 Okay. I think we can get started. So good afternoon, everybody. Welcome to the 2022 Abdu Salam distinguished lecture series. And this year it will be given by Professor Alessandra Bonanno, who is joining us from Berlin. Welcome Alessandra. Good afternoon. Good afternoon. Let me say a few words. This is a wonderful tradition at ICTP. We have this lecture series, three lectures, aimed at a broad audience. And this way the ICTP community sort of comes to know about the really exciting latest development in the, in a broad field of science. And they are usually organized. They're always organized around the birthday of Abdu Salam, which is on the 29th of January. This year it falls on Saturday. So the lectures will take place on the 27th, 28th and 31st. And we have had in the past in the last ten years, it has been a tradition at ICTP. Very illustrious scientists have lectured in the series. And I'm particularly happy this year. It's a pleasure to have with us Alessandra Bonanno. She's a theoretical physicist and director of the Max Planck Institute for Gravitational Physics, the Albert Einstein Institute in Boston. And this association with Albert Einstein is particularly appropriate given the work that she does, which is in the field of gravitational waves. I would like to welcome all the diploma students. You'll be, you know, you would have liked to have this event fully in person, but within the constraints we are trying to have it as, as much in person as possible as an hybrid event. And it's very nice to see all the new diploma students joining here. Alessandra, I don't know if you can see them, but... Yeah, no, I can see that. Okay. Hello. And also some of the faculty who are joining in person in the Buddhist lecture hall. I would like to thank the Kuwait Foundation for the advancement of sciences, KFAS, for their continued and very generous support of ICTP. I think they have been funding this activity for and many other initiatives of ICTP for many years. And we are very grateful to their continued support. So let me say a few words about Alessandra. She studied theoretical physics in PISA and held faculty positions in Paris and University of Maryland, where she was a full professor since 2010. She's a principal investigator of the LIGO scientific collaboration, which, as you know, has the major experiment for detection of gravitational waves. And for her pioneering contributions to LIGO and Virgo discovery, she was awarded several prizes, including the 2018 Gottfried-William Leibniz Prize, the most prestigious research prize in Germany, the Galileo-Galileo Medal in 2021, and in particular, ICTP's 2021 Dirac Medal, and more recently, the 2021 Balzan Prize. So congratulations to our speaker today. And she's a member of the German National Academy of Sciences, Leopoldina, of the U.S. National Academy of Sciences, and so on. The list is long. She's a fellow of International Society on General Relativity and Gabitation, American Physical Society, and so on. So, and I'm really looking forward to her lectures today. She has a, of course, she has an Italian connection, but she also has an ICTP connection. She has been to ICTP in the summer of 2006 as a lecturer in the summer school in cosmology and astroparticle physics, a workshop in non-Gaussian studies in cosmology. And we look forward to, I hope, that she's able to come for the Dirac Medal ceremony in this year, later in summer in 2021. So let me say a few words. I mean, I am also a theoretical physicist working on gravity, but maybe more towards quantum aspects of gravity. But the Dirac Medal of 2021 and the work of Alessandra is that this was the theoretical work which was essential for interpreting the observations from LIGO and Virgo, which, as you know, is an unusually subtle experiment for detecting gravitational waves coming from really billions of years ago, with very extreme precision, almost unheard of precision. And together, this theory and experiment, I think they provide really an impressive check of the accuracy of Einstein General Theory of Relativity. And I think it's really a marvelous tribute to the remarkable power of our understanding, theoretical understanding of nature, that we are able to say something so precisely about something which happened a billion years ago. And this is all based on Einstein's General Theory of Relativity created 100 years ago, not long ago on the cosmological scale, and it's, as has been observed, I mean, that it really opens a new eye onto the universe very much like with Galileo's telescope 400 years ago, we are able to sort of see things that we could not see before. And so it's really a very fascinating and exciting field that's only going to grow, and therefore it's appropriate for all the young scientists training at ICTP to really know this very exciting field. Usually these lectures are three lectures. The first lecture is to set the overall stage and it gradually becomes more technical and more demanding. So she will tell you about how the lectures are organized, but I think the idea has to start with a global view of the field and then go more towards the most recent excitements in the field. So there will be a question and answer session which will be moderated by my colleague, Professor Paolo Criminelli who is, as you know, is the head of the high energy and cosmology section. And this we will do after every lecture and these talks will be live streamed on ICTP's website. And as you know, there will be a special session with the students, usually we hold it in person here, really to make it possible for the students to interact with the leading scientists on a one-on-one basis and really ask questions about whatever is that defined exciting in that colloquium. And today you will have that opportunity on Zoom after this lecture. So thank you and welcome. And I look forward to your talk, Alessandro. Please, the floor is yours. Yes, let me first share. Sorry, I'm starting from the first slide. Okay, so first of all, I would like to thank you for the introduction and also for having me here today. I'm delighted and also honored to be the Abdul Salam Lecture Series this year. Very sorry not to be there. And I hope to be at ICTP soon, in fact, very likely in July. So if you remember in 2015, a bit more than six years ago, the LIGO and VIEGO collaboration observed the first collision of two black holes which produced a burst of gravitational waves, which is represented here on the left in the still picture of the simulation that we did at the time. Now in this first lecture, which will be more general, I will introduce what are gravitational waves, how they are produced and observed, which unique information they bring to us from the dark and deep universe and what we can learn from them. And also what, which kind of outstanding questions in cosmology, in fundamental physics, the field of gravitational wave astronomy promises to address in the future. We will see this also toward the end of my lecture. So let's start with contrasting Newtonian gravity, which I think perhaps everybody here in the room is familiar with, with Einstein's theory of generativity. As we learn in classical mechanics, Newtonian gravity is based in time, do not depend on the presence of matter or energy that is present, and time is absolute. It flows at the same rate everywhere and always. And this concept changed in 1915 with the introduction by Albert Einstein on the theory of generativity, and this time is, on the other hand, dynamic and elastic. And it can influence, it can be influenced by the distribution of mass and energy that is present. So we have a geometric, we say geometric gravity. It's basically gravity can be interpreted as the effect of curvature in the geometry of spacetime. This is the usual picture that we show where you can interpret and understand the motion of the Earth around the Sun as due to the curvature in the spacetime produced by the mass of the Sun. Now, in this gravity theory in which that can be elastic and dynamic is not surprising to think that there are perturbations that can propagate the gravitational waves and Einstein predicted the waves in the first paper in 1916 followed immediately after two years with another actually publication. And if you have a distribution of mass that deforms the spacetime, this deformation can propagate at the speed of light away from the source and they oscillate reflecting the