Welcome to Tofface TV. It's the Everton News Daily. Lakebanks has been offered an extra year at Everton Football Club, a lot of outlets report on that today, including the echo, something we reported four weeks ago that Banes was set to be offered another twelve months in generation. That looks likely now. It's very important play to Everton to what the sources are saying behind the scenes. a y 35-year-old left-back looks set to put penta paper and remain a good as some park until the summit of 2021. I think it's a good deal forever and it's a good deal for Baines. Obviously he's played I think seven times this season and has never let us down to be an excellent in most of those games. You know, Luke Aden had a couple of injury problems and Baines coming and did brilliantly in those games. So for a player who keeps himself really fit and is an excellent pro, I think it's a good sign for Karl Amantulotti as he really tries to put his imprint on the Everton squad. Having someone like Baines around, who's an excellent footballer as well, is I think it's really good. So delighted with that news. There's been no decision made at the moment on whether to extend Martin Stechlenberg, Cucamarty, Oru Maniasas contracts past the 30th of June. A decision on that is expected within the next week or so. Just basically so Everton have got a squad to finish the season, which restarts on the 20th of June and looks set to finish on the 30th of July. I think it is so possibly an extra month being offered to those players. If they've been offered deals at other clubs, they might want to take that instead, but no decision at the moment on those players. Mo Bezzic is expected to leave Gothersham Park this summer for a fee of around £4 million. That seems to be the valuation that Everton have on him. The Bosnir Mifffield plays being on loan at Sheffield United for the last season. Couldn't agree an extension. Chris Wilder was very outspoken about a player's agent. It's thought to be Bezzic now, asking for more money than Sheffield United had for an extra four weeks. It means that Bezzic is in limbo. He can't play for Everton because until the season finishes, so Everton aren't getting the players. He's not going to return to Sheffield United, but now it seems that Marcel Brans has made his mind up on him and he will be allowed to leave Gothersham Park. He's still got a year left on his deal, but 27 years of age he needs to be playing 15 football somewhere. So Everton want to see him off their books. According to Gazeta Dello Sport, Cynllunder is again linked with a move from Roma to Everton today. They say that Everton have taken the first steps now to sign the Turkish winger. He's an excellent player on that. He's got good pace about them. Left footer plays off the right-hand side. But the quote in 30 million euros, I'm not sure Everton will be paying that much for anyone this summer. But interesting, it'd be a great sign and I think if we got him, he's highly rated. Only 22 years of age. Obviously anti-Lotty knows him from his time in Serie A. But according to Gazeta Dello Sport, Everton have made the first steps to sign him. And Everton target to Pierre-Emile Huyberg, the Southampton captain, Ralph Hasselhut, who signed any four-year deal with the Saints this week, has spoken about Huyberg's position and said he's very worried about losing his captain. He only has a year left on his current deal at St Mary's. And he's 24 years of age now, Everton have been linked with him quite a lot over the last few weeks. I think he'd be a brilliant sign for Everton. Good age, being a bi-amunic. Schalke, he's got Premier League experience too. And Hasselhut basically said they can't afford to let him walk out the door for nothing in 12 months time. And he said they don't think it's a good situation when your captain isn't going to remain at the club. He said we have to sit down with him and find out if he intends to sign a new deal or make a decision on his future. But I think he would be a good sign for Everton getting a centre of midfield player who is a defensive midfield player but can get about the pitch and has got Premier League experience. I think he would make a really good sign for Everton. Should they choose to go after him? And that is it. Make sure you give this video a thumbs up, subscribe if you haven't. And if you want more videos, join us on pitch. See you later.


Let's see how this goes. Awesome, I think we're live. Welcome back everyone. Thank you for joining us for today's No Physics webinar.  Today we are presenting Interferometric Measurement of the Magnetization and Spin of Supermassive Blackholes by Daniel Palumbo. Daniel recently this year, often his PhD from Harvard University, he got his Bachelor in Physics from MIT and he's going to start his postdoc at the Black Hole Initiative as a fellow. Daniel, in my opinion, is one of the youngest rock stars in the EHD member. He's an expert in polarization in images processing and I'm very happy to have him here today. Remember you can ask questions over email through our YouTube channel or Twitter and the questions will be read at the end of the talk. So without further ado, we will turn time over to Daniel. Thanks for joining us. Great, thank you so much. So first of all, it is a huge pleasure to be here and many thanks to Alejandro and the Law Physics program for inviting me to come talk about the stuff that I'm super excited to share. So let me try to share my screen here. Hopefully this works uneventfully. There we are.  So perfect. Excellent. So yeah, as Alejandro mentioned, I'm here to tell you about interferometric measurement of magnetization and spin of supermassive black holes. So I come to you from the Event Horizon Telescope, which is an extraordinary instrument and an extraordinary collaboration that set out a long time ago, really sort of time has flown to make the first images of supermassive black holes. And if you had asked me in 2016 or 2017, what the purpose of the EHT was, it would have been just that. It would have been just to produce these two images here. So on the left, this is a picture of the Messier 87, which is a, or the supermassive black hole, the heart of Messier 87, which is a giant elliptical galaxy. And on the right, this is a picture of our very own galactic center, supermassive black hole. And on the left, you see these little white tick marks.  