The first image of a black hole
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Leibniz MMS Days 202219 / 22
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Object (grammar)Universe (mathematics)Multiplication signSpacetimePairwise comparisonTheoryModel theoryComputer animation
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Sign (mathematics)Image resolutionDistancePresentation of a groupOrder (biology)2 (number)10 (number)Flow separationMetreObject (grammar)Different (Kate Ryan album)Multiplication signWaveDirected graphPairwise comparisonMassMatter waveImage resolutionDistanceDegree (graph theory)Electromagnetic radiationWavefrontOpticsDot productMereologyMaxima and minimaArithmetic meanClosed setTerm (mathematics)Numerical analysisExpressionLecture/ConferenceComputer animation
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Event horizonAverageSpacetimeMultiplication signTransformation (genetics)Different (Kate Ryan album)LengthDirected graphFourier seriesVariable (mathematics)Group representationTrailProcess (computing)Term (mathematics)Fourier transformFrequency
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Trigonometric functionsTerm (mathematics)Position operatorFaculty (division)Group actionQuantum stateMomentumFood energyImage resolutionNichtlineares GleichungssystemTheoryHeat transferConservation lawMassCombinatory logicCurvatureDerivation (linguistics)TensorThermische ZustandsgleichungPairwise comparisonKörper <Algebra>Boltzmann constantDimensional analysisSpacetimeInductive reasoningCategory of beingStandard deviationThermal radiationEvoluteNumerical analysisThermodynamic equilibriumRing (mathematics)Water vaporCurveProcess (computing)Point (geometry)Moment (mathematics)Computer animation
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Inclined planeAngleSpacetimeThermal radiationRing (mathematics)MereologyLine (geometry)PropagatorOrder (biology)Körper <Algebra>CurveComputer animation
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GeometryMereologyDoppler-EffektRing (mathematics)Inclined planeSymmetry (physics)
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Mach's principleMereologyAcoustic shadowInfinityRotationCircleSurfaceEvent horizonProjective planeDirection (geometry)Quantum stateDirected graphMultiplication signOrbitComputer animation
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Chi-squared distributionDistribution (mathematics)TurbulenceGravitationDistribution (mathematics)Exterior algebraModel theoryMereologyMultiplication signParameter (computer programming)Natural numberAcoustic shadowTerm (mathematics)Fraction (mathematics)Category of beingThermal radiationDirected graphDynamical systemCondition numberBoundary value problemPressureFood energyKörper <Algebra>Object (grammar)MassHypothesisTheory of relativityTurbulenceSocial classMaxima and minimaFundamental theorem of algebraSurfaceBeta functionLine (geometry)Computer animation
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Parameter (computer programming)Matching (graph theory)Maxima and minimaDirected graphMereologyBasis <Mathematik>ResultantPrincipal component analysisGroup representationImage resolutionPhase transitionPairwise comparisonAlgebraic closureModel theoryTrailCategory of beingDistribution (mathematics)Curve fittingMultiplication signLine (geometry)Matrix (mathematics)Computer animation
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Model theoryTheoryNumerical analysisObject (grammar)Matching (graph theory)ConvolutionLogicCategory of beingRight angleParameter (computer programming)Point (geometry)Energy levelRotationModel theoryReal numberGoodness of fit
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TheoryGeneral relativitySpacetimeMetric tensorCategory of beingExterior algebraModulformParameter (computer programming)AreaAdditionCoordinate systemTensorStatistical hypothesis testingObject (grammar)Series (mathematics)Metric systemCompact spaceStandard deviationOrder (biology)Identical particlesDecision theoryMassNormal (geometry)Binary treeCoefficientConstraint (mathematics)Event horizonObservational studyMultiplication signMeasurementComputer animation
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Electric fieldObject (grammar)Acoustic shadowDifferent (Kate Ryan album)Angular momentumExterior algebraSurjective functionKörper <Algebra>Multiplication signCondensationEvent horizonHorizonSurfaceTheory of relativityGravitationTerm (mathematics)Uniqueness quantification
Transcript: English(auto-generated)
00:00
to give this talk. It's been a long way to get here, both in time and in space. I had to get three times at the railway station, you know, building works because I always got it wrong. I managed at the end.
00:21
And so it's a pleasure to be here and to give this talk about the first image of Michael. Okay, so here is what I will talk to you about. First of all, I will tell you about how you actually do the observation. How do you take a black hole and you take a picture of it? Something that you may think it's a logical contradiction.