variation in time of the source that has produced the waves. So sometimes we call them ripples in the fabric of spacetime. This is another still picture of the simulation of two black holes going around each other. I don't know if you can see them very well and you see here the patterns of the waves going away from the source. Now, as in electromagnetism, the waves are transversal to the direction of propagation and they come with two polarization that we call the plus and the cross polarization. Now, gravity among the fundamental forces in nature is the weakest and in fact the waves are very weak, unfortunately, and we need in order to upset them from the space, from the universe, we need objects that are very compact, that move at very high speed, very compact so that when they move at very high speed they are not disrupted. And so we need actually the most promising sources are black holes and neutron stars. So first of all, what are black holes? And what is the role that they play in the universe? So black holes are just made of workspace time, no matter, and they are produced by the collapse of massive stars. And let's say it starts with a mass larger than 10, 15 solar masses. But they can also be produced actually in the very early universe in over dense regions. In this case, they are called primordial black holes. And I think you are familiar with the fact that a black hole just from the name cannot emit light. There is a region from which light cannot escape. In fact, we generally associate the radius of the black hole with what we call the horizon. And just to give you an idea, if you take a black hole which has a mass of 10 solar masses, the radius of your horizon will be 30 kilometers. And you can contrast this with the radius of the sun, which is much larger, 700,000 kilometers. So you put basically a mass in a much, much smaller region of the sun. That's why it's very compact, we say. And the gravitational pull is so strong that in fact it can distort also light that comes from galaxies around. It can distort the geometry around. If the black hole is rotating, it will also twist and bend the geometry around. But besides that, what is also quite amazing is that the black holes, the astrophysical black holes actually are already described by two numbers. The mass and the intrinsic rotation that we also call the spin. And this is quite interesting because you can contrast this with objects, even human beings, which we have described by so many different parameters. But the black holes only two. So sometimes we say they are the simplest objects in nature for this reason. But nevertheless, they really play a very important role in the universe because of their relationship with the galaxy, the interaction through the gas with the galaxy and the other astrophysical objects in the galaxy. And that as a consequence also influence the way in which the structure grows on also large scales. Moreover, black holes, they increase their masses during the revolution over cosmic time. We think through mainly two ways, through accretion of gas and also through mergers. So this is a merger tree where just to represent the fact that you can have two black holes at the center, for example, of galaxy like ours in one case, not in the other, then at some point they merge and you have another merger and so forth up to the end here. Okay, now how do we observe black holes? The first actually candidate of a black hole was discovered in the 60s, although studied more in the 70s, Cygnus X1 was actually an X-ray source and in a binary with a companion, a super giant star. And in fact, today I think still today the mass of these black holes is around 915 solar masses. I'm sure you are familiar with the fact that there is a black hole at the center of our galaxy of a mass of 4 million solar masses and we discovered it tracking the orbit of stars around, as you can see in this animation here, in particular the star S2 or S02. Recently, a few years ago, the event horizon telescope took a picture of a black hole in Messier 87 galaxy and of course we can also discover black holes through gravitational waves in a binary system. And sometimes we say that, you know, when black holes collide, space time rings, as you can see also in this other animation and if the black holes are merging in vacuum they don't have any more gas or around them, which is the case for the black holes that we are discovering with LIGO in Biogo, then no electromagnetic telescope will ever see the events and so we can discover these only through gravitational waves. Okay, so before discussing the gravitational wave astronomy I want to make a parallel. So in electromagnetic astronomy as also we just heard a few minutes ago, 400 years ago Galileo started this electromagnetic astronomy with a telescope and since then we have observed remarkable discoveries also through the fact that the electromagnetic spectrum from the beginning Galileo opened the optical band but then since then many more bandwidth have been discovered. We have seen objects in gamma, x-ray, infrared, radio, etc. And what is important is that if you look at the universe in different bandwidth you can discover new objects even the same galaxy as shown in this plot here Centurus A galaxy can be seen, we can discover new aspects and properties of it by observing it in different bandwidth. In gravitational wave astronomy the gravitational waves as we will see also more in a moment are produced by the coherent, we say sometimes coherent bulk motion of huge amount of mass which accelerate and the spectrum that we expect from gravitational waves is also very broad. So currently we have opened this bandwidth in the kilohertz between 10 hertz, 20 hertz and the kilohertz with LIGO and VEPO detectors. We also are observing gravitational waves through pulsar coming array, pulsars, gravitational wave that pass between the pulsar and the earth and also very low frequency through the polarization we would like to detect them through the polarization on the cosmic microwave background radiation. Now, the lecture will focus mainly on binary system although today at the end I also will mention few other sources. But when you think about the wavelength of the gravitational waves or the frequency because the gravitational wave waveform or the gravitational wave let's say frequency it's a multiple of the orbital frequency. When you change the frequency when you observe a different bandwidth means that you are looking at either you are observing the binary after different separations or different time in their evolution or you are observing the black holes or neutron stars with different masses as we will see. Moreover, besides binaries these different, the fact that we have access we have access to different wavelengths allows to probe different cataclysmic phenomena in the universe that are dominated by gravity including the sweet changes in the gravitational field during the cosmic expansion especially at the very beginning during the so-called cosmic inflation. So with gravitational waves we are probing astrophysical objects and gravity at different scales and sometimes we see these spots that shows the evolution of the universe from the beginning to the end and we think about electromagnetic astronomy actually with gravitational waves we can probe all these phenomena these times in fact even going much more earlier than what the cosmic wave the gravitational radiation can do because gravitational waves can be produced from the very beginning and they pass they are not absorbed so we can actually peer back to the very early moments of the formation of the universe but also the formation of the first stars from that epoch we can produce gravitational waves and in fact even with future detector we can look at our galaxy at the galactic center compact object going around the Sagittarius star unfortunately in the solar system the planets do produce gravitational waves going around the sun but the frequency is too low and the signal is too thin to be observed. Okay so now what are the sources what are the mechanisms that produce gravitational waves and let's try to get some order of magnitude so the source is dominated by gravity with respect to other fundamental sources now if we take in general if we think about electromagnetism the first multiple moments that produce electromagnetic radiation is the dipole the variation of the dipole