And all that they mean is in a little patch of the images that I will be showing you around each little tick mark. That's showing you the total electric vector position angle in that little patch. So if you imagine light coming at you like a wave in that little bundle, that is the way that that light is oscillating. It's the polarization of that light. And so given these two images, these are a massive achievement on the part of hundreds of people over decades. And yet a few of us on the theory end have the temerity, have the audacity to ask, what if we actually learned from these images? Are they just pretty pictures or have we gained an understanding of something deep? Or is there something missing? Or is there something more that we can learn from looking at these in a different light or looking at them over and over again? And so much of my work has been tackling theoretical understanding of images of these sources and particularly polarization. So polarization results have been published for messy 87. They are very physically rich, much physically richer than total intensity, which is what we refer to the image on the right as when you don't have this polarization information. But this is soon to be arriving for a SADJ star. So stay tuned. And so just to outline some of the things that we've been able to infer so far. So these are existing conclusions from event arising telescope results, which set the scene for what I'll be discussing today. We've seen from our simulations, this is a statement rooted in general relativistic magneto hydrodynamical simulations, this GRMHD, which you'll hear me say a lot. You'll be very sick of hearing it. We infer that M87, SADJ star have masses that are consistent with prior measurements. And the way we do this is we can run simulations of black hole accretion flows that we think are sensible for low luminosity active galactic nuclei, which we believe messy 87 and SADJ star are. We can run these simulations in a essentially scale invariant way. We can fit the mass of the black hole. We can fit the density of plasma around the black hole in a way that's very efficient. And so we can perform a procedure where we change the mass and densities to fit the compact flux that we observe and to fit the angular size that we observe in EHD images. And when we do this procedure, we see masses that track. So that's a great first step in convincing ourselves that we're doing something right. When we simulate black holes to the best of our ability, we end up with masses that match measurements which make very different assumptions and fewer in many cases. When we look at our models, especially in polarization, when we put on our polarization goggles and look at the morphology and the strength of polarization in these sources, we see a preference for dynamically important magnetic fields in the accretion flow. And I will spend a great deal of time unpacking that statement, but just at first glance, you can look at those little tick marks around your image of a ring and draw some conclusions in comparison to simulations. And these tend to favor strong magnetic fields which has sort of echoing ramifications for what we believe about these sources. And more generally, our models resemble actual black holes but we know for a huge number of methodological reasons and physical reasons that our models aren't good enough. They're not just not perfect. We know there are massive missing pieces limited by computation, limited by a lack of scalability. And I could spend a full hour just talking about all the things we don't believe about these models. Though I won't do that. It would be a very, very morose talk. And so we believe our results much more when simple, universal, physical arguments back up these detailed GERMHD comparisons. If we can write down simple sort of causal arguments for why we might see certain things and convince ourselves that these might be general or get a sense of what is required to be able to make deep statements about these sources, we are much happier than when we have these huge complicated black box simulations that are sometimes difficult to interpret and which have deep methodological limits. The best in the world, but the best in the world is still very difficult to make sense of sometimes. And so my work has been largely on building tools and future experiments that connect these messy astrophysical measurements to fundamental physical properties rather than trying to avoid the messy astrophysics allowing this astrophysics to illuminate the spacetime of these black holes to make the next generation of VLBI as physically exciting as possible. And in this light, I see the next holy grail to be spin. The spin of the black hole, the angular momentum hidden in the horizon. And so with that in mind, I think it's useful to consider why this matters at all. So spin is a very special property in the field of studying black holes because it is important both at the sort of messiest ends of the problem and the most elegant and fundamental. It's one of only a handful of parameters that fully describes astrophysical black holes in their spacetimes along with mass and spin. It basically describes the whole spacetime around the black hole and with inclination are whole viewing geometry with respect. So in a geometric sense, it's one of only three parameters we really care about. And in an astrophysical sense, it's deeply important to outflows, for example. We believe that the way these powerful jets that we see here in messy 87 viewed in the optical, you can see this thin blue feature. This was, it's a 100 year old discovery that M87 contains this linear feature. We believe these jets, which are coming at us at near the speed of light, these are launched on thousands of light year scales, sometimes exceeding the scales of their host galaxies. We believe these are launched by the actual extraction of the rotational energy of the black hole through a process called the Blanford-Sneig process. And so understanding the spin of a black hole lets us understand, is this process really going on? Is it possible to extract energy from a black hole in nature? And we know it's theoretically possible, but is it happening? And is that what's powering these sources? And that, if so, that tells us something about feedback. When we look at models of stellar growth, it's impossible to get the right number for how many stars should be forming or growing in a galaxy without accounting for black hole feedback, without accounting for these jet outflows, disrupting their environments. And so the history of structure formation in the cosmos is tied into the spin of the black hole, both through feedback and also through accretion and merger history. As you might imagine, if I have two black holes that are in some random misaligned angular momentum arrangement, and they merge, I might end up with a lower angular momentum in the final supermassive black hole. Then if there was a single black hole, coherently creating material from the disk for eons and eons. And so theoretically, there's a great deal of interest in understanding spin. And observationally, it's very, very difficult to measure in low luminosity active galactic nuclei. At the moment, the only spin measurements of supermassive black holes that exist come from X-ray observations of very bright AGM, which are very much in the minority. The quiet, sort of boring majority of supermassive black holes that we believe to exist are rather quiet, rather dim. And the only tools that we have to think about them come from methods like those that I'll describe. And so there's great value in building out a toolkit for understanding the spin of these sources. So that is the motivation for trying to make any assumptions that are needed to get any handle at all on spin. And hopefully I will convince you that there is some hope by the end of this talk. So here's the outline for the work that I'll be reviewing today. First, I want to tell you about the polarization spirals that we see in M87 and simulations of M87 and how we've used those and how paper eight in the EHT series of publications on the C87 used some of my work to conclude that M87 is a magnetically arrested disk or hosts a magnetically arrested disk and a little bit about what that means for our ability to understand