00:41
Then I will tell you what we, which is more relevant for what we will be discussing here, that is how you do an interpretation, a theoretical interpretation of a supermassive black hole. And that's the modeling part, which is the one I have been more closely exposed to. And then how you go from, you know,
01:00
an important comparison between theory and observation. And because I am basically a, you know, a theorist, I want to take you to across another question, which is the question of asking, do we really believe that this is Einstein's theory that is right, or are there other alternatives?
01:23
So let's start with setting up the stage of why this is a difficult problem. First of all, black holes are the most compact objects we know in the universe. You take a certain amount of energy, you compress it in a very small volume, and then you produce a black hole. We don't have black holes on earth,
01:41
we have black holes in the heavens. So they are all astronomical. And that means that they are also very far apart from us, very distant. So if you have something which is intrinsically small and intrinsically far, you can imagine that seeing this object in the sky, just the projected size will be very small.
02:01
So, and of course, if you want to take a picture of this, you better have something that you can see. And if you want to solve this problem, then essentially you have just one way. That is, you have to take black holes, which are for some reason, this doesn't work anymore. You want to have black holes that are,
02:23
sorry, I can't control it anymore. Sorry, let me try again.
02:45
So we thought that, you know, zoom problems were over when you have a live presentation where it doesn't seem to be the case. Okay, of course there's going to be some delay. Okay, so what do you want is to have black holes which are as big as possible.
03:01
We call them supermassive black holes because the bigger they are, the more massive they are, they have, the larger they are in the sky. And they are sufficiently close, okay? You can play with these two degrees of freedom, size and distance. And then of course you have a certain resolution. That's what you physically can resolve.
03:20
And you check all the black holes that you have and you know about, and there are just two that fits the size. One of them is M87, the black hole at the center of the M87 galaxy. And then the other one is the black hole in our galaxy. The black hole in our galaxy is smaller than the one in M87, but it's closer.
03:41
So they both conjure to have the right size. So this is M87. This is a supermassive galaxy as a mass of three billion, sorry, it has a mass of, you know,
04:01
of several billions of solar masses. But in the center there is a mass which we don't know, which is of the order of say six billion solar masses. This is the way it looks like in the optical. And you can see already in the optical, there is this little filament coming out. We know that that is a jet.
04:22
Now, the beauty of astronomy is that you can see the same object in many different wavelengths. So if you start looking at this in the radio, you see that this is a much bigger object. And there is a very large cloud of plasma, ionized plasma, which is emitting in a radio. And now that you can use a technique which is called interferometry,
04:42
which allows you to essentially zoom in into this image. And so depending on the way in which you're making an observation, you can go and zoom in. For instance, you can have a look at what happens at the very base of this jet where the jet is produced. And you can further zoom in in the very inner part of the jet.
05:01
And you find something like this, or you can even further zoom in. And nowadays, radio astronomers have studied this in very great detail. They name all of these little dots and little maps, maxima.
05:22
But of course, what would be nice is to have an image of where this jet is actually coming from. And this is what has been done with the Event Horizon Telescope. And to give an idea how more advanced the images done by the Event Horizon Telescope are, this is just a comparison of the resolution
05:42
that the Event Horizon Telescope has reached as compared to the best resolution that was available before. So the technique used is called DLBI, or Very Long Baseline Interferometry. And as many other techniques in astronomy, it relies on a very simple equation. If you want a given resolution,
06:00
then you have to consider the wavelength in which you're making your observation and the telescope in which you are collecting this information. So the telescope size plays a role in determining how resolved your image is. That's why we tend to build large telescope because we want to have high resolution images.
06:21
Now, when you ask yourself, well, what does this mean in terms of black hole? You can't get any light. Any light is producing a black hole, but not all of the light reaches us because most of it is trapped between us and the black hole. So you want to get the light that is produced near black hole as close possible to a black hole that reaches us. And then you find out that the light
06:41
that does that is radio. And so in particular, something of the order of 1.3 millimeter radio waves. Okay, so this sets the numerator of that expression. And the number you want on the left is of the order of tens of micror second. That's the resolution you need
07:01
in order to see the little object where the jet is starting from. And in order to get that resolution, you need intercontinental distances. So you just have to build a telescope which is as big as the whole planet. You may think, well, it's impossible. Well, if you do it physically, yes, it is impossible,
07:21
but you can do it virtually through this technique, which is called VLBI. So the idea is as follows. You take small size, 20, 30, 50 meter telescopes across the planet, in France, in Spain, at the South Pole, in Chile, at the Hawaii, and you connect them.
07:40
You connect them so that they are observing at exactly the same time, same wave front. And when you do this, then you can do interferometry. And so when you do this, for instance, and you connect a telescope at Hawaii with one in Arizona, you have virtually the size of the telescope, which is of 2,500 kilometers, which is the separation between the two.