in the case of gravity and gravitational waves is actually the quadrupole so we generally talk about gravitational waves like a strain a dimensionless quantity which is proportional to the second derivative of the quadrupole this goes back to the paper of Einstein and it's inversely proportional to the distance of the source to the earth now if you think a binary system and you consider for example a neutron star at the galaxy let's say Virgo plaster in the Virgo plaster you can compute what is this number and unfortunately it's very very small it's 10 to the minus 21 and if you compute the luminosity so you take the derivative of H square it like you would do in electromagnetism you get this luminosity in gravitational waves many many order of magnitude larger than the luminosity electromagnetic radiation from the sun but this power it's emitted in particular at the very end when the two objects merge with each other so although this luminosity is you know larger or similar as I wrote of the old visible universe is still you know emitted for a very short amount of time and then another thing I wanted to say that really makes these waves unique is that the propagation through the universe from the source to us is almost unaffected by whatever the waves encounter so they are really pristine probes however I wrote almost because you will see at some point I will mention the fact that the waves gravitational waves like electromagnetic waves are also lensed are also affected by a sudden level although very small level from you know crossing galaxies and other objects in the universe now how do we detect them where we built interferometers here is the LIGO and the VILGO in Italy and these are four kilometer interferometers and the key idea is that we use the way in which the waves interact with free falling particles so here is represented like a ring gravitational waves that impinges on the screen of the ring and the waves put in motion the ring with a particular pattern and so what we look at is the variation in the proper length between the mirrors that hung by wire at the extremity of the cavity and we want to basically observe differences in travel time between these two length now what we are measuring is a very very tiny variation in the length so if you want to detect something of the order of 10 to the minus 21 you would need to measure displacements of the order of 10 to the minus 16 centimeters so the technology took years and decades to develop but it's available and now these interferometers are working ok so I mentioned the way it brings information about the source they are pristine probes but they are fingerprints of the source and here is just an animation that shows some of the black holes detected by LIGO and VILGO and this is a binary Newton star and I want to explain a moment this formula here the Newtonian gravity that was the problem in Newtonian gravity in classical mechanics I'm sure you have learned that the orbital frequency is inversely proportional with this power to the orbital separation in the binary and just the total mass in the binary gravitational wave frequency so this is just a Kepler law ok the gravitational wave frequency is a multiple like twice the orbital frequency and what happens is that at some point the two objects interact with each other and that depends on the total mass in the binary so for a binary Newton star which is still sweeping because the mass of the Newton star it's around 1.4 not more than 2 to 0.1 for a mass this this frequency is in the kilo hertz and the bandwidth of the vector starts at 20 amps so the signal is very long and the black hole at the mass larger than the Newton star the black hole that we are observing at 30, 40 for the masses it will merge at lower frequency and that's why the signal is shorter in order to expect information from the signal we use sophisticated techniques like Marco Ciemontetalo Bayesian analysis but I want just to give you an idea of how the information is imprinted in the waveform so the binary loses energy because of the emission of gravitational waves so it shrinks in time the frequency increases by the frequency evolution we infer the masses from the amplitude and the masses we can obtain the distance of the source to the earth from the time of arrival the amplitude and the face of the waveform at the vector location we infer the sky location where the source was in the sky we see modulations in the amplitude and also in the face and actually extract information on whether the two objects were on a circular orbit or where an eccentric orbit whether the two compact objects had intrinsic rotation or not and finally we can compare this waveform with a theory of gravity alternative to general relativity we can prove gravity we can conclude whether there is general relativity or something else I want to also highlight the fact that it's very important to understand the way in which we detect the signals and why it's important to have high precision waveform models and extract all this information so we use much filtering or signal processing so we basically have a template bank of pre-determined pre-computed waveforms and we correlate the data with the templates in the template bank and we look at when the correlation or we compute the signal to noise ratio when the signal to noise ratio becomes larger than a certain pressure that is fixed by you know how well we we understand the noise in the detector this is shown in this animation here so this is the correlation of signal to noise ratio you see the template is light now it sees the signal it can correlate with the signal here and you see a spike in the signal to noise ratio so with the LIGO and VUGO detectors sorry this is now covered we use actually in the template bank of the order of 100,000 of signals for Bayesian analysis of the order of a medium so in order to produce all these waveform models we need to produce them very quickly and we need actually to solve this problem using the Einstein theory of generativity and now there are basically two tools that are at our disposal we call them analytical numerical so I want to make an analogy so to talk about analytical and numerical so in Newtonian gravity game something you are familiar with we have actually an exact solution a closed form solution for the orbit which I remind you I wrote here but we can also plot numerically the solution we have an ellipse here this is the sun and the planet unfortunately in generativity it is much more complicated theory we don't have a closed form solution for the orbit moreover the ellipse not only actually rotate as you can see here but also shrink in time because of the emission of gravitational waves nevertheless we can try to find an approximate analytic solution for the orbit and this is what we are after and so we work together with between analytical and numerical so analytical means paper and pencil although it is a bit more complicated and numerical relativity solve the problem on supercomputers just to give you an idea even if you would say supercomputer would be of course the slow but accurate best way of doing it is very time consuming to produce even 15-20 orbital cycles of two black holes going around each other it might take one month even more depending on the mass ratio the spin etc now in a little bit more sophisticated way what we want to do is that we have to solve the two body problem in generativity I wrote here the Einstein equation in full glory so this is the energy momentum tensor speed of light this is the tensor that depends on the metric and its derivatives it's a non-linear dependence on the metric and so these equations are complicated to solve and as I said we use these two methods and we take advantage very much on the synergy between these two approaches and I want to highlight although this will be nearly the topic of tomorrow lecture which focuses on the modeling we have post Newtonian theory so we can expand the Einstein equation with the power of the velocity in the binary on the speed of light which because of the viral theorem is also intertwined with its function with the strength of gravity and the post Newtonian theory in this picture here this says that it's valid for any mass ratio in the binary but when the two objects are very close to each other because the velocity becomes almost the speed of light you can expand the Einstein equation in power of