 So I share my screen now. Not yet. First, I will present. Not yet. OK. OK. I don't share the screen. OK. OK. So hello, everyone, and welcome once again to the Latin American Webinars in Physics. I am Joel Jones from the PUCP in Peru, and I'll be your host today. This is webinar number 55, the last one of the year. And we're having Isabel Cordero Carrion as our speaker. Issa is an assistant professor at the University of Valencia in Spain, and is a member of the Virgo Valencia Group. She finished her PhD in Valencia itself at the Department of Astronomy and Astrophysics. She later carried out host dogs at the Max Planck Institute of Astrophysics in Munich, Germany, also at the Observatory of Paris Moudon in France, and at the University of Namio and Lisch in Belgium. In 2016, she returned to Valencia and joined the Virgo Valencia Group, where she is also the coordinator of outreach and communications. So of course, today Issa shall talk about the recent observation of rotational waves, and we're very happy to have her as our speaker today. So before we begin, we remind everybody that you can be part of the discussion by writing questions and comments on the YouTube live chat system, which should be on the upper right. So I will now hand you over to Issa. So they're all yours. OK, before starting, I would like to say thank you to the organizers. It's a great pleasure for me to be here. I have a lot of friends. So let me share the screen. I also want to thank all the members of Virgo Valencia Group, but in particular, our coordinator, Professor Jose Antonio Font, because he has helped a lot in the elaboration of some of the slides. So I go to the slides number two. I will start this webinar by introducing gravitational waves. So as you know, Einstein equations of gravity can be interpreted as a geometry of a spacetime. So in Einstein equations, you have a term which denotes the curvature of a spacetime, the geometry of a spacetime, and is connected with the matter content of the spacetime. So one of the first things that actually Einstein did, and you can do also to understand the behavior of these equations, to analyze these equations, is to consider the so-called weak field approximation. So basically, in this approximation, you consider that you are far from the source that generating any modification in the metric of your spacetime. And you can basically write your metric as the flat metric, the so-called Minkowski metric, plus another term that can be viewed as a perturbation of this flat Minkowski metric. Actually, this perturbation, H mu nu, is not the right or let's say the proper quantity, but you have to define the transverse traceless quantity associated to this H tensor. This H is here nothing else than the trace of this H mu nu tensor. And once you have considered this bar H tensor, it can be viewed that the Einstein equations can be rewritten as a wave equation. So you have a wave operator, the Lambert operator here, of this quantity equals to a matter content. In the case of Einstein equations, one has to take into account the gauge variables. And also, one has to take into account the constrained equations. So once you have imposed all these degrees of freedom, the only two physical degrees of freedom remaining are the so-called polarization modes. Here, you may have seen these two polarization modes as H plus and H cross. This is nothing else than the two degrees of freedom associated to the gravitational radiation. Once you take into account the gauge degrees of freedom and the constrained equations. Basically, this polarization mode corresponds to the two possibilities of the formation of a spacetime when a gravitational wave pass. So imagine that we have a gravitational wave, which is a perturbation of this spacetime, of the metric of the spacetime that is traveling along the zeta direction, so perpendicular to our screen. The two possibilities in general relativity is the formation in the so-called plus polarization. So you have vertical and horizontal distance increasing and decreasing. And the cross polarization, which is here, which is basically a rotation of 45 degrees with respect to the previous one. In case of other theories of gravity, you can have other degrees of freedom. But in general relativity, you only have these two possible polarization modes. OK, I go to the next slide. So basically here, we can see that the gravitational waves, these perturbations of the metric of spacetime are generated by the acceleration of masses. Actually, it can be viewed that if you include only symmetric or axisymmetric acceleration of masses, you don't generate gravitational waves. You may have a tensor H mu nu, which is not 0, but it's stationary. So you don't have propagation of any kind of information. Sorry. OK, so these waves can be basically viewed as a ripple of spacetime. And they propagate at the speed of light. And basically, if you imagine a wave at the surface of a lake when you throw a stone, these waves basically modify the distance with respect to the bottom at the surface. So you can increase or decrease this distance. In the case of gravitational waves, what you increase or decrease is the distance between two test masses. So basically, you are contracting or expanding distances. The amplitude of a gravitational wave can be expressed in terms of