08:02
Now, if you think a little bit about this, this sounds funny, right? It sounds like, how is this possible? Why don't we build all of the telescopes like this? The reason why this is possible is because you need to make sure that you are really recording the same wave front, the same electromagnetic wave front. So together with the recording of the electric field,
08:21
which is our radio telescope, you're recording electric fields, you have to make sure you record the time of arrival exactly and as precisely as possible. So that is why you need atomic clocks at each of these telescopes. Once you have these two pieces of information, then you can combine them together and obtain an image.
08:42
And of course, because we have telescopes across the whole planet, this is useful because not only we have, we have then telescopes of different sizes. And so virtually by this very simple expression, we have different resolution in which we can see the image. We can see the same image, a different resolution. And in addition, because the earth is rotating,
09:03
we always have a few telescopes that are observing, that are able to see the source. Because of course, at one point, the French telescope will stop seeing the source because it will be on the other side. But then there's going to be other telescopes in Chile, for instance, that will be able to see it.
09:22
And okay, so this is basically the technique is called, as I said, DLBI. And you can think that there are baselines between different telescopes. And mathematically, what we say is that out of these information, we can build a Fourier transform.
09:40
This is a two-dimensional Fourier transform in space that provides you quantities which are real and imaginary. These are called the visibilities. And essentially, these tracks that you can see here in this diagram, these are the representation of the Fourier transform of the intensity on the sky,
10:00
I of X, Y. So just think about what you know of the Fourier transform when going between time and frequency. Now you are going between visibilities and the aperture on the sky in terms of the intensity of the source. So once you have a certain length in the tracks, you can build a certain image.
10:22
And the longer the time, the longer the tracks, the more the Fourier space is filled, the better is your image, okay? So that's a basic principle. And now I really show you with a concrete example. As the different telescopes are building these tracks,
10:42
we are able to see more and more higher definition details of this image. And of course, you can see that at one point, there's going to be no telescopes that are able to see the source. And also you will see that this visibility space, the Fourier space, is not going to be perfectly filled.
11:01
In principle, you would like all of this space to be perfectly filled, fully filled with information. And we don't, okay? So there'll be some piece of information that needs modeling. So these are the four images that we obtained and published in 2019. These refer to essentially four days of observations.
11:25
Normally the way it works is that, you know, you ask time on all of these telescopes. This is a competitive process. We don't want to own the telescopes. We have to ask for the use and then we get the use and then during those days, we make the observations, no matter how the weather is.
11:42
If it is bad weather, we have bad luck. If we have good weather, we have good luck. And that's why not all of the days that were available, there were some days where either the weather was not sufficiently good in all of the telescopes or there were too few telescopes that provided images. But four days were enough to produce these images.
12:01
And as you can see, they are all consistent with each other, but all this different. And that's because we expect a certain variability from day to day. So the image was published on the 10th of April, 2019. This is the 11th of April. So the day after, essentially the image has gone
12:22
on all of the first pages of newspapers across the world. It's been calculated that in less than 24 hours, 4.5 billion people have seen the image. That's a good portion of the human population. And I think the reason is that, you know, it was a fantastic source of inspiration for the social media that used it for, you know,
12:46
explaining to us what is it exactly where we were seeing. And of course, you know, that's how, that's why an image is so much more powerful than anything else. If I were to build this, you know, show this in terms of a Fourier transform,
13:03
no one would appreciate it, but in an image, everything understands. So now the question is, and this is where we enter into this game, what are these rings and whatever to do with black holes? Okay, so to answer this question, we need to go through three steps.
13:21
The first one is we have to perform GRMHD simulation. GRMHD stands for General Relativistic, because we are in a curved space time, Magneto-Adodynamic simulations. And this, we want to do them in black hole space times, in the Einstein theory, but also in other theories.
13:40
That will tell us how is it that plasma moves near a black hole. The second point is how does this, the plasma that is moving in this space time produces light and how does this light reaches us? So we have to do radiated transfer and ray traced radiated transfer.
14:00
Radiated transfer tells you how light is absorbed and emitted, ray traced tells you along which path. And then the last step is, compare observations and theory. We have four images, which we have observed, and we built 60,000 synthetic images. So 60,000 mathematically consistent,
14:22
physically consistent images, and we had to compare. We were very lucky here in Europe that we had received a synergy grant and which is called Black Hole CAM, and essentially in Frankfurt, we built an infrastructure, a computational infrastructure that does exactly these three steps.