g, this is called the post Newtonian expansion which is valid for still a large separation but you don't do an expansion in the velocity so it's also for fast motion or you can expand the Einstein equation in the mass ratio so for some sources one body is much smaller than the other so you can do an expansion in the mass ratio and as I said that you have also numerical relativity that can give you the solution in principle with very high accuracy and then what you can do is that you put together these approaches, these analytical approaches approaches in the federal body theory or using phenomenological feats and then you calibrate this with numerical relativity we will see this more tomorrow today I'm not going to focus on this but at the end of the day you can build a very accurate way for models ok so now you remember in 150914 there was the first gravitational wave the first gravitational wave was detected this is the famous plot on the left the confidence the physical confidence was over five sigma which generally we use to claim a detection, a discovery in physics and I'm sure you remember the sound of the chirp which I just reproduced here there were the two amazing first girlfriends one by the lego I'll let you hear the sound by the lego scientific collaboration and the other from the Virgo collaboration there was in 2070 the Nobel prize that was the event twice by which and torn now from the point of view of what we have learned from that source before telling you what we have done since then I wanted to again show you in a more in a simple way how we extract the information the parameters so in this again animation here in blue it's the signal gravitational wave 150914 and in orange it's a template that we try to match against the data and what you see here you can see how this number change this number change because now you are trying to change the parameters in your template the distance the total mass and at some point this will match quite well with the signal and that will give you the parameters of course as I said we do Bayesian analysis in fact to be a little bit more sophisticated when you do a Bayesian analysis on the entire parameter space of the waveform which for binary black wall is 15 dimensional because you have the masses the spins, each spin is a vector the distance all the angles that describe the orientation of the binary with respect to this vector then you can marginalize on all the parameters and you get except the masses and 1 and 2 so you get posterior distributions with 90% credible regions and for 150914 using two different models here we end up concluding that this was the distance these were the masses we could even reconstruct the mass after the merger including the intrinsic rotation of the black wall that formed after merger now this was very good well since then more than 6 years ago LIGO and VILGO have discovered have observed 90 cosmic collisions actually including also the first one and this is represented in full glory by this plot here that shows all the observation in blue by LIGO and VILGO collaboration also recently CAGRA this is the mass of the compact object in solar masses and you can so the way of looking at this is that you have one object the other object in the binary after merger and this is the mass of the object that formed after merger you can appreciate the variety in the distribution of masses going up to 100 in solar masses also LIGO and VILGO discovered two binary neutron stars the neutron star here represented in orange and even a couple of neutron star black holes and what is also interesting to notice in this plot are the dots here which are the binary neutron star that we have discovered as pulsars with electromagnetic radiation and in red the black holes that we have discovered in our galaxy through X-rays so this would be similar to signals X1 that I described at the very beginning of the presentation you can see that typically actually the black holes that we see in X-rays have a mass smaller what we have seen with LIGO and VILGO so now I would like to spend the second half of this lecture trying to address some of these questions we are going to go in more details especially in the lecture on Monday but so the important question we want to answer now that we have a statistical distribution of black holes and neutron star binaries how they form, how they form binaries in which kind of environment they live also we have discovered binaries with neutron stars so we want to know how matter behaves under very extreme density which is the case of neutron stars can that matter make compact objects moreover with gravitational waves can we actually address outstanding questions related to highly energetic phenomena in our universe that are puzzled and we want to try to shed light on what these phenomena are and finally can we discover new fundamental particles with gravitational waves or even in fact the cosmological model of our universe so I want to give some examples now of the sources that we have detected so that you can see which kind of information we have extracted and I want to start in 1908-14 we label the observation with the year 2019, the month and the day so this one we consider a binary with a puzzling companion why? because this binary we extracted the mass of the primary object had a mass 23 times the mass of the sun so certainly a black hole but the smaller object had a mass of 2.6 times the mass of the sun and typically we expect neutral start to have a mass up to 2.1 solar masses 2.2 and the black hole also maybe not less than 3 or maybe 5 so this poses some challenge in understanding what this object is now this binary has also a very large mass ratio because you can see 23.6 almost 10 the mass ratio of the binary with a symmetry you can actually have a much richer gravitational wave radiation and this is shown in this simulation here that we did on the right this visualization where you see for this event the black hole and the two black holes going around each other this is the quadrupole radiation 9 seconds before merger and then the octopolar radiation L equal 3 M equal 3 and now when you go 4 seconds before merger the higher modes the higher harmonics become important this is the L equal 4 M equal 4 and finally very close to merger we have also some imprints due to the L equal 5 M equal 5 now if you want to be a little bit more quantitative as species we do this is just the last part of the visualization of course we have to do some vision analysis and we extract for example in this plot the mass of the secondary of the smaller object with our vision analysis and what I want to emphasize here again using the different waveform model from two families P so if you take a model without HM which means higher harmonics and P precession of the spin you can see that if you don't add harmonics and precession the posterior distribution are broader once you add precession in the higher harmonic you can get a tighter posterior distribution which means you can nail down the mass of the secondary more precisely and this is what's important because we wanted to understand the mass of the smaller object because as I said it's between a black hole and a neutron star and I appreciate now the importance of the model in here now another example I wanted to give on the left it's the first binary black hole that we discovered which had asymmetry in the masses around four and this is a numerical relativism of that event again here you can see the two black holes going around each other the pattern you know the waves going out and now if we zoom in okay the arrow on the black hole because we could observe also the spin, measure the spin of the black hole of the order of 40% of the possible maximum value allowed by general relativity and finally another example I wanted to give is the largest mass binary that Ligand Virgo had discovered until now the animation on the right, the visualization is a numerical relativism duration this was a source that lasted for a fraction of a second in the detectors and the interest of this source is that the mass of the two black holes is quite large the final black hole actually has a mass of 150 solar masses but the mass of the primary black hole is between 80 and 90 solar masses which poses challenges in theoretical astrophysics because of the phenomena of supernova pair instability we should not actually see from cold