a dimensionless quantity. I know that in physics, you like a lot of units, but coming from mathematics, it's very natural to work with a dimensionless quantity. And actually, this quantity gives you an idea of the relative measurement we have to perform to be able to do in our gravitational waves observatories. For a length L between two test masses, it can be viewed that this gravitational wave, that this relative displacement produced by a gravitational wave, is of the order of 10 to the minus 15 times energy over radius. And for an illustrative example, if we consider, for example, a gravitational wave source at the distance of the Virgo cluster and radiating the energy equivalent to a solar mass, we get a relative displacement of around 10 to the minus 21. So if we think in our detectors, Earth detectors nowadays, we have detectors of three, four kilometers, the baselines. But for example, for a 10 kilometers baseline detector, this relative displacement corresponding to h equal to 10 to the minus 21 is of the order of 10 to the minus 15 centimeters, which is the order of the order of 100 of the size of a proton. This estimate is quite optimistic. And actually, in real detections, we have to lower this quantity about two or more orders of magnitude. Sorry, I need to drink a little water sometimes. OK, so in next slide, basically, I have put an image of the three current observatories on Earth, gravitational waves observatories on Earth. Here you have a handful. This is Livingstone, both at the United States. And here, with more sunny weather, I would say, you have the one in Virgo, the European one in Italy, close to Pisa. So basically, we have seen that when a gravitational wave passes, there are two directions, perpendicular to this direction of propagation, that the distance can be larger or shorter. So this is the reason why the gravitational waves observatories have these two orthogonal large arms. The distance of these arms is restricted because of several reasons. So for example, curvature of Earth and also other sources of noise, I will comment later on this. And basically, the technology we use to measure and to detect gravitational waves is basically to measure distances. And basically, what we use is the so-called LASER interferometry. So basically, you have a LASER. This LASER is splitted in two aces, which travels along the two arms of the gravitational wave observatory. Basically, they do the way back, and they again arrive to the same splitter. If the distance between arm A and arm B are basically the same, you have a cancellation of the two waves of the two LASER waves. And basically, you don't see anything. So in this detector, what we do is basically register if we see anything in this detector. If we don't see anything, then the two arms have exactly the same length. If there is gravitational waves that passes through this gravitational wave observatory, and the arm, for example, arm A is shorter, a little shorter. And arm B is a little larger than arm A. Basically, once this LASER is splitted and then they are again together in this splitter, what we have in the detector is that the light waves do not cancel out. So we do see a light in the detector, which means that we have difference in length between arm A and arm B. So basically, this is a very basic technology, but there are a lot of problems that can occur. So in next slides, I just want to briefly mention some of the technological ingredients that we need in these gravitational waves observatories. Of course, what I have said is a very simple scheme of what you can find in a real gravitational wave observatory. In order to have these LASERS, you need these LASERS to propagate in vacuum. So we use a ultra vacuum arms. The temperature of these arms are around 1.9 Kelvin. Basically, this is more vacuum than the vacuum of the interstellar medium. OK, a part of having these ultra vacuum arms, in order to avoid movements of the test masses, due to, for example, seismic noises, another kind of noises, for example, also thermal effects, we have a very important suspension systems. If I am not wrong, we are a system of seven pendulums in order to suspend all the mirrors and all the test masses in order to avoid these noises. On the other hand, we need high power LASERS. And the shot noise is one of the problems we have in the sensibility of the gravitational wave observatory in order to be able to detect gravitational wave signals. One important ingredient in these observatories are, of course, the highly reflective mirrors. And here I would like to mention that, actually, Virgo had a very important role in the collaboration because not only for the Virgo Observatory in Italy, but also for the observatories at United States. OK, apart from the thermal noise and the shot noise, one of the more important problems we have for determining the detectability region is the seismic noise. So as I also mentioned before, we need suspensions, not only of the test masses, but also of the detectors. And we need to isolate vibrations from seismic noises. I would like to mention that I am not an expert at all of this technology, but it's amazing the ingredients we need to introduce in these observatories in order to be able to measure a relative displacement of 1,000 part of the size of a proton. In this point, both