spin. Then I'll talk about some polar imagery of the photon ring. My understanding is that you've had some speakers here tell you about the photon ring before. Alejandro himself is of course an expert on the photon ring. And there are beautiful symmetries and really anti-symmetries of polarization that reveal themselves in the photon ring and which are very rich for detecting it and for understanding it. And so I'll be going through those as well. And lastly, I want to touch on black hole tomography how we can use some of these polarization tools to understand not just our two favorite black holes but potentially many more, perhaps an order of magnitude more in the near future and another order of magnitude in the further future depending on where telescopes get put over the next few years. So without further ado, I'll be reflecting on some of the EHT work on M87. To kick this off, it's useful to think about some zoology of accretion flows in low luminosity act of galactic nuclei. We generally bin the accretion flows in these systems into two buckets. There are standard and normal evolving disks. So the standard normal evolution state is another way to say it, which for a long time historically was considered to be the default state for low luminosity accretion flows. They have weak magnetic fields that tend to go with the flow and have small scale turbulent structure which are generally more disordered. But overall, if you imagine just pouring water into a kitchen sink and watching it spiral down the drain the plasma itself is mostly coherently accreting towards the black hole. There's a sort of continuous inflow and the magnetic field because there is generally flux freezing in these systems is just dragged along behind the plasma. And so on small scales, the field is disordered. Overall, you might expect a roughly toroidal structure in the magnetic field following the plasma. Whereas in magnetically-arrested disks, which is what's being diagramed here and in Ramesh Narayan's sort of salmon paper there are strong dynamically important fields that pile up on the horizon itself. And so in this situation, you get very strong radial and vertical fields which really can't be supported in just a coherent inflow picture. And most importantly, as you can sort of see in this cartoon the magnetic pressure is sufficient that there is no actual steady state inflow solution. The material can't smoothly kitchen sink into the black hole because the gas pressure is being balanced by the magnetic pressure. And so you get this very clumpy accretion where blobs of plasma have to sort of sneak through the magnetic field in order to make their way to the black hole itself. And one very important prediction is that sane disks become magnetically-arrested over time. If you have a sane system sitting out there in nature coherently accreting from some torus of material in the center of a galaxy, one day it will be mad. Now that can be disrupted if the source of its gas changes, but all else equal, it will one day be mad. It will obtain stronger, more ordered magnetic fields. And this will tell us something about the outflow mechanisms and the history of its creation if we don't find magnetically-arrested disks or if we don't, both are exciting. It tells you something about how coherent accretion has been in the recent history of the black hole if you see that it's mad. And if you see that it's mad, you know something about the coherence of the magnetic fields very near the horizon, which are innately tied to this Blandford-Snike process, which is launching these powerful jets. In principle, both mads and saints launch these jets in slightly different powers because of the different magnetic field strings, but these are all intricately tied. And so in the broad quest to understand what the magnetic fields are doing very near these supermassive black holes as a minimum, we must understand whether we are looking at a mad or sane disk. And unfortunately, at the EHT resolution, total intensity is not sufficient to distinguish the accretion state or really anything else. So there are three sort of parameters to keep in mind if you have fixed your viewing inclination. So from SC87, we think we're looking at a accretion disk that is nearly face-on. We know this because when we look at the jet that's coming at us, we'll look at the kinematics of material in the jet and conclude that it has an inclination of roughly 17 degrees from normal. So it's nearly pointing directly at us. And if we infer that the disk is similarly aligned, that means that we only need to determine the accretion state, the spin, and some properties of the electron distribution function, which is here encoded by this R-high parameter. And the punchline of the theoretical analysis of the total intensity images of the EHT is that we can paint in any of these parameters that we want. But when we retrace these fluid models, blur them to the resolution of our EHT. So we put on our blurry EHT goggles, these all look very similar. Once you get the direction of motion of the material right, they all have a Doppler brightness asymmetry on the bottom and they all look basically identical. And so in a sense, this is a big triumph. We're great at making real images that look like real black holes, but it's very difficult to distinguish them. And so we need a new handle on the key differences between maths and science. And these key differences are magnetic field geometries. And so here I've taken this diagram from Nuran at all and I've tilted this so that it matches the M87 orientation. And I'm sort of painting a picture here of the kind of information we get because these sources at 230 gigahertz where the EHT is observing are generally dominated by singleton radiation. And so the singleton radiation is innately polarized perpendicularly to the magnetic field. So in this picture, each little field line that I can draw in my accretion flow is surrounded by a bath of particles moving in all directions. But if I isolate a single particle in this diagram for my vacuum light, you see that it has a helical trajectory around a magnetic field line or just through the uniform magnetic field. So I can always find some local patch which sort of permits this description. And so as a distant observer, I see polarization of radiation aligned with the axis of acceleration of individual particles or the average of a sort of thermal bath, you might imagine. And so I can look at my image and I will see a projection of the magnetic field onto my screen. Now, there are a lot of things that complicate this. It's not so simple in practice. There are propagation effects which twists the polarization of light as it passes through cold plasma sort of ferridae rotation, ferridae conversion. And there's also lensing. We're looking at emission which by and large is dominated by the inner fused short-shield radii from the black hole. And so lensing is critically important to getting this right. It makes a huge difference to the appearance of polarization in our images. But at the sort of zero of order, we are just seeing the magnetic field in wherever is emitting projected onto our screen. So the hope then is that we can take simulations of these accretion flows. We can blur them to the sort of blurry resolution of the event horizon telescope. Look at polarization which is