collapse black holes with mass between 60 and 120 solar masses so this is something also to be understood okay so other things that we are doing with this observation is of course test of general relativity and with Ligand Virgo we can do this test in an unexplored region something that is not available in the solar system or with experiment like gravity that is looking at the galactic center or with binary pulsars because here we are having the space time becoming dynamically in the highly velocity when the two black holes merge this is again another simulation of another event that was discovered by Ligand Virgo just to show you the fact that you have this dynamical space time now in fact one thing that you can do is that this event was discovered actually in the first one in 1226 you can do a an analysis to extract the parameters for this event using your waveform models then you use the parameter to do a numerical relativity simulation as I showed here and then you can build a plot like this where you you have the reconstructed signal using the waveform models and in red you have the numerical relativity simulation and you can see that the red is always within 90% critical region which are here displayed in gray which means in a qualitative way that actually this gravitational signal very closely matches the exact solution from Einstein equation so two core black holes going around each other and merging but we do many more tests the Ligand Virgo collaboration does many more tests and I want to mention actually one of them which is the quasi-normal models so you see here again the same simulation as before but just zooming at the end when the two black holes merge you form a new black hole and the black hole so I want to do an analogy you can have spectral lines that identify chemical elements you can identify the hydrogen neon mberidium well it turns out that something similar you can do with black holes because each black hole if it is perturbed or forms after the merger it brings the spacetime emitting quasi-normal modes and this quasi-normal mode only depends on the black hole mass and spin for astrophysical black holes and you can try to measure these black holes and this in fact has been done by the Ligand Virgo collaboration again in a more quantitative way you can do Bayesian analysis this is a plot of the posterior distribution of the fractional deviation from general relativity of the frequency and the decay time of the dominant mode because you have different modes with different decay time this will be the dominant mode for two gravitational wave signals you see here the posterior distribution they encompass 0, 0 will be the gr so until now we have found consistency between the dominant quasi-normal mode for a black hole in general relativity for a black hole in care ok now I want to mention one thing that besides looking at black holes which have a mass larger than 5 you know 2, 5, 10, 50 solar masses the Ligand Virgo collaboration has also done a search in a very interesting part of the parameter space when the mass of the component objects ranges between 2, 1, so let's say sub-solar masses in particular in this case I will show you the results for a search that assume no spins for the black holes because actually the template bank in this case is very, very big very quickly because you have many, many cycles so already in this case you have about 1 million of templates and why this range is interesting because we don't expect black holes coming from the collapse of a star in this mass range so if Ligand Virgo discover black holes in this mass range they will come from over density fluctuations in the universe so this will be premordial black holes so I want to show you here the most recent result from the Ligand Virgo collaboration this is the upper limit of the latest run actually the first 6 months they run the fraction of that matter in premordial black holes if they had a mass in this range here okay so now let me focus in the last 20 minutes on a couple more topics so the first one I want to now consider binary system that contain neutron stars so neutron stars are very interesting also component objects they have a mass between two solar masses the radius let's say between 9 and 15 and a question of state of neutron stars in particular in the inner core is actually not known now we are starting putting some bounds but we really don't know what the neutron star is within the inner core where the neutron you don't have any more description in terms of because of the pressure the identity and pressure you talk directly you look directly at the components of the neutron star so we don't know for example if in the inner core there are hyperons py condensate, py condensate if there are even phase transitions etc now I want just to give you an idea putting it in context so this is Berlin this is Potsdam so if you take a neutron star mass or one point solar masses and you consider the size of a black hole this will be the black hole the neutron star is a little bit less compact than a black hole but depending on the equation of state you could have a neutron star with a radius of 8 km or with a radius of 15 km so how can we probe the neutron star we can do it with a binary neutron star with a neutron star composed of two neutron stars or with a binary where you have a black hole and a neutron star the neutron star is tidally disrupted at the very end there is a parameter that is described by these deformations which is called the tidal deformability parameter which is zero for black holes and for neutron star is not zero and it's that parameter that we want to measure so in idea if you take a waveform from a binary black hole and the two neutron stars the waveform if the two objects have equal masses so the binary black holes and the binary neutron star the waveform will be identical when the two objects are very far from each other but as they approach each other the waveform becomes different even before merger of course the merger will be also different and we want basically to measure these differences and understand the question of state so I have here just one plot we will come back to this in the next lecture but I want just to give an idea of the fact that already the measurement of the observation of the first binary neutron star has allowed to put some bounds on this plot this is the pressure toward density this is nuclear density twice nuclear density which is actually inside the neutron star you have density that are above twice nuclear density and I also wanted to say the radius for example of the neutron star has been constrained at the level of around 12 kilometers with these first measurements observations but of course with binary neutron star perhaps the very well known result has been the opening of the multimessenger astronomy that happened in 2017 you might remember so this is the track of the gravitational wave signal from the binary neutron star 17 zero and 17 and soon after the merger around two seconds after the merger we could observe actually the Fermi satellite observed a short gamma reverse and thanks to the Virgo detector together with the LIGO detector could localize the source in the sky so well that optical telescopes were pointed and they could actually observe the so-called Kironova signal so here you see basically the telescope that observed this little spot here which corresponding to this event which was not present at 20 days before where a picture was taken so this is the simulation that we did at the time of this event choosing some of the parameters that came out from the vision analysis of the two neutron stars going around each other the two neutron stars expelled material which is decay very rapidly you see here the material that give rise to the Kironova signal so we had the gravitational wave the gamma rays the Kironova which was seen in the ultraviolet optical infrared and this event after weeks and months actually I showed up also years also produce radio waves that were observed and another important consequence of this observation has been actually a very interesting test by comparing the observation of the gravitational waves with the electromagnetic radiation a very tight constraint on the speed of the gravitational waves was also established ok, another important thing from this event that you might have heard well there was there is still actually people are