Virgo collaborations work as a joint group. So not only, for example, this point I mentioned about the mirrors from Virgo that is also integrated in LIGO. But there are a lot of points, like the instrument design, all the technologies, the analysis of the data, or for example, the outreach. That is a joint work among all the people involved in the collaboration in LIGO and Virgo collaborations. I would like to comment a little about numerical challenges. So one of the topics of my research is in the numerical relativity field. So it's very important to mention that one ingredient in this field of gravitational waves are the capability of being able to simulate astrophysical scenarios that are going to generate gravitational waves. So stellar mass compact objects like neutron stars or black holes are basically the most promising astrophysical sources that we know that are going to generate gravitational waves that we can, at some point, be able to detect. So for example, a measure of these two compact objects, or if you consider a perturbed neutron star, rotating neutron star, or supernovae, these are all sources that, in general, we expect to detect gravitational waves from these events. Of course, we will have, I hope, gravitational waves coming from unknown sources. As I mentioned, a very important point here is to be able to generate, to simulate, sorry, these astrophysical scenarios in order to generate the template of the radiated gravitational wave. So once we have a template of the emitted gravitational wave, we can use this template in order to extract from the noise the signal we are interested in. Actually, this point was a challenge. And in 2005, it was possible to be able to simulate, for the very first time, the measure of two black holes of equal masses. This is vacuum. We were not including at this time a matter. But this was a problem. So before 2005, the people working in the field of numerical relativity, we were not able to simulate a vacuum measure of two black holes of equal masses. The point here was that there were mathematical problems related to the formulations of H10 equations. So we needed to rewrite H10 equations in a way such that you have good mathematical properties of the system of partial differential equations you are trying to solve. Moreover, not only from a mathematical point of view, but also we need to use appropriate numerical methods in order to solve this highly nonlinear system of partial differential equations. So there were a lot of works before 2005. But that was the year we were able to simulate this step. After being able to simulate a vacuum measure of black holes, we were able to simulate also non-equal masses the measure of two black holes with non-equal masses. And now we are also able to simulate the measure of neutrons. As I have mentioned, this is very important because without these templates, we cannot extract the information we want and the physical properties from the noise. Actually, these simulations in numerical relativity are very, very, very expensive. So in order to perform thousands of numerical relativity simulations, now we have a combination between numerical relativity simulations and other effective approaches in order to have effective templates that can be used in the analysis of the registered data. From this analysis, we can extract the information and then derive the physical properties involved in the astrophysical scenario we are analyzing. So in next slide, I would like to say that in the first simulation I mentioned, this measure of two black holes, we were talking about vacuum spacetime. Now let's say the measure of two black holes is a point that is quite well understood. There are still several things to properly analyze, to analyze better. But one of the challenges now in the field of numerical relativity is the matter content. So apart from, let's say, in addition to solve instant equations, we have to deal with the numerical resolution of resistive relativistic magnetohydrodynamic equations. We need to know and to solve the neutrino transport equations, and these equations are very coupled with instant equations and can be very, very difficult to solve. Apart from the difficulty of numerically solving these equations or simulating these astrophysical scenarios, including the matter content, there are a lot of uncertainties about the matter content. For example, we don't know which is the exact interior structure of an internal star. Or basically, we have no idea of the correct equation of state when you go to density beyond a nuclear matter. And for example, these kind of scenarios are going to appear when we simulate supernova explosions. So apart from these uncertainties and these difficulties in the simulations, basically, we need to simulate a lot of possibilities. And we need more data coming also from the gravitational wave detections in order to understand, to understood properly, which are the right ways. A century ago, Einstein was able to derive this basic approach, this fundamental approach, in order to derive that you have some waves coming from the metric of space-time. Sorry. But the Einstein also was concerned about the amplitude, the so extremely small amplitude of these gravitational waves. Actually, Einstein himself thought that we were not able, we will not be able to