telling us about the magnetic field and look for systematic quantitative differences in the polarization between magnetically arrested disks and standard and normal evolving disks. And so in this diagram from a paper I wrote with beloved colleagues, George Wong and Ben Prather, we looked at a massive library of simulations produced by Charles Gammys group in Illinois for use with EHD observations. And we looked at patterns of polarization. So fundamentally, we're looking at polarization morphology in the hope of telling apart Mads and Sains. And remember the picture here is that Sains, we have a sort of smooth kitchen sink of accretion flow. And so we end up with magnetic fields which are roughly circular when viewed top down. And synchronomission tells us that the polarization should be perpendicular to a circle. So a polarization field that is everywhere perpendicular to a circle appears roughly radial like a starburst. And that's roughly what we see that the event horizons over here and we see with a huge Doppler asymmetry lines spreading radially outward from the horizon. Whereas in this magnetically arrested disk, we see a spiral of polarization. There's more gradial magnetic field contributing here. And so we wanted to quantify these differences and look at thousands of images to see if these really do shake out in practice. And we don't need to get into the weeds here but the basic idea is that you can do what is effectively a Fourier transform around the azimuthal angle of the image to build a basis for different kinds of rotationally symmetric structure. So we called these modes the beta M modes. I regret using beta, it's very overused in plasma physics and we should have called it anything else but we're stuck with it. It's too frequently used now to go back. But the sort of key observation here is that one of these modes, the beta two mode encodes rotationally symmetric structure. Now other modes here have also a sort of interesting interpretation and there's lots of rich structure there but for now we're going to focus just on this M equals two coefficient. So this is a complex number which is encoding rotational symmetry in EVPA where the real part is radial or circular EVPA and the imaginary part is handed spirals. And if you're familiar with sort of curl and divergence free decomposition sort of E and B modes the beta two mode you can think of as just a linear combination of E and B sort of E plus IB but the picture here is just that this is a single number that we can report for an image which is an integral of this rotationally symmetric structure over radius. So you need to define an image center but it's telling you something about what this spiral looks like. The phase of this number is telling us the overall twist of the polarization in this very special physically motivated basis. We are looking at a system that's roughly axi-symmetric and we're looking at it from the top down. We're looking down at a kitchen sink. We're looking down at a spinning top and so that favors a basis like this one. And so if we take this massive library of simulations and we compute this beta two coefficient for all of them we see some very interesting patterns. So on the left, this is the one that I personally find most exciting and which has some deeper ramifications that will sort of echo throughout the rest of this talk which is that the phase of this coefficient. So here we're looking at it in the complex plane but the phase tells us something about the spin of the black hole. So here in green, I have spin zero. In yellow, I have retrograde medium spin, spin one half. Spin is a number between minus one and one for our purposes where one is the absolute limit beyond which you have a naked singularity. And so blue here is in spin 0.5. And these tend to cluster on the lower left of the complex plane. So in morphological terms these have more circular or spiraling polarization. Whereas when you crank up the spin to really high magnitudes your polarization patterns become more and more radial. And you can ponder why that might be for a moment I'll give you the answer shortly. But just sight unseen with no physical understanding this is already useful because this little gray circle is showing the constraints that we got on emity seven from imaging. We get thousands of possible images explained by our data but they all land in this little zone. And so this zone tells us a few things. One, it's probably not maximally spinning or even very highly spinning. And two, it's probably not a same. Why? Well, in this plot on the left I'm showing everything altogether binned by spin alone. So Mads and Sains and various electron distribution functions are all thrown in there together. But if I were to color this by Sains or by Sain versus Madd you would see that virtually all standard and normal evolving discs are tucked away at the origin or sprayed out here in these black points which are a retrograde high spin. What this means is that in the Sain paradigm the magnetic fields are generally so disordered that the magnitude of this number is very small in a way to this easily distinguishable from magnetically arrested discs except for certain special models. And so the utility of this observable in the EHT work is that we were able to knock out these last few standard normal evolving discs which were otherwise very good at mimicking the polarization that we saw in M87. And so the decision that we believe M87 is mad hinged on the fact that we had some morphological constraint on the polarization. And that's what's shown in the plot on the right is that the phase of this number disfavors this dark orange pile here. And this dark orange is these retrograde Sains where the large-scale accretion flow is going counterclockwise. The interior of the accretion flow is going clockwise because it's being framed dragged by the black hole. And those were otherwise very good at mimicking our images except for by this token. Now, whenever a single discriminator is giving you your final answer, you should worry. And so this is something we're going to be confirming with future publications on new years of data. But it is, it would be a little surprising for this conclusion to change significantly. I would say it would be very surprising. And so the more interesting takeaway from the plot on the left, and here's the answer to the riddle I've put to you is that the spin is telling us something or rather the polarization is telling us something about the spin by way of the spiral pattern in the image polarization. And this is the crucial takeaway of the entire talk. It informs the rest of everything I'll be telling you today. And so if you take one thing from this, may it be this slide. So we're looking at these magnetically-arrested disks at a frequency where they're optically thin. And we see that the emission is peaked very near the horizon. It's in the ergosphere, which is a region where the frame dragging from a spinning black hole is most important, it's most significant. It's forcing material to rotate along with the black hole. And so the picture is that spin, the spin of the black hole, drags space-time around it. The space-time drags the plasma, it's setting the direction of rotation. The plasma drags its magnetic field behind it, fluxes frozen in, and these magnetic fields are revealed to us