trying to understand how heavy elements are produced in the universe we understand more light elements etc but for the high elements could they come from supernova core collapse or binary neutron star mergers well this observation certainly pointed out that elements like the gold thorium, uranium and plutonium are likely coming from the merger of neutron stars so this was also a quite important consequence of this observation together with all the other multi-messenger observations in electromagnetic radiation ok quite amazingly the latest run from the LIGO and VIGO collaboration has also observed for the first time a so-called mixed binary now we have a neutron star and a black hole this was 210115 you see here a numerical relativity simulation its visualization the neutron star goes around the black hole and then is eaten swallowed so because of the parameters of this binary black hole the neutron star we believe was not entirely disrupted by the black hole that was just as I said swallowed all and this means that no accretion disk was formed and no electromagnetic radiation could have been produced although I mean this is still this is what we believe unfortunately this event was not reconstructed very well in the sky so it's not that optical telescopes could be you know they were pointed but you had a huge area in the sky to look for but in the future we will discover more neutron star black holes with other parameters depending on the spin of the black hole and the mass ratio the neutron star can be disrupted and form a disk and this is a beautiful still picture from a simulation in the case in which this happens and we hope to see this in the future okay so another important thing that we can do with gravitational waves and we have done in the case in which we have a binary neutron star or a neutron star black hole is to do cosmography so gravitational complicated binaries are like standard candles or let's say sirens so they are actually they are sources so what is a standard candle so let me say first this these are astrophysical sources whose distance from the earth can be inferred from the luminosity so we can extract basically the distance by observing the gravitational wave directly and if we know the distance through the the Hubble the Hubble flow velocity is related to the distance of the source through the Hubble constant so if we can actually determine the Hubble flow velocity we can and then we know the distance we can extract the Hubble constant and through the identification of the host galaxy that I was showing you before with the Theronova we could actually obtain the Hubble flow velocity and we could extract like when we go could extract the Hubble constant the posterior distribution is shown here at one sigma and two sigma and you can see here now you can contrast with the very precise observation with Planck and the supernovae so the the uncertainty is not so good at the moment but this will improve in the future so now let me say another thing that we can do like a vehicle is already doing but we don't have yet a detection which is gravitational lensing I mentioned this before so in the same way in which light can be lensed and this is an example if you have here a quesar and a galaxy here and you are observing you can have multiple images the same thing can happen with gravitational waves so gravitational waves can be lensed by intervening objects and the magnification produce an overall amplification of the gravitational waves and quite interestingly for gravitational waves you don't have multiple images but you have repeated signal in the sense the same source produce a signal that you observe today now and maybe it might have another signal from the same source in a few days or the same day or maybe a week in the year produced by the same source so until now the light of new collaboration has not been able to measure the splenzy but this could be done in the future by the way I had still 8 minutes is that correct? okay I still have a few slides I think I should be okay so now I want to switch to a couple more sources before concluding and one of them is the fact that from the core collapse of massive stars like supernova explosion we can produce gravitational waves in this case the signal is very short it's like a burst and you can hear something like this very quick there are searches to look for this kind of signals until now have not been discovered with gravitational waves we can have also gravitational waves produced by pulsars which are highly magnetized neutron star that rotates and if they have some irregularities on the crust some mountains with a height of 1 centimeter or less they can produce continuous periodic gravitational wave and you can hear something like this okay so these signals are there all the time so in fact you gain by accumulating doing the observation for very long periods and finally you can have gravitational wave from the universe from inflation for example and in this case it's more a kind of random noise as you hear here now in order to be a little bit more quantitative I want to give you two examples of these searches the first one concerns non-pulsars so the live video collaboration has recently released a paper just in December of an analysis of these periodic signal continuous ones during the last run and what you see here is the sensitivity of Virgo and the two Legos during the run and let's focus on this particular upper limit here so this is the crab pulsar so the crab pulsar is supposed to emit gravitational waves at the 60 Fs which is this frequency here so what you see here what is that so if you have a pulsar like the crab and it's emitting gravitational waves it's losing energy because of that and the frequency of rotation decreases a little bit now the major energy loss in a pulsar like the crab is not through gravitational waves it's through a electromagnetic radiation but if you assume that all that loss of energy comes from gravitational waves you have this limit here it's called a spin down limit today like of Virgo can put a bound much lower by more than one order of magnitude with respect to the spin down limit which means as you go below the spin down limit you are in a realistic situation because it means that you have access to the loss of energy to gravitational waves and this has been done also for other 19 actually around 19 pulsars these are all now known pulsars and the other example I wanted to give very important looking for gravitational wave signals cosmological ones is the upper bound on the energy density in gravitational waves that the live and video collaboration I put recently this was last year using the third run so this the monopole part of the stochastic background of gravitational waves you can parameterize in terms of amplitude and the tilt alpha and you see here the analysis again a Bayesian analysis this result is obtained by assuming the alpha zero so a flat spectrum then to the minus nine is interesting that you may want to keep in mind that cosmic inflation the model with single inflation single model in cosmic inflation so the I think I got a little bit wrong there you will get an omega of the order of 10 to the minus 14 at the frequency of live and video so we have many order of magnitude above but in the future this can be improved and also going to space okay so let me now conclude with a few slides about the future so the landscape in 2030 so the third run by the live and video collaboration concluded last year live and video are going to an upgrade that will end at the end of this year with the fourth run reaching this range to look for observe a binary neutron stars so at the end of this year we will go through the fourth run then there will be a fifth run the fourth run will also include Kagura by the way the Japanese detector the fifth run that will start sometime 2025-2026 will also include hopefully LIGO India and going to the future we will see many more events even during the fourth run we expect three binary black hole coalescence per week which is quite a lot and also binary neutron stars and neutron star black holes now if we think even the next decade will be even more interesting I go back to this plot here so we are going to open new frequency then there will be a detector in space launched in 2036 which is called VISA which is primary from the European Space Agency but with large participation from NASA