detect gravitational waves never. Actually, we needed 100 years of theoretical, numerical, and technological improvements. But the truth is that we have been able to detect gravitational waves. This is, as I mentioned, a long way. I am relatively new in this field, but you can imagine that there are a lot of people dedicating his entire life for working in this field. And here I would like to thank Abelino for the help in the figure in these slides. So before going to the recent detections of gravitational waves, I would like to mention that before these direct gravitational wave detections, there was an indirect detection of gravitational waves coming from the Hulse-Taylor binary pulsar. In 1967, Josephine Bell discovered pulsars, which are very compact stars rotating very rapidly and with a very strong magnetic field. This binary system, this binary pulsar, was orbiting, it was a binary system that there were observations where the period was decreasing. In the figure here, you have basically, the dots are observations, and this line corresponds to the prediction of general relativity of the decreasing of this period due to the emission of gravitational waves of the system. This agreement is basically amazing. And thanks to this discovery, to this decreasing of the orbital period in accordance to general relativity, both Hulse and Taylor received the Nobel Prize in 1993. So going to the recent detections of gravitational waves in next slides, as you know, we are now, we are talking about other Nobel Prize, Nobel Prize due to the direct detection of gravitational waves. The first direct detection of gravitational waves was in September 2015. Here you have the reference in case you want to have more details. And here you have basically the spectrogram in frequencies for Hulse and for Libystone. At this time, only the two observatories in the United States were operating. Basically, here you have in the top part of the figure the gravitational wave detection and the reconstruction of the gravitational wave using numerical relativity and other templates. In this first detection, we were able to detect the gravitational wave signal coming from a merger of two black holes of around 36 and 29 solar masses. The final black hole was of 62 solar masses. We have enough confidence that this is a real detection. This merger occurred 1,300 million light years in distance. And we were able to basically see this signal in our detectors during 200 milliseconds. The total amount of energy radiated in form of gravitational waves was of three solar masses. And all the information we can derive from this detection was consistent with general relativity, but in this case, in a strong gravity regime. So it's a very important detection because it's the first direct detection of gravitational waves that confirm existence of black holes, existence of binary black holes, and is a test of GR in a strong gravity regime. OK, sorry. So even if I did mathematics and I come from the field of numerical relativity, I know that there are a lot of friends listening in these webinars in the particle physics community. So I would like to comment about an upper bound for the mass of the graviton that can be derived from the detection of direct detection of gravitational waves. In general relativity, the graviton has zero mass and moves at the speed of light. So basically, we have zero mass and speed of light. If we have a non-zero mass for the graviton, the dispersion relation relates us these quantities. So we can basically measure, well, we can basically have this relation of the velocity of light here, the velocity of the graviton, the mass of the graviton, and the length, and this lambda g, this length. Sorry for my voice. So in the case we have a non-zero mass of the graviton, this lambda is finite. And actually, the low frequencies propagate slower than the high ones. So this dispersion relation can be incorporated in the analysis of the phase of the signal of the binary. I have not performed this analysis, but you can go to the paper for more details. And the idea is that once we have a bone for this lambda coming from the velocity propagation of this graviton, we can induce a bone, an upper bone, for the mass of the graviton, which is actually, I think, a very nice observation. So after this first direct detection of gravitational waves in 2015, the Ligo-Virgo collaboration, we have been able to detect other mergers of binary black holes. So here you have basically a figure with the other mergers that we have been able to detect. At this point, only the two observatories in the United States were operating. So we have basically very bad information about the localization of these mergers. Well, as you can see, one important point here was that these binary black holes were in a range of masses above a few solar masses, but below the supermassive black holes at the center of our galaxies. So thanks to the gravitational waves, we are able to observe a range of masses for the black holes that we were not able to detect before. So in the next slide, I would like to mention one of the other important direct detections of gravitational waves. In August this year, the Virgo, the Advanced Virgo Observatory in Italy, close to PISA, was able to join Advanced Ligo for the observatory observation run to during this