however if you were to try to separate out which parts of this image come from the mid plane of this black hole versus which parts of the image come from the area that's between us versus which parts come from the area that's behind the plane of the black hole. You can also see that kind of the percentage of light that each of these different components contributes and so the point here is that yeah all three of these different areas are still contributing to your image but most of the total flux that we get in at least this particular example of a GRMHD simulation most of the total flux is actually coming from the other side of the black hole. It's essentially the jet that is directed away from us is still some of the light from that jet is still going to reach us and it's going to get lensed around the black hole and so the answer to your question simply is yes but I think that this kind of illustrates that a little bit better. Thank you so much. Yeah. Okay Lee I have a question. From your talk and also like the papers I've read them a little bit like it's like you guys found there the sense of rotation of the black hole but then there is a couple of numbers that are curious to me so the simulations say minus 0.94 in the dimensionless beam there's also positive 0.94 zero and then you say okay for some cases zero is not okay for the simulation so we know it's rotating and also like you can infer that so you know how what that particular number like if I if I ask what's the dimensionless beam value we are not very sensitive to the actual magnitude of the spin at least in this particular black hole so part of that is because the black hole yeah orientation of the spin axis of the black hole is almost directly towards us and so there is some possibility that if the if we were looking at this edge on we might maybe be able to see some difference because of the spin but the take-home recipe really is that at least at the current resolution just looking at an image isn't actually enough for us to measure the magnitude of the spin of this black hole there are some possibilities that we might be able to do something if we were to be able to look at some statistics for how this varies as a function of time but still being able to measure the spin of this black hole is very hard but I actually think that that's a good thing because the thing that I want to measure is whether or not it's a curved black hole and if the black hole changed significantly depending on its spin you'd have kind of a degeneracy there right which you wouldn't know if the black hole image looks different because the spin is different or if it looks different because the black hole is not a curved black hole okay thank you we have another question from Diego Restrepo which is which are the perspectives to increase the data including satellite telescopes yeah so right now we currently have 11 telescopes that are ready to observe the next observation cycle and originally we had eight telescopes so we've already increased the array significantly specifically we've added the telescope in Greenland the GLT that telescope already observed with the array in 2018 we are also adding the kit peak telescope the receiver for kit peak is ready to go and we also hope to add no emma which is an array of telescopes we also hope that no emma will join us shortly as well as far as space vlbi we are definitely talking to people about this we do have some concepts that we're working on at least in my opinion the biggest issue with going to space is data so one thing that I didn't mention in this talk is that we collected about five petabytes of data in these observations and so that is an amount of data that you can't possibly transfer over bandwidth you physically have to carry a crate of hard drives from one location to the other and we literally put like hundreds of hard drives in cases and FedEx them to the locations of the supercomputers in Germany and in Boston and it's actually kind of funny because at one point instead of getting a case filled with hard drives we got a case filled with fabric which was concerning and so obviously there was some fat some fabric uh you know some company some factory somewhere that you know really needed fabric and they got left with all these hard drives and you know so bad for them but luckily we were able to track the hard drives down the company got their fabric we got our hard drives we did not have to make matching uniforms with the fabric um and it all worked out but the main thing here is that if we were to go to space actually putting these telescopes into space would not be the hard part the hard part would be figuring out how you can possibly transfer the data from your satellite back to the earth or maybe you would have to create an entire set of telescopes that would be its own little interferometer of space and then they could maybe um just communicate between each other and then correlate in the air that is one idea that people are considering but at least right now with the current um technology that we have transferring the data from the satellite to the earth is a significant challenge thank you and I think we have uh one more minute for the last question which is a very nice question to end up this webinar what's the next step now that we have these observations and this question is from Carlos SC yeah so the the next step at least for me is SAJSTAR so currently I'm working on the SAJSTAR project that I mentioned um in the last little bit of my talk so hopefully we'll be able to actually create a time series of images for that black hole as well um but I'm also working on this other project which is simulating a really large number of non-curb black holes and so I did kind of allude to that a little bit in the beginning of my slide I showed a few examples for what the black hole shadow could look like if you were to take the curr metric and perturb away from it and I'm working on a project to try to measure the allowed perturbation the size of the allowed perturbations given our data and we are um working on that and hopefully that'll be out shortly as well okay uh thank you very much for this nice webinar and then I think you can google lia's webpage which is I think iammedatus.org perhaps.com so if you have a business also and then uh if you have more questions you can just follow up thank you very much for joining us today and we'll see you in the next low physics webinar