you see here the animation the constellation going around the sun training the earth and finally we will have hopefully new facility on the ground the Einstein Telescope in Europe and the Cosmic Explorer that will broaden the frequency band on the earth going more at lower frequency up to around one hertz I cannot not mention the fact that since there are many young people here in the audience and you can be the players in 2050 so last year the director of science the science program committee announced the next science program of ESA which is called Voyage 2050 which was agreed on the recommendation from the senior committee and with three scientific themes so one is the moons of giant planets temperate exoplanets to the Milky Way the third one is called the new physical probes of the early universe recommending two possible ways of addressing questions about the early universe one is through gravitational waves and the other is through microwave spectrometers to explore the early universe so there will be a selection and by the way this is looking this scientific theme to red sheets larger than so focusing in this part of the evolution of our universe so there will be a selection in a few years from now if the gravitational wave will be selected it will open two new one actually not both of them either the DC hertz frequency band or the micro hertz so as you can see we are hopefully opening more and more of the bandwidth in the very large spectrum of gravitational wave so I conclude here thanking my group a lot of work that I presented was also based on what you know with based on what they have done and I want to thank you stay tuned I also want to say that the material that I presented is also work supported by the LIGO laboratory several agencies the European gravitational wave observatory many national agencies and overall the work of the LIGO collaboration which are many many members so I stop here and I take questions I guess thank you very much thank you very much Alessandra I don't know if you heard the clapping but yes I because I actually end up not seeing anybody so should I actually keep my yes I am still sharing but I'm a little bit confused as you want there will be a few questions so maybe maybe you can stop sharing yeah I don't know how to I wanted to go back to see something because I'm talking against the screen and I wanted to put back the you know that I can see the room and I do remember how to do that now please stop sharing maybe I should yeah you're right maybe I should oh okay okay hi ciao Paolo maybe I can also now go back and I think it will appear now the maybe no actually not so then I prefer to stop sharing I don't think maybe if I need a slide I will open up but I prefer to see some people sounds good okay there are two questions from zoom but maybe we start from some questions from the audience by the way tomorrow the students some of the students here they have the GR exam so I think it's perfect there are waves so it is a spoiler so so questions maybe I can start with some questions from zoom so one question is can two gravitational waves produce in two different events interfere with one another I think you said something about this and if yes how do you distinguish between the two and is it possible to know which wave is produced by which event yeah okay so first of all like we will go observations for the kind of events we are seeing you know targeting this binary black hole binary useful stock at the rate we do it today it will be very difficult to see two events at the same time I think we had I was saying we called the waveform with a certain name at some point we had to add the time of the day so the minutes hours because in the same day we saw two events but not at the same time you see we don't have so many events that we would have that problem of overlapping signals but for example with Lisa and also with ground based detectors of next generation we could have overlapping signals in the same you know at the same time during the run and so people are developing you know numeric data analysis tools to be able to subtract events signals in order to then analyze what is below okay now it could happen you know I mentioned the lensing so the lensing you could have a repeated signal maybe the same day what you have to look at are signals that have the same masses the same parameter so two lens events for example you could recognize them if the parameters are exactly the same but they happen at different times of course this is not tricky because it's a bit tricky because you have also an uncertainty in the observation measurement of the parameters but that's a way to recognize a lens then then there is another question how practical are gravitational wave measurements across different wavelengths to study the gravitational wave background and to verify existing cosmological models such as various types of inflationary models or cyclic cosmology yeah that's an interesting question because for example in the for the cosmic inflationary background they want to use you know cosmic inflation so slow roll inflation I call that word I don't remember it before slow roll inflation would predict a background which is in omega gravitational waves basically flat starting from 10 to the minus 16 up to the frequency of the light going to be able but if you have some different rock in the evolution of the universe different from radiation and matter non-dominated by radiation and matter with stiff equation of states you could change the slope of the spectrum in some cases you can have a blue spectrum instead of being the flat or slightly red so if we could have access gravitational wave detectors at different frequencies we could actually shed light on the fact that you know if the background was the same everywhere or had different slopes etc so we could reconstruct different epochs but I also have to say from the early universe cosmology different backgrounds have picked a different frequency so you could have first order phase transition produced by model beyond the standard model of particle that is picking in the mid-air region or in the desi-air region or you could have gravitational wave spectrum due to diffused transition that will be even more at lower frequency than the mid-air so depending on the frequency band you can observe also different kinds of cosmological backgrounds and also astrophysical ones Thanks Any question here from the audience after this the diploma students will have also a chance to talk with Alessandra privately I'd say without Hello I'm Min Hazel Gibria from our system physics My question is can gravitational wave affect cloud system and if it is yes then how can it affect yeah I didn't actually hear they can affect system cloud cloud the systems but what do you mean cloud do you mean in the atmosphere oh I see really the real clouds I was thinking about more complicated well I think this will be very difficult because of the very weak gravitational field that the waves bring and so I would imagine that I mean it's true that the waves you know can move freely falling objects around but the cloud I think the cloud is dominating the force that keeps the cloud together is much stronger than what gravitational waves can do you know I think it's not going to modify the cloud because the interaction that keeps the cloud together are much stronger than what you can have with the effect of the gravitational wave that would be my answer but yeah that would be my answer I don't see how the effect is any other questions I have a question it sort of went too quickly so maybe you can you said something about the stability range of black holes 60 to 120 or something can you yes yes so yeah what happens is that people who study the collapse of stars they have this you know many years ago the theory was developed they have found that when the star collapse if you have a very massive star so to produce a black hole of 60 you need a very big star so if the star is in a certain mass range and when the star collapses you can basically trigger during the collapse because of the pressure and high heating you can produce pairs so normally you have a balance between the gravitational force that brings the time to collapse the body with the pressure imposed by the photons that tend to counteract that but at some point you can produce pairs so the gamma produce or other interaction produce E