through polarization. And so if you believe the critical assumptions of this problem, which is that we're looking at a magnetically-arrested disk, so far is a supported claim both for MIT7 and Sagittarius A star. So if you're looking at a map, if you believe you're optically thin, so you're seeing down to the horizon, then you can run this backwards. You look at polarization, you conclude something about the magnetic fields, which lets you conclude something about material rotation very near the event horizon, which lets you conclude something about the space-time, which tells you about the spin. So this causal trajectory and running the ability, the confidence to run it backwards gives you a great deal of information. And so believing those assumptions in the full generality of what this plasma might be doing is a major task for simulators. And my hope is that simulations, which are vastly different in paradigm and character and resolution and assumptions and initialization conditions, all of these things will harmonize. That they'll give holistically comparable answer and so far they are. And there's many papers looking into this and in different simulations, I've thrown a few of them on the bottom of the screen. And so far this holds water and it's very exciting because as long as it does, we can potentially extrapolate. We'll be getting into that in a bit. But for now, I want to digress for a moment to polarimetry of the photon, right? So you've possibly heard about this before, but I want to go through this once again, just to introduce this beautiful, beautiful feature of images of black holes. So it is the case that black holes lens light around them. And so if you have a disc of emitting material passing through the origin of your sort of black hole coordinate system, it is the case that a disc produces rings on the image. And the reason for this, you can sort of imagine in two ways. In the forwards picture, any point in space has an infinite number of light pads connecting to the observer. And these pads correspond to an increasing number of windings around the black hole. And so these windings, or we typically indexed by half orbits, are this number N. And so here on the left, in blue, you can see a trajectory which leaves an emitter, and here are observers at the top of the screen. This emitter releases a photon away from the observer, but it's a lens around and makes a single half orbit and comes and hits us in our eyeball, in our telescope. And so we call this an N equals one photon. It releases another photon towards us, which is half orbited once, half orbits again, and then comes and hits us in the eye. We call this N equals two. It's made two half orbits. Now, you can also imagine a backwards picture where a point on the observer image corresponds to a single photon path, which might intersect a plane around the black hole, any number of times. So here we've made this problem for a single point on our image, no longer are there many trajectories, there's one unique trajectory, and you can imagine, if I launch a photon with a very large impact parameter towards the black hole, it's not going to wind around at many times. It's very weakly lensed. And so in this example, if you look at the one launch that 10 angular gravitational radii at the top, it sort of zooms by weakly bent and it only hits the midplane once after making zero half orbital windings. So this is an N equals zero photon. Now, either way, you think about it, you launch geodesics closer and closer to the critical curve, which is this feature on the image, which I'll show you in a moment in more detail, but either way you cut it, you can imagine that the closer photons are to the black hole, the more they will wind around. And this winding produces a very special image feature, which is that we see an infinite sum of lensed images when we look at optically thin accretion flows. That's the asterisk. It's that if these are optically thick or they even marginally optically thick, eventually they will wind enough that this light is absorbed. The trajectories become too long and they're too diminished. But in the optically thin picture, when we look at a full image, so on the left, this is all of the light we see, we are seeing a stack of a big, fuzzy, complicated direct image, it's weakly lensed, plus a more strongly lensed N equals one image, which already looks like a very sharp ring. And as we increase N, as we increase the number of half orbital windings around the black hole, these images get exponentially sharper and exponentially dimmer around a critical curve, which is extremely well approximated by the N equals two image, and which is encoded just by the mass to distance ratio of the black hole, which scales the whole system in and out. The spin of the black hole, which warps the photon ring and warps the critical curve, and the inclination, which tilts and sort of vertically, or I guess along the projected spin axis is also sort of squishing the curve and making it more asymmetric. And so having sensitivity to the photon ring is incredibly exciting for understanding the parameters of the black hole in a way that is very insensitive to the astrophysics. You can change a great deal about the accretion flow and its large-scale fuzzy structure while changing very little about the N equals one and N equals two images. It's also a good test of GR to see whether this thing even exists at all. Are these objects behaving as we expect black holes to behave? And it's worth worrying about, and I don't want to dwell on this because I don't want to get too much interferometry into interferometry here, but by and large, the event rising telescope observes Fourier transforms of images. And so if you look at the Fourier transforms of these two decomposed images where I've taken the full image and broken it apart into the weakly lensed and strongly lensed N equals zero and N equals one images on the short baseline. So what you might see with a very small sort of micro-EHT that wasn't very high resolution, we are just seeing a blob and the majority of light in that blob is coming from the direct image. But as we go out to longer and longer baselines, we spread our telescopes apart, we are sensitive to finer and finer structure. These scales become separated and the contributions to our signal from the direct and indirect image become more comparable. And so at the longest baselines we see at the HD which start at eight gigalamta and as we go to higher frequencies we'll push higher, we see roughly half of the signal we expect from simulations is coming from the photon ring. That doesn't mean it's easy to make strong claims about it but it means that we darn well better be ready to think about it because it might be about half of the light we're seeing on our longest baselines and even more as you go out to longer baselines. And so where this all enters the polarization picture, I can be motivated just by taking this diagram and I want you all to think about this, picture taking this diagram and flipping it upside down and looking from the underside. So when you do this procedure, a radial polarization pattern stays radial. A circular polarization pattern stays circular but these handed spirals flip. If you see a right handed spiral when you look at it one way, it will appear left handed when you flip it upside