14:42
So Bach does the GRMHD, Bosch does the ray tracing, and Gina does the comparison with the images. And the real heroes of this story are these guys here, who were the members of my group. None of them is with me now. They're all moved to faculty positions in Europe and elsewhere.
15:01
So because this is a mathematical modeling, and I guess you will not be scared of equations, this is the kind of equations we need to solve. First of all, we have an energy momentum tensor. So this is, sometimes tells me about the properties of my plasma.
15:20
And I have a covariant derivative. So this is a conservation equation on a generally curved space-time. And then I have a conservation of rest mass. If you are familiar with the aerodynamics, you can think these are other dynamical equations in a generic or more complicated space-time.
15:40
If you're familiar with plasma dynamics, this is, again, plasma dynamics, but on a space-time where curvature is not necessarily zero. Then of course you need an equation of state. And this energy momentum tensor, well, this is the combination of all a number of elements, you know, that to do with the actual plasma
16:01
plus the electromagnetic fields and so on. And so you need to carrying along also the Maxwell equations. So again, you can think these are the standard Maxwell equation, induction equations, in particular in GRMHD. And you have to solve this in full generality in three plus one dimensions. In addition, as I said,
16:21
you need to study how light is emitted and absorbed, essentially this is the Boltzmann equation, which you can convert in terms of an evolution equation for the intensity of the radiation along a given path. And this is the path followed by photons in this space-time.
16:42
So once you have that equations and you have spent 10 years building a code to solve those equations, you obtain something like so. So this is a typical simulation. We start with something that is a ring of matter in equilibrium around a black hole.
17:00
And I'm showing in red and yellow, the rest mass density of the plasma and with white and blue, the magnetization. Yeah, the movie is a bit choppy, but you can see that this is a geometrically thick object and they're essentially along the polar direction, there is very little matter, there is a lot of magnetic fields.
17:21
So there, the magnetization is very high, you can think that the magnetic fields are very strong. That's what produces the jet. As you can see, the accretion is not a steady process. It's a bit like water falling from a waterfall. There are moments where there is larger amounts of water or plasma being accreted.
17:42
This is the inclination at which we think we're seeing the jet in M87. And now you have to imagine of, you know, going away from GLMHD and looking at emissivity. So this is the actual radio map you would see at that inclination if you had eyes which were sensitive to the radio.
18:01
It looks pretty much like a ring, okay? But it's not exactly a ring. Looks like a ring because we have this very special inclination. If we were to go around, you would see it's a far more complicated radiation field with holes, which I'll try to explain. And this is if you now take the very same imaging
18:22
and now allow it for the way it would be observed by a radio telescope. You can see there is an image which is flickering and the flickering timescale is of the order of days. And that's what we have observed, okay? So what we have observed is very close to what we would expect to see from a plasma
18:43
of accreting onto a black hole. But I will explain a bit more in detail, you know, why we are so confident. So the second step, if you remember, is understanding what happens to light, so photons. So I have a pointer, I cannot use it.
19:03
But, you know, if I press the pointer, I get, you all know there is a beam of, a laser beam that is shot from here and then reaches the wall and then from the wall reaches your eyes. The reason why we know how to use this is because light propagation on earth is trivial. It just goes on a straight line, okay?
19:21
But in a curved space time, that's not the case. Light can go all over the place. And so you may get light from regions where on, you know, that are not directed to you. Let's make an example, okay? This is, imagine you have a black hole and you have a thin disc of light, which is emitting light, and you wanna take an image at a given angle.
19:43
Then of course, you're going to see all of the photons that come straight to you from the direct image. In principle, photons that go in this direction, you will not receive them. They would go straight if the space time was flat. But in a space time which is curved, you can actually see also what's behind the black hole.
20:03
So this is the part of the sheet which is behind the black hole. And to make things even more interesting, you can even, sorry, you can see even the lower sheet of the disc, okay? So this is essentially the way you would see a geometrically thin sheet of light.
20:23
And if you are interested in science fiction, this is interstellar, the image of interstellar, which is a very accurate, although not realistic, image. And you now understand why interstellar looks like so. So there is this, the part of the disc which is in front of the spaceship.
20:41
This is the part of the disc which is behind the black hole and this is the part of the disc below the disc. And this tells you that if you have to go and hide, don't do it behind the black hole, it will not help. Okay, now this was accurate, but not quite right.
21:03
As I explained, the plasma that is accreting is actually very hot. And this means that it's geometrically thick. It is optically thin, but geometrically thick. So you have to think that in general, we look like so. Now I'm just rotating my camera so you can see.
21:21
And now you can see there are two holes. There is a black region and another black region here. If I'm looking at it phase on, it's perfectly symmetric. But I lose this symmetry as soon as I move away from that very specific inclination. Another thing you can also appreciate, it is always a bright side.