plus minus then you have a drop in the pressure so the pressure is no longer able to sustain the gravitational collapse and this phenomenon can happen very very quickly if the mass is very large of the star you have a kind of runway solution and the star explodes without leaving any remnant so you don't have any more black hole as remnant but just the star explodes so there is a mass range for which this phenomenon happens and so you cannot produce black hole based on this with a mass between 60 and 120 solar masses if they come from the collapse of the star so some people say that ok a way out to explain the sources is that this could have been black holes that come from a merger of two previous black holes so that in that case you don't have a limit to the mass but also here there are some you know it's not completely clear if you can do it, what's the rate of this events etc so it remains an open question Thank you Any other questions? There is a question here Good afternoon The first gravitational wave was detected in 2015 and from then until now there were around 90 what changes were made from 2015 to now were there improvements in the waveform models or did we improve the hardware of the detectors? Yeah, very good of course so the first run was only for three months and it detected actually two gravitational waves the first one that is very famous and the other one in December of that year the 26th of December I showed one of the simulations and you know after that there have been two other runs from LIGO and VRGO and these runs took advantage of better sensitivity so the sensitivity became better in fact I had actually let me open again because I have so you see my slide again I think I had this plot so let me show you this plot so this was the run the first one the one that made the first detection by the way this number is the distance at which we can see a binary neutron star and claiming detection so it's also a way to understand how much more sensitive the detector is so the second run you can see here a larger distance and you can see from the curve here there is an improvement in particular low frequency with respect to the first one the third run even more sensitive 130, 110 and you can see here the improvement in sensitivity by the way this is also for VRGO so VRGO joined the run starting from the second one and you can see the improvement with the blue and the green so this was certainly a reason of the improvement but also the duration of the run so the first run was also was only three months the second run lasted longer and the third run was one year and also it's not that for the entire one year you have the detectors working and having triple coincidence between them because some of them sometimes are offline so overall the network worked better over the years so you had more time of observation and better sensitivity so I think these are the two crucial things and now the interferometers are improving even more so in the next run we expect to have more events in one year that's why I said the three events per week we have a question here yeah hi Alessandro my name is Troublou from the high-energy physics session and thank you for your representation I have several questions related to your slides so it is good if you can share it again yeah let me do it the first one related to the gamma burst you showed that there are three three types of signals one from the gravitational waves one from the gamma rays ah yes I think this was one slide there's a plot of three lines so I see that at the end of yes that one so at the end of the gravitational wave peak then after that there's a peak from the gamma rays so my question is why is there such a delay in the peak of signal sorry I didn't get sorry but I didn't get the last a difference between the two peaks of the for example the gamma ray signal and the one from the gravitational wave ah why the two seconds why there is two seconds of different why there is a delay between the gravitational wave let's say peak of the luminosity and the gamma ray is this your question yes yes I believe that people explain this with the fact that so you have the two neutron stars going around each other then they collapse they very likely this object forming a black hole with a disc and then you had the production of so the disc so the black hole produce a jet and then it took kind of some time for the jet to propagate out from the material all around you know the black hole that formed after the merger this is the way in which I understood it don't work in you know gamma ray bursts but I think this is what I understood that this is a kind of delay ah in some sense the jet has to find a way to go out from the material around and I think it takes of the order of two seconds to do that this is what I think I understood ah the same question related to how can we measure there's a figure that you show we can from the wave form a signal that we can measure the frequency and the mass and the distance to from us to there so I don't understand the one that we measure the spin and actually if there's two black holes then how can we measure each spin of each black hole separately I see yes so I will explain this more I think between tomorrow and the lecture on Monday but so the wave form depends on the single spins so I'm trying to think yeah so as I said the wave form depends on 15 parameters and it depends also singularly on the spin of the primary object and the secondary one so you have s1 and s2 and these spins can be aligned with the orbital angular momentum so perpendicular to the orbital plane of the of the binary or they can be misaligned if they are misaligned they are going to recess so they are going to impart a modulation because there is the now another frequency which is the precession frequency that is imparted its present on the wave form the amplitude and the phase so if you have something like this this wave form has no precession you see that it is different from this so if you take your and you try to match with the data if the signal has precession you will obtain a better fit with the wave form with modulations with respect to this one okay now in fact we will see tomorrow or on Monday that is not very easy to disentangle the two spin we are more sensitive to a particular combination of the two spins actually which is called effective spin but this we can discuss more I think the next time but did I answer your question one last question related to the experiments so what is the main source of the noise that goes into the signals in the observation in LIGO and VEGAL yeah so there are so the main source of noise when you see the noise curve that I was showing just a minute ago so let me take in this one so there are typically three for this sensitivities that we have today because then when you improve the sensitivity there are also other sources of noise but typically at low frequency you have seismic noise and this is actually improved by using the very good seismic isolation system VEGAL use is also inverted pendulite etc to reduce the seismic noise here at low frequency in the intermediate region here you are dominated by the so called thermal noise of the mirrors and the high so there is the thermal noise on the mirrors and there is also the thermal noise of the wires at which the mirror are attached that also produce a noise and at higher frequency you have the shock noise the shock noise can be decreased by increasing the power of the laser you can bring it down but the three main noise for this detector are seismic, thermal and shock noise you got frozen for 10 seconds so maybe you can repeat the last sentence ah ok I was saying the main sources are thermal seismic noise and shock noise I don't know if you know thank you so I would propose to stop here we have time to ask other questions also in the other lectures so let's thank first of all Alessandra we are going to leave and the students will stay so please take this opportunity to ask questions not only about physics but also about suggestions, careers you can complain about the GR course also so but I understand that we have to move to another doom and also I will go out an hour from here hello thanks Alessandra see you tomorrow ok bye thanks Alessandra for a beautiful lecture and yes you do connect on another zoom for the interaction with the students ok so I go there bye bye that's alright see see see see