down. That is a B mode anti-symmetry is one way to think about it where you will see sort of twisting patterns flip in handedness. And so in this very silly sort of flat space construction that corresponds roughly to what the n equals one image sees. The photon ring includes the image that would be seen from the underside as it is projected around the origin and loops back to hit you. And so you would expect that the photon ring if the direct image looks like a beta two of for example, minus I, you'd expect that the n equals one ring has a beta two of I or if you can think of this just in terms of B mode signs if you wish. And so that's very exciting because that would be an intrinsic difference in the light that we see from direct and indirect images. So it turns out there's a lot of deep reasons for this. The first was, well, and also a sort of recent history of papers looking into this. There's a wonderful paper by Mina Himwitsch, Michael Johnson, Alex Sbsowska and Andy Strominger which found that the Penrose Walker constant which encodes polarization structure along sort of parallel transport, it's a conserved quantity of parallel transport should complex conjugate across sub-images in this high end regime where everything behaves very nicely in curve. So in the space time of spinning black holes. And there are a lot of assumptions that go into this assumes equatorial emission, single radius but fundamentally, if you look near the critical curve you will see a little dance done by polarization where it will jiggle as you move across adjacent sub-images of increasing windings. Now, this is very tricky to get this high an end into this universal regime. It's very dim, it's very sharp. But even if you just look at the sort of n equals one like the simplest case in GRMHD simulations there's a wonderful paper by Alejandro Jimenez Osales and collaborators in 2021 which found without reference or really knowledge of this other theoretical work that if you just look at simulation images the photon ring region looks depolarized. And so here in this diagram from a paper of mine with George Wong you see in total polarization that there are strange dark bands which tend to appear very near the photon ring where the polarization suddenly plummets specifically in magnetically rested discs. And it turns out that this is coming from precisely the effect that we motivated with this flat space argument. And where the direct image might have one beautiful handed spiral going one way. And when you look in the indirect image and it's a little hard to see because these ticks are pretty tiny the spiral will be going the other way. This is super exciting because it is something intrinsic to look for. It's something special about the photon ring which makes its radiation easily distinguishable from the direct image. It tells us that we're looking at fine structure that can't be coming from the direct image because there's no reason for the accretion flow to be producing stuff going that way if it's moving progradely. Now the situation is more complicated if it's retrograde because then you can get the wrong handedness coming at very different image scales and you need a little more subtlety. But as you might imagine since these two images are overlaid there is destructive interference within the image from the photon ring interfering with the direct image because their polarization is oppositely spiraling. And you can work this out analytically this Penrose Walker conjugation which is sort of complicated it's not something you have access to in observations just reduces to a pure B mode negation in the face on zero spin limit. It's very simple to work this out. And it's approximately true that this B mode negation persists in spinning inclined black holes in the limit. And so this is a beautiful feature to look for and it forms a tapestry with the rest of what I've been telling you in this talk where the polarization in the direct image the primary weekly lens image is telling us something about the dynamics of the plasma on the smallest scales very near the event horizon where frame dragging reigns supreme where as we spin our black hole up so here in the center we have just short shield black hole with a very weak spin and as we move to the left we are increasing our spin in magnitude but orienting it oppositely to the right to the large scale accretion flow and on the right we're spinning up our black hole aligned with the large scale accretion flow in both cases because we're looking so close to the horizon where the black hole is forcing all of the material to rotate with it we see the same thing higher spin equals more radial polarization because of that causal chain I mentioned earlier where the black hole sets the tune for the plasma drags the magnetic field and we see polarization perpendicular to that magnetic field when we look at the photo rings we see the handedness of these spirals flip which is something to look for and I'll give a teaser in a moment for that this might actually be very elegantly observable in the Fourier domain but this is something to look for in images as a depolarization there is destructive interference between the direct and indirect images of accretion flows around low luminosity AGM it's a generic property as long as you're optically thin and you're magnetically arrested and one last exciting little tidbit is that the retrograde flows reverse handedness in this polarization signature on large radii where it's too dim for the EHG to see it but future arrays with denser coverage and better dynamic range can look for a flip and you can see this on the left hand side of the top left image where the spiral is going one way and then turns around this is a generic property of all retrograde magnetically arrested disks and it's a signature that something is changing direction that frame dragging is present it would be very exciting to see this and at the bottom I just want to highlight that there's a whole cottage industry of fellow obsessives who care about polarization in these flows who have been developing this reasoning and yeah just as a teaser there's a very elegant Fourier representation and a potential single baseline PLBI experiment that you can do to look for this that might be relevant very soon so I just want to use my last few minutes to tease something I find very exciting which basically is arguing that you can assume a great deal and learn a great deal that is sort of in proportion to how much you're going to assume about the black holes that fill our local universe so if you assume all AGN are magnetically arrested which you can argue from the fact that we've seen two black holes they both look magnetically arrested and also from the fact that all standard normal evolving disks eventually become magnetically arrested you get access to all this machinery that I've been outlining and so for a given population you assume a bunch of things about mass distributions and accretion rates which are mostly phenomenological and empirical you can always find a frequency where they'll be optically thin and for the roughly half of these that will be weakly inclined enough that all of this machinery applies where we get this natural basis for thinking about this problem where we're looking roughly downward at a rotating system then we can apply all of our reasoning