summer. So you may know that here in Spain, summer is a holiday period. August is a holiday period. But actually, all the people in the collaboration, we were working very hard in order to be able to join Ligo for this observation run to. Actually, I have to say that Advanced Virgo did a very good job during this August, because we had a duty cycle in science mode of about 85% during the four weeks. We were taking data together with Advanced Ligo in this observation run to. I have to say also that nature was extremely generous with us. And we were able to detect a signal, 14th of August, that was able, that was detected in the three of the observatories, of the gravitational observatories that were operating at that time. So Livingstone here at the center and for is in the first column, and Virgo is in the last column. You can see that actually Livingstone is the detector who had a most clear signal, but also Hanford and Virgo, we were able to detect the gravitational wave coming from the same source. Thanks to the fact that we had three detectors observing at that time, and we had the signal in the three detectors, we were able to restrict significantly the direction, the origin of this gravitational wave detection. The details of this signal can be found in this reference. I don't want to extend too much because I would like to restrict to this 30, 40 minutes of the talk. Again, it was a binary black hole measure of around 30 and 25 solar masses. The final black hole had around 53 solar masses. And again, this range of masses of the black holes was above a few solar masses, but below the masses of the supermassive black holes at the center of the galaxies. This is very important because not only about the position, the localization in the sky, but also because having more gravitational waves observatories means that we can control the systematics of the instrument and we can better control the noise coming from one or other detector. So I say that Rachel was extremely generous with us. Let me mention again that I am talking about four weeks of observing data. In this time, we had a few binary black hole measures, including the one that was detected by the three observatories. But a few days before ending this period, we had an amazing detection that, for me, is basically the surprise. This is a detection that will be in the books for the students learning physics in the next years. So in August 16, we received an alert of a detection, but a very special detection. It was a signal that was coming not from a merger of a binary black hole, but a merger of a binary neutron star. As I commented before, this is a very different scenario. Now you have a matter content, and this can give you a lot of information, not only from the metric, let's say, the curvature of the space time itself, but also about a question of state, structure of neutron stars, and a lot of other information from other aspects I will comment later. This merger actually was expecting, was the kind of signal we are expecting to see. But with only four weeks of observing period, we were very lucky. We were very lucky also, because this detection was the closest signal that we have been able to detect. So in this slide, you can see here you have the reference, and if you want to see more details, I will comment the main points here. You have the spectrogram by Ligo Hanford at the top, Ligo Livingstone in the center, and in the third row, you have Virgo. As before, in the Ligo Livingstone Observatory, the signal was very clear. Here, I have to comment that instead of milliseconds of observing, let's say, of detection of the signal, in this case, we had around 100 seconds of signal in the range of frequency, where the gravitational observatory, gravitational wave observatory can detect the signal. So these 100 seconds, here you have the signal very clear. We are able also to detect by eye, basically, the signal here in Hanford. And actually, we see no signal in the spectrogram of Virgo. The point here is that any gravitational wave observatory has blind spots. And luckily, or not so luckily, the direction, the origin of this signal was in a blind spot for Virgo. Anyway, thanks to this information, we were able to restrict the area in the sky, the localization in the sky of the source, the direction of this source. Actually, this is the lowest signal yet observed with a signal to noise ratio of 32.4. The masses observed for this neutron star are in the range of the known neutron star masses and below those of the known black hole masses. Here, you have a plot of estimation of masses for the two binary neutron stars before merger. Sorry. You can see that this range is not very narrow. This is because we don't have a lot of information about the spin effect in this merger. So basically, we are able to restrict the range of the masses for the first and the second masses of this binary system of neutron stars. The blue color corresponds to an effective spin below this value and the brown color corresponds to an analysis, including an effective spin below to this quantity. I will not enter into details, but basically, in the case of binary black holes, you can determine with more precision the masses of the black holes, but in the case of the neutron stars, this is more difficult. And also, you have a lot of uncertainties