21:41
And that's because there's always a part of the disc which is moving towards you, just like there is a part of the disc which is moving away from. And so this is called a Doppler effect, a Doppler boosting. And so this explain pretty much why what we see is a donut. It's a half a donut because we are the inclination
22:00
such that only the lower portion of the donut is coming towards us and so is amplified. Now, let me give you some, the ABC of black hole imaging. So this one is, as I said, the upper sheet behind the black hole. This is the lower sheet. This is the part which is boosted and so amplified.
22:24
And this is what is called the light ring. I will explain what is the light ring in a moment, but it's a very important, maybe the most important part of a black hole image. Okay, so yeah,
22:42
I should say that this part here is the shadow, okay? This part here and this part here is essentially the shadow. So what is a shadow? People often misunderstand the shadow with the event horizon. The event horizon is this surface, mathematical surface, which absorbs photons.
23:03
Or if you want, is the surface which cannot emit photons. The shadow is the projection of something which is related to the event horizon, it's not the event horizon. So to explain this, I created this movie. So imagine that you have a black hole and you have a source of light, okay?
23:21
So you can imagine that this source is just producing photons, light rays, and there's going to be light rays which are going to be immediately absorbed by the black hole. They would be just, you know, hitting the event horizon. And so if you are an observer here, you simply will not see those photons. But there are also photons
23:41
that do not enter the event horizon directly. They get very close to it. They are below what is called the unstable photon orbit. And these photons, they will eventually go on to the, and be absorbed. So at a large distance, an observer will see a region, which is here, which is essentially devoid of light,
24:03
or very suppressed with the largest suppression of light, simply because all of the light that should have arrived here has been absorbed by the black hole. And to give you the sizes, in case of non-rotating black hole, this is twice the mass, the photon circular orbit is three times the mass,
24:21
and the projected size at infinity is four to 27, so 5.3 roughly, okay? So what we see is the actual shadow. And you can also appreciate that the shadow should not be perfectly dark. It's not the event horizon. Because if you take a photon here, where my pointer is, and you emit a photon,
24:41
this photon wouldn't have any problem reaching an observer, okay? That is why the shadow is not necessarily dark. And this region over here, sorry, this region over here, this, this, I'm trying, okay, nevermind.
25:00
The edge of the shadow is a very important surface. That's because it is a perfect sphere, and so a circle in projection, if it is a non-spinning black hole, but is not a circle, a perfect circle, if the black hole is rotating. That's because there is a relativistic effect,
25:21
which brings in photons from this side closer to the rotation axis, okay? So if we were, in principle, able to measure exactly the shape of the shadow, we could tell what is the spin of the black hole. Okay, Mr. Chairman, you keep an eye on how I'm doing.
25:43
Okay, so now, of course, we don't know much about what is happening in the M87 star, okay? So in principle, we have to scan all the possibilities in terms of the physical parameters.
26:01
So we need to be able to change the black hole mass and spin. We need to consider black holes in other theories of gravity. We need to consider alternatives to black hole, something that looks like a black hole. It is a compact object without an horizon and as or does not have a surface. We don't know exactly.
26:21
No one has gone at the center of M87 to tell. We also don't need much about the plasma properties. And I haven't explained this in detail. Actually, I haven't explained it at all, but the reason just a single way in which plasma can accrete onto a black hole,
26:43
depending on the initial conditions, you may have two fundamental classes of accretion. One is it's called SANE, the other one is called MAD. MAD stands for magnetically arrested and SANE stands for standard accretion. Basically, they differ in the amount of magnetic field
27:01
that is accreted onto a black hole. And MAD tends to have a lot more magnetic fields being accreted, so much so that sometimes the magnetic pressure can be so large that even the accretion is prevented. And whether one is preferable over the other, it's hard to say.
27:20
It's a matter of boundary conditions, and so unless you know exactly what are the conditions near the horizon, you can't tell. It's the observation that reveal whether nature prefers one or the other. And then, of course, there is light dynamics in the properties. So how we can study in great detail
27:43
how matter evolves, but how light is emitted, that's part of our modeling. And that's because our simulations in magnetodynamics, they model the inertial part of the plasma, the heavy part of the plasma, the ions, the protons,
28:02
and not the light part, the electrons. And the two are, in principle, related, but not one-to-one. So there is a lot of freedom in determining the emissivity properties of the source.