and so you can argue that by assuming a particular observing frequency and some empirical population properties you can estimate what you can see what you can fit what you can analyze with a particular array and so here I especially want to shout out my wonderful colleague Don Pesci who has done some wonderful, wonderful work studying black hole demography using these techniques and others for measuring both masses and spins in marginally resolved sources and so he's done some very detailed simulations here this is just a very simple picture argument where as you blur out one of these simulations where as a reminder as we increase spin the polarization pattern becomes more and more radial as you blur and more and more weakly resolve the source this polarization pattern persists much longer than the shadow you lose access to the sort of image claim that we're looking at a black hole much faster than you lose access to this polarization information they're both there eventually destroyed if you don't resolve the source and in detail you can use an example array so one instance of a potential future next-generation event horizon telescope which has very dense coverage and much higher signal-to-noise ratio to look at what you can access in a black hole that is less than 10 micro arc seconds on the sky and I want to highlight how small this is the EHT images are about 50-ish micro arc seconds in angular size this is about two or maybe three resolution elements it's about three grapefruits across on the moon this is less than half of a pixel this is the art you can imagine this is a super resolved roughly pixel scale measurement for the EHT and so the the intuition here for why the NGHT within this gradash green band on on the right and this sampling space of all of the black holes and their expected masses that we know of in our local universe supermassive black holes I should say we are able to access this spiral polarization pattern information even when we can't access the shadow and the intuition is just that we get roughly one spiral per pixel and so for all of these supermassive black holes which are about one pixel on the sky we can sample this property over and over and over again and if we see coherent polarization structure over and over that's evidence for madness for a magnetically-arrested disk it's also evidence for madness of the observer but we're going to do it anyway if we can but and if we if we see this coherent pattern with a smooth average over time that's telling us about the spin and so that could be 10 and potentially even 100 depending on on how the uncertainties on these these sort of phenomenological patterns or properties slide around where right now we have zero no low luminosity HN spins have trustworthy measurements and so this would be groundbreaking for understanding the creation and merger history of our local universe I find this very exciting and as you might imagine if you expand into space these numbers get much better so I will conclude I think I'm at 45 minutes at least by my own little watch so just to say optically thin accretion flows reveal a great wealth of information in polarization and M87 and Sagittarius A star which we will be studying for the rest of our lives with any luck we'll serve as a testing ground for our phenomenological understanding of these sources or our qualitative belief that we're doing anything right in our GMHD simulations and as our simulations improve there will become there will be a a meditation a question of faith and trust in are these representing nature at any level that we are willing to extrapolate to sources that we cannot image where we just get a single pixel an integrated view and if we do believe it and this I really do think that the crux of this debate will be in the next few years as these simulations are improving at an alarming rate we will be expanding in tandem our arrays themselves and so as our simulations improve our ability to just stare at these sources and look at all of their rich structure and look at how wrong we are measure ideally how wrong we are will also improve and so the way I see it is we have one very special tool a sharp probe that is very sensitive both to astrophysical effects and and and radiative transfer effects but also very sensitive to the structures of the spacetime it will be critical to have this polarization handle on the physics of the system and next gen VLBI and how exciting it is to the physicists in the room you all you know the many physicists listening to this that relies sensitively on polarization I see it as as a a uniquely powerful tool for learning anything deep from these images and these images will be getting better and better and so I will end with a teaser that I really do think the first hints of the photon ring the first hints of light orbiting matter may be accessible in the near future with 345 gigahertz observations by the next generation event horizon telescope if this story hangs true that magnetically arrested accretion is pervasive and indeed present in the galactic center and so I personally I feel very lucky to be alive to see this and so for now I will conclude and thank you so much for listening awesome thank you very much Daniel for this very very nice talk let me see if I find questions or you too here let me start with one question by myself so do you have an idea of a forecast of this pin you can we might be able to measure like how large the bound might be in the best scenario case or something that I can do just I totally get what you're saying so I think there's there's sort of two steps to this the first step is if you assume that all you get is this sort of blurry image integrated measure and you look at a source over and over and over again if you believe you have a sense of the electron distribution function then these distributions where you see this wild variation in the polar metric structure actually shrink a great deal the main limitation there is actually a radial uncertainty and not an a sort of argument uncertainty here coming from how depolarized the source is and unfortunately that's the part of our gmhd and a ray tracing that we believe least and so the thing I'm very comfortable stating is that we will be able to draw a line in the sand between a spin of say point eight and lower and point eight and higher where as you get to very high spins you see very qualitatively different accretion whereas lower spins because the the effect of spin is very non-linear are very difficult to tell apart and much more sensitive to different thermodynamics in the flow that alone is still very exciting because whether low luminosity agn or maximally spinning is like a deep unknown yeah thank you and then just to clarify so this applies to both salutators a star and m8x7 it's roughly the same picture type of like so that that is a major caveat and it's something that is is an unknown for for our era right now is why is it that when we look at sagé star we see something that looks like a gently inclined black hole why does its inclination look like it might be 30 or 40 degrees when we are just sitting in some random part of a spiral arm at a disc with a black hole that you would guess would be pointing out normal to to the plane and it might be a question of coincidence it's something where we are not the first to see this