regarding this spin, this effective parameter regarding the spin that is used in the parameter estimation. Anyway, as I mentioned, the range of these neutron stars are in the known range for the neutron star masses. So here, you can see what I was mentioning before. An example of sky localizations of several detections of gravitational waves. These waves, GW-17, O-104, or GW-15, 1226, were detected only when the two observatories in the United States were operating. So you can see here that the sky localization is very poor in order to identify the origin of this source. On the other hand, for example, for the first detection of gravitational waves coming from the three observatories, regarding the binary black hole merger, or this gravitational wave coming from the merger of the neutron star also with the three detectors, you can see that the area in the sky is very, very small. So small that you can localize with a lot of precision the origin of the gravitational wave signal. In this case, we were able to have a very rapid localization using Ligo Hansford and Ligo Livingstone of 190 degrees squared using Virgo and using a very rapid localization. We were able to restrict to 30 degrees squared. And with a little of time and our final localization was in area of 28 degrees squared. We were able also to measure the luminosity distance of this gravitational wave source. It was around 40 megaparsecs. Actually, this is also the closest localized gravitational wave signal. So with this rapid localization and in an area in the sky small enough to be able to give alerts to other observatories. Well, in Ligo Virgo, we have agreements with a lot of instruments, around 200 instruments across the entire electromagnetic spectrum, as well as the neutrino observatories. So I'm talking about gamma rays, x-rays, ultraviolet, infrared, radio, optical, all the range. So basically, as I was saying, we had a very rapidly localization and in a very small area. So we were able to alert our colleagues from other observatories all around the world, on Earth and also in the space. That day, we gave the alert to all of them. Basically, you all know also that our colleagues from optical were not able to shut up enough in order to have in secret all this news. But at least the people working in the Ligo Virgo collaboration, we tried to be silent, to be shy. OK, what happened that day? Well, before talking about what we detect not only from gravitational waves, but also in the electromagnetic spectrum, I would like to mention that this was a scenario that was full of uncertainties. Basically, simulations, numerical simulations and theoretical analysis of the merger of two neutron stars but only suggested it was not checked at all, that these two neutron stars merge. Then you form a central black hole. You have material around this central black hole forming an accretion disk, which is absorbed in seconds by the black hole, by the central black hole. In the symmetric, in the, let's say, North and South Poles with respect to this accretion disk, you have the emission of a jet of material that is a relativistic emission of material that is known as a gamma ray burst. Apart from this emission of the symmetric emission of the jets, one expects an emission, and symmetric emission later on, which is called kilonova, which has a characteristic spectrum. And basically, it was thought that all the heavy elements from, I mean, all the heavy elements like platinum, uranium, gold, and other elements beyond the elements that you can form in other astrophysical scenarios, like carbon, oxygen, then these very heavy elements were formed in this kilonova emission. All these ingredients were just part of simulations or analytical studies. But there were no check, no detection to link the merger of a binary system of neutron stars with this emission of the short GRBs. So let me comment that there are two GRBs of gamma ray bursts. The one is the so-called long GRB, and the other group is the so-called short GRB. The one I am talking about here is the short GRB group, which has a very short duration and a prompt gamma ray emission. So I'm not going into the details about this emission, but basically all these elements, the merger of the neutron stars, the formation of the black hole, the formation of the accretion disk, the emission of the relativistic jet as a short GRB, and the emission of the kilonova was just a simulation in the computer or theoretical studies on the papers. On August 17 this year, the gravitational wave detection was followed by the detection by Fermi, an integral around 1.7 seconds later of a short GRB in an independent way. So it was from two to six orders of magnitude less energetic than other GRBs observed. But, well, with a similar redshift, but maybe this is due to the fact that we are observing the GRB of axis. Here you have basically in the center, in the central part, the spectrum of the gravitational wave, and in the first and in the last rows, you have the spectrum of integral and Fermi. So you can see that basically from the same origin in the sky localization, we had an emission of gamma rays, which is in agreement with our model of merger of binary neutron stars and production of a short GRB. Not only gravitational waves and gamma ray bars were detected that day, actually I think this is