28:21
What we know for sure is that if you get radiation at 1.3, that's to come from synchrotron radiation. Synchrotron radiation is the radiation produced by relativistic electrons going rapidly around magnetic field lines. As I was saying, we evolve ions, okay? So we need to have a distribution,
28:42
energy distribution of the electrons, but this is undetermined. And the simplest thing you can do is you can create some relation between the temperature of the electrons and the temperature of the ions. You can say, again, this is the simplest hypothesis that you can make, is that the energy distribution
29:01
of the electrons is a thermal one, a Maxwell-Yutma distribution. But you still have to get the temperature. And the temperature, you can say, the temperature of the ions, Ti, is related to the temperature of the electrons in some shape, in some analytical prescription.
29:22
And one which we have used in the simulations I will show you now is very simple and goes like so. Essentially, we have a single parameter which relates the temperature between the two species. And you have another parameter, which is called the plasma beta.
29:40
Essentially, it's the ratio between the gas and magnetic pressure, and allows, essentially, to put more light in the disk or in the jet. And these three parameters are three parameters, and we just change it in all of its possibility. So this can go from one to 160,
30:02
and essentially allows you to recover the two extremes. One is you have most of the emission coming from the jet and the other one coming from the disk. And this is a very crude, handmade recipe, but you can do much better, much more sophisticated,
30:20
involving turbulence and reconnection. And you find out, after all, this very simple recipe works pretty well and can reproduce much more complicated energy distributions, even non-thermal energy distributions. So, you know, it looks crude, but works. Okay, so we have then run a number of simulations.
30:40
In particular, in Frankfurt, we have done about 50% of the simulations in the whole EHT. These are high-resolution, three-dimensional simulation. Then for each simulation, we changed the emissivity profile, which we painted differently the electrons. And in this way, we got 400 scenarios. And this is just a movie which should allow you,
31:04
in principle, to see a small fraction of the library of scenarios we have considered. So the situation where you have black hole going counterclock or clockwise, you have shadows which are very small or very large.
31:21
Your emission comes mostly from the disk or mostly from the jet and so on and so forth. And out of each of these scenarios, you can produce images, okay? Because each of these frame corresponds to a given time interval, which is the one associated with the observations. Now, I would like you to think a little bit
31:45
about how involved and the geneticist problem is. So these are four images that have been produced. The first two are called, come from a mad, and they are high, 160 and 110,
32:02
so they essentially are the extreme of the mad regime. And these are the same, again, the extremes. And you can ask yourself, okay, well, so of these images, we know everything because we know all the properties of the plasma, we know where photons are emitted, we can trace them.
32:22
And if we ask ourselves on the basis of these images only whether we know where the light is emitted, the answer is no, okay? Once you have just an image, it's very, very hard to tell where the light is actually produced. So to explain this, I convinced you,
32:41
let's imagine we decompose these images in three parts. Okay, as I've shown you, in general, you have a torus, a disk, we call it torus disk, independent, equally, and then you have two jets, one which is coming towards you and one which is receding. And the one receding can actually also be
33:00
the dominant source of light, because as I explained, light can be bent. So you see it here that depending on the, now this is a matrix representation of the different parts, so this is the mid plane, this is the near side, or if you want the approaching jet, this is the receding jet. And then you can see, essentially,
33:20
you can fill any of these cells in this matrix, that in this case, most of the light comes from the mid plane, but in this case, most of the light comes actually from the jet which is moving away from you. And this is just because we're considering this specific model with this specific R high.
33:40
So don't ask me where the light comes from in the image because we simply cannot tell, it's highly degenerate result. And then, as I said, we built 60,000 images, and we had to find the best match. And luckily, this is not such a, this is the easiest of all of the problems
34:01
because there are algorithms which are very accurate and fast and allow you to make this comparison rather easily. To give you an idea, again, this is an example, imagine that your data is the blue, this is in the visibility,
34:20
those tracks you can decompose into closure phases and visibility amplitudes. And the blue lines are the data. And for each image, this is an image of a simulation which is then deconvolved to consider that your telescopes have a certain limited resolution.
34:43
What you can do is you can run this, all of your simulations, every time you run a simulation, you can have a fit of the data, you can calculate that chi-squared, and then out of this chi-squared, you can have a distribution of images that matches the observations.
35:02
When I try to explain this, half of my audience understands and the other half doesn't understand what I'm talking about. So here is another way of thinking about what I'm doing. Imagine you are at a stadium and you have an image of a person, this one, which is very blurred.
35:20
You don't know whether this person is in the stadium and you don't know actually who this person is. But the stadium has CCTV cameras that take pictures of all the people that go into the stadium. So what you can do is you can scan across all of the images in the stadium and the software will return a distribution of images.