indication you know there is these gravity results where they see face roughly face on looking hot spot very curious time will tell thank you let me see does someone here of the coordinators have a question let me go to you to find the meantime okay someone is asking me here how do you know like roughly half of the photons are coming from the photon ring the first I guess is the first photo ring what they mean yeah so I should clarify and if I might if I might ask also a follow-up because this sort of depends on the on on the source right like if you change your model here this plot that you have to write might change let me let me back up and say I went through this very fast far fewer than half of your photons are coming from the photon ring it is the case that when you look at large spatial frequencies you are selecting structures in your image which are very fine scale and so it's more that half of our signal at large spatial frequencies is coming from the photon ring the actual fraction of light coming from the photon ring you can look at the ratio between this blue curve at UV distance 0 and the red curve at UV distance 0 so in this case it's more like 20 now yes this is also super model dependent it is the case that magnetically arrested disks tend to have brighter photon rings there are deep reasons for this that I don't want to get into but a lot of it is actually the fact that our emission is not isotropic and so you get beneficial Doppler boosting into the photon ring and beneficial k cross b sort of synchrotron anisotropy effects that tend to slightly amplify the photon ring but even in our most optimistic case like you pick the highest flux fraction of the photon ring simulation that's only 20% to 230 gigahertz and all I'll comment on is that as you go to higher frequencies and it becomes more optically thin the source gets dimmer but the relative flux in the photon ring gets higher and so this this whole procedure gets easier as you go to higher frequencies thank you there's some minor delay so there might be a follow up or something no that's like yeah okay okay any other question have another one so do we I know nothing about scattering and I would like to know should we be worried about this type of observables because scattering that's something what I mean is like the the polarization leaves but then something happens between the source and ass is that is that a real concern so there are there are two big concerns for trying to apply this to Sagittarius A star that we don't have to worry about from SC 87 so from SC 87 there is a you can imagine that in between the image and us so in between the source and us there is some Faraday screen which might coherently rotate all of our polarization we can usually estimate this but it's generally fairly low for M87 whereas for Sagittarius A star there is much more stuff between us and the galactic center because we're sitting in the disc with it and so this adds both much bigger Faraday effects and much stronger scattering to the point that we actually have to worry about scattering it all at all the good news is scattering can be broken down into two effects one of which is a sort of diffractive blurring effect which you can actually kind of get around with clever observational tricks there's also a refractive effect which is much deadlier I would say to this observable and I have a student Caitlin Chevelle who's working on this very problem of a 230 gigahertz it's likely that this is not possible for Sagittarius A star but at 345 there's a critical turning point that makes it just accessible from the Earth's surface on new long day signs don't really exist yet but there are places you could put telescopes that would make it just possible to get around the scattering so it's very close it's marginal it's in the regime where if our simulations are 10% wrong it's not possible but given what we currently believe as our best bet we might have some hope which is very exciting Thank you but then why do you think the first evidence might come from Sagittarius A star and not from M87 if in some sense might be easier yeah so the trick here is that M87 is smaller on the sky and so there is a turning point that you can expect in these simulations for where the photon ring becomes dominant in the polarization on long baselines and for M87 that turning point is 15 giga lambda and unfortunately that is just not accessible from the Earth's surface until you get to 460 gigahertz and I don't think anyone's planning to build anything there anytime soon if the Greenland telescope is moved to the summit and gets a new receiver that I think is not planned yet but it might be I will change my tune Okay Thank you Okay I don't see your questions any questions from the coordinators here Yeah I have a question for Oh yes So very nice the webinar Daniel congratulations but I was wondering is any other correlation that you can get from other type of wavelengths like when it's an x-ray so like to compliment the analysis like a normalization of the amount of photon flux that could close I mean I'm wondering because usually kind of in the for the case of the Milky Way you have that sometimes the protons that are in these gas clouds right around the black hole produce pions and these pions produce x-rays because of the decay of the pions so I don't know if these photons also would also could generate this have winding in two and three but in another much higher energy level Yeah so I guess the there's a few sort of complications there one is that when we look at Sagittarius A star we don't always see a correlation between sort of radio flares and x-ray flares another sort of infrared flares so we don't always know we're looking at the same structures and so even if they we were seeing the same lensing effect it's not clear that we could associate them with the same same emission regions but in principle if you think that the accretion flow or just the material around the black hole is optically thin to the emission you're excited about then you can always argue that there will be this sort of lensing echo and I think the problem is that at those higher and higher frequencies or at those sort of ultra high frequencies you don't expect optically thin transport from wherever this this emission is coming from to where you would see it and also I guess separately there's not always enough flux or enough really high temperature electrons or high density to generate enough of this to see this in an expectable way but I want to sort of acknowledge that there are some people working on sort of untraditional photon ring-esque projects looking for lensing for example from some mazers that kind of thing where you don't need to look at the high end images from stuff in the accretion flow you might expect temporal signatures from stuff from way out there as long as you're optically thin so I want to leave this on the table it's just very tricky to observe okay thank you awesome just on time Daniel thank you very much for this lovely webinar people might contact you and look your data on your web page and if there are more questions so thanks thank you all and thank you Daniel and I hope to see everybody in the next webinar thank you so much yeah please feel free to email me with questions I'm always happy to chat awesome okay bye bye great thank you bye bye