the event that astronomers all around the world were expecting to see once, at least once in the life, in a life. So we were extremely, extremely lucky because we were able to detect very clearly the gravitational wave to localize very good the origin of the source to detect the gamma ray, but also we were able to detect this source in X-ray with shift in ultraviolet. Also we were able to identify the host galaxy thanks to optical observations all around the world. We had also infrared and radio emission. And basically this is not only, I am not talking only about that day. As you can see here, there will be a observation of this source in the days following the event, but not only the days, but in the weeks, amounts following that day. Just to let you know, the amount of people working in this event I would like to mention that over 3,500 households were a part of the beginning of the multi-messenger astronomy. And I think this is an extraordinary example of what international collaboration means. I'm not going to give more details about this multi-messenger detection. You can find all the details in this reference here astrophysical journal letters, but they think it's just amazing the amount of information we have in all the possible ranges in all the possible frequencies of the electromagnetic spectrum plus gravitational wave. I have to say that we had also, we sent also alerts to neutrino experiments and they were observing the source, but there are no confirmed detections of neutrino particles. This is the last link we need, but I am quite confident that if nature has been so generous with us in the past, it will be in the future. And in the next detections of gravitational waves, we will hopefully have also detection of neutrino associated to these events. So here you in the next slide, I just want to again highlight this binary neutron star short GRB connection that was for the very first time confirmed with an observation. In magenta, you have the region coming from the localization in the sky of Fermi. In gray, you have the localization coming from Fermi and internal timing. And this green small area is the one, is the 90% Ligo Virgo credible region that was about 28 degrees square. We have a very high significance of coincidence. And for sure, this is the very first direct evidence that binary neutron star mergers are the progenitors of these short gamma ray bars. As I have just mentioned, let's wait for the observation of a neutrino that will be also very, very important to analyze the physical properties of these astrophysical scenarios and is the basically the last link in the chain. I would like also to mention that this multi messenger detection was amazing and we were able also to provide some important constraints for the people working in cosmology. We were able to measure the Hubble constant. You can see all the details here in the referencing nature. I'm going just to mention very briefly the most important point here. Basically, if you combine the distance that you can infer from the imperial face of the gravitational wave signal and the red shift that was able that we were able to measure thanks to the identification of the host galaxy of the source coming from the electromagnetic signal, we are able to measure the Hubble constant from this relation. The observed value is this quantity here and in the plot you can see basically the relation with the value derived from Planck in green, the value derived from choose in brown and the very broad line that you can get from the Hubble constant value measured in combination with the gravitational wave signal. Of course, we still have a lot of uncertainty for this value, but basically we are combining somehow the two values that has no intersection. So we are basically more or less in the middle but with a lot of uncertainty. We hope that with more detections we will be able to narrow this error bar and to give a more precise value for this Hubble constant. So I have arrived at the end of my talk. I hope it was not too long. Sorry for my voice. I just want to say that we are starting this multi-messenger astronomy just now. This is an amazing new time for astronomy. We are looking forward to the future and who knows which kind of gravitational wave detections we will have and which kind of amazing information is waiting for us to be able to reach thanks to the gravitational waves in collaboration with all the rest of observatories in the world and also out in the space. So I will stop here and just thank you very much for all your attention. Okay, thank you, Issa, for this very nice talk and thank you especially for giving it with such a complicated scenario for you with the voice. Yeah, sorry for that. But it won't work. So now we proceed with the question round. So let me remind everybody again, watching us in YouTube that you can make questions and comments on the upper right part of your screen. So let's begin first with questions from our audience. Maybe somebody here would like to ask something. Let's see. Hello. Hi, thank you, Isabel. I have a short question out of curiosity. You mentioned that the first time that we were able to like simulate equal masses of black holes collation in the computer, I believe it was Franz Petrodius. Could you please comment a little bit? Like what was different? Like what