35:44
These are all the images that match very well the image that you have produced because they have, the principal components are the same. And of course, you cannot tell whether the person is in the stadium or not because you have at least 10 top best matches. You can have many more if you decrease the tolerance.
36:04
But that already gives you a lot of information. First of all, you know that this person most likely is a woman. And because all of the top matches are women. And the second thing that you know is that this is a woman with long hair, okay?
36:22
Again, because all of the top best matches are women and with long hair. So although you don't have a perfect match, you can extract already a lot of information. And that's what we've done essentially with the chi-squared and the distribution in parameters.
36:42
This is an example, okay? So this is the observations and this is the theoretical model. So there is, out of these 60,000 images, there is one, this one over here, that matches to this level of precision, okay? And because the one on the right is a theoretical model, you would think, okay, I know exactly what's on the left
37:01
because the one on the right is exactly the same as the one on the left. This is a flawed logic because I have lots of images on the right that are looking exactly the same as on the left with the same level of bounty. And that is why there are certain aspects of this problem
37:22
we cannot model, okay? So to give you an example, these are three real simulation images. These are the images before the convolution. And they give you the same match with the observations, but they correspond to three completely different objects. This one is a black hole, which is counter rotating.
37:43
This number is the spin. So it's negative, it's counter rotating. This is a black hole, which is maximally rotating, but is in the other direction, spin 0.94. And this is actually a black hole, which is not spinning at all. And yet they give you the same quality. So how do you take this?
38:01
Well, you know, from one point of view, this is good. That means that your model is so robust that it will provide you with the right answer no matter what. On the other hand, it is bad because essentially you are not able to distinguish the parameter that distinguishes this black hole from this black hole, so the spin. And that is why we have not published
38:22
the spin of M87 star. This is a property we cannot measure yet. Okay, I may need maybe 10 more minutes if I can. So all I've shown you is there is a very good match
38:41
between general relativity, Einstein theory of relativity, and what we observe, okay? So there is a consistency, which is what you would expect. But you know, you may ask, because this is an observational science and there are degeneracies.
39:01
It's impossible to avoid them because there are many different theories that they can explain the same observations. As long as the observations are very few and not very precise, there are many possibilities. And so what you want to do is, can you really use this image to test gravity? Can you tell, A, this is a black hole
39:22
and B, is Einstein's black hole or is it a black hole in a different theory? For those of you who are not expert, you should be aware that there is a lot of work nowadays in trying to find alternatives to Einstein theory of relativity, okay? So there are lots of people who are trying to use the observation to say,
39:42
oh, Einstein is not right, this other theory is better. So we have tried to follow these possibilities and see whether or not it's Einstein theory or any other, or even maybe it's not a black hole at all. Maybe it's an object which is sufficiently compact
40:02
as the ability of producing a shadow, but it's not even a black hole. It doesn't have an event horizon. And there are black hole, sorry, there are objects of this type that are possible to build, even within general relativity. So in order to address this problem,
40:22
what you can do is you can have a either an agnostic, that is you simply don't know, and you parameterize your ignorance, or agnostic approach where you say, okay, I test my observations against a specific alternative and I check whether or not this alternative
40:41
is good or bad. So it's either positive or negative, while the first one just says, okay, given the observations, these observations provide me certain parameters. Okay, so because I spent quite a lot of time in this, I'll give you a flavor of what this amounts to,
41:01
this agnostic approach. So essentially, what you have to do is study particle plasma motion and photon motion in a curved space time. So you need a metric tensor, for those of you who have taken a course in general relativity. And this metric tensor is a tensor
41:22
which depends on coordinates. And we know very well the form of this tensor, the Schwarzschild solution, the Kerr solution, so there is no problem about these. But what you would like to have is a space time which is more generic than that, that has additional parameters, A's and B's,
41:42
such that if all of these parameters are zero, you end up with Schwarzschild or Kerr. And if they are not, then they measure the deviation away from general relativity. So we, together with other collaborators, we have derived these metrics. These are called the RZ or the KRZ,
42:02
or it's all Agdenko, Konoplya, it's all Agdenko. And I will not go into great details into this, but this is a very powerful way in which you can build any metric, black hole or compact object metric. And then determine what are the values of the coefficient,
42:21
and this series converges very rapidly, so you really need the very first few coefficients to measure to percent precision. The other approach I was mentioning is, okay, kind of binary decision. Can we distinguish Kerr black hole from something else?
42:40
And what we've done is we consider either a dilaton black hole, which is a black hole in alternative theory of gravity, or a boson star, which I will explain in a minute, or black holes within general relativity or other theories which have certain charges. Normally we tend to think that black holes have just mass spin and electric charge,
43:03
and even the electric charge is essentially zero. But in other theories, there are possibilities of having black holes which have other charges. These are not electromagnetic charges. These are properties if you want. And then you can compare whether your measurement
43:21
sets constraints on the size of these alternative charges. So let me give you a flavor of what we're doing. So here we have a Kerr black hole, and we have a disk in Kerr space time, and this is a dilaton black hole. You can run exactly the same simulations
43:41
on Kerr space time or a dilaton black hole space time, and of course you have to make sure that some of the properties are the same, for instance the mass, but also maybe the size of the horizon or whatever. And then you perform the simulations, and you can start convincing yourself that, okay, they look different, but they also look very similar.
44:02
And of course we're not gonna do plasma simulations. What we will end up with are images. Unfortunately, the quality of the movies is pretty bad because of the zoom. But what you can do is you can take the image coming from Kerr or coming from a dilaton black hole
44:21
and look at it very, very carefully. And then you consider yourself, well, they are different, okay? But they're also very similar. And if you then add the fact that, if you refer to the Sagittarius star to the center of the galaxy, then there is additional scattering, then you really have to compare this guy
44:41
with this guy over here. And of course they are different because relativity provides you uniqueness of the solution, but they are so close that the conclusion that you obtain is that it's not possible to distinguish a dilaton black hole from a Kerr black hole with the present precision of the results, okay?
45:05
Another popular alternative of a black hole mimicker is called a boson star. So this is really not a star, it's actually a huge object. But its core is very, very compact. So compact that it looks like a black hole,
45:22
but it's not made of, doesn't have an horizon and doesn't have a surface. You have to imagine it's a condensate of bosons and mathematically there is nothing wrong with them, physically they are allowed to exist. So the issue is really whether or not at the center of our galaxy there is such a boson star.
45:42
And if there was, or at the center of M87, what would it look like? And so once again, what you do is you carry out simulations. You have to imagine here there is a boson star, you don't see it because this field doesn't interact with matter in any matter, it just interacts in terms of gravity.
46:01
And what you see is that as the simulation proceeds, matter, because of the surface, there is no surface of this object, and there is no event horizon, matter can go very deep inside the boson star, almost to the center, not quite at the center because once it gets very close to the center, it has a lot of angular momentum
46:21
and will just feel a centrifugal repulsion. But you can see that as compared to a black hole, there is a lot more matter and luminosity, therefore, at the center. And so the size of the shadow will be different. And this is a curved black hole,
46:41
this is a boson star, you can see how the image is much smaller. This is particularly evident when you look at the de Kombol image. And you can see that the shadow, or the dark, this is not a shadow really, but the dark image here, it's much smaller than the image here. And of course, you measure the shadow.
47:00
So you measure a size, you measure a mass, and so you can convince whether or not what you're seeing is a boson star. And what we have shown with our observations that at least in the case of M87 and the simplest cases of boson star models, what we observed cannot be a boson star. So we have excluded this object
47:20
from the possible explanations. Okay, I want to come to the conclusion. The Eventuition Telescope has provided the first evidence of supermassive black holes. And of course, as boosted, I want to send off strong gravity. Because of having to deal with this and explaining these observations,
47:40
we have carried out in maybe 18 months, more simulations and more understanding of what happens on accretion onto black holes in the previous 10 years. That's also because there were a lot of people working together on this. We're starting to study alternatives for black holes. Boson stars can be distinguished from black holes,
48:01
other black holes cannot. And if you want, the Eventuition has transformed really an Eventuition from a concept, something we write on a blackboard when we explain general relativity, over to a testable object. And the last is, if you're interested in this,
48:20
you are not a general relativist, but you want to know more about this, there is a book which has been just published that explains all of this in a bit more detail. Thank you.
48:49
Maybe I can be. Ah, ah, for the, yeah, sorry, yeah. Maybe this is changing for the, for the questions?
49:00
Okay. So are there questions from the audience here? Yes, it's. My question concerns observation. You use different telescopes on the Earth, and how do you decide that the different signals from different stations do not save the waveform?
49:21
Right, so this is when you use the time stamp. At each telescope, you measure a given electric field at a given time, to the precision of a nanosecond. And then when you, then you take the data, so this is maybe something I omitted, each telescope records the data, and then all of the data from all the different
49:41
telescopes are brought together into a correlator. These are supercomputers where all the data streams are put together. And of course, before you put it together, you have to align it so that the time axis is exactly the same in all telescope. Once you have the correlated signal, then you can, you can do the next step,
50:01
which is doing interferometry. So that's how you, you know, you are certain that you are really measuring the same way.