was the big change? Just entering a little bit on the details. Like what did we do as a community to be able to do that? Like what was it just for the common reader? Okay, so thank you very much for the question. This is very close to my research, so I can give you more details about that. Basically, before that moment, there were, let's say, analytical studies and we were able to simulate, not to simulate, let's say to calculate less than one orbit, just a short time. The problem here is that, first of all, the formulation, the way you write instant equations can be critical. And I want to mean that, for example, there is a property called well-posed net of the equations. No, for example. So that means that the properties of the partial differential equations you are trying to solve can change a lot if you write them in a way or another. For example, this well-posed net means that if you start from a solution that deviates very small from your, let's say, exact initial data, and this will always occur because you have numerical approximations, then the evolution of your system can deviate dramatically from the exact evolution. So basically, it means you cannot believe at all what you are simulating. This is one thing. Another very important point here is that when you talk about black hole in general relativity, you are not including quantum physics, and you are including singularity at the center of the black hole. Okay, if you want to include a singularity in a computer, in a computer, this is a mess. This is a nightmare. In this case, you have two singularities, one of each black hole. You have to move these two singularities, and there are crucial quantities that diverges at this singularity. So it's not only, I mean, there are a lot of quantities related, for example, to the curvature of the space time at that point is infinite. So you have a lot of quantities that basically you cannot handle with a computer. So you have to do some kind of trick. Sorry, one moment. Don't worry, thank you. Okay, the two main tricks that we have been able to use for that is the first one is the so-called excision. This is the one that Pretorius used in his paper, but in the same year, there were other groups that also were able to perform the simulations with other formulation and other techniques I will comment later. So excision means that you basically, you don't want to simulate the interior part of the black hole where the singularity is included. Okay, this is nice in principle, because you basically cut inside the upper and horizon, and because of casualty, you will not have information propagating from inside the black hole to outside. But you can imagine that the complexity of Einstein equations is very, very big, it's very hard. So you have non-linearity phenomena, and you have to do all these things with a lot of careful. So basically the way excision was included in the code was critical. And this excision was associated to a particular way of writing the questions, which is the harmonic generalized harmonic formulation. This is one option. The other option that basically most of the groups nowadays are using is to use another geometry of space-time. So when you are close to the upper and horizon to the trap region, to the border of the trap region, you cut this interior of the black hole and you paste another regular solution, which is compactified in this interior part. So this interior part in your numerical grid is no more a singularity of a black hole, but another, let's say another regular solution. In both cases, the point is that from a classical point of view, what happens inside the trap region will not affect to the outside part. So this second approach about this other geometry is called the Trumpet geometry and it's using combination with another formulation, which is called the BSSN formulation of instant equations. So you see that you have to be very careful, both taking into account which equations are you going to evolve and which geometry on which streak are you going to use in order to avoid the singularity at the center of the black hole. Moreover, sorry, Moreover, these two formulations are in the group of the so-called free evolution schemes. As you may know, in instant equations, you have several kinds of equations. You have evolution equations. And for example, if we are talking about gravitational waves, you do have evolution equations. You have a physical degree of freedom, which is propagating, which is evolving. But apart from these evolution equations, we have constraints. We have a Hamiltonian constraint and we have momentum constraint. There is a, let's say one approach which is not to solve constraints, but try to solve them initially and then just evolve the evolution equations. This is more less easy if you are solving the equations numerically and if you don't do, let's say, if you do the things properly, then the constraint equations will also be satisfied in future times. But this is not guaranteed when you are talking about numerical methods. So there were also a lot of numerical tricks in order to avoid the growth of the violation of the constraints. These are only very general comments, but let's say that there were mathematical, numerical problems related to the evolution, to the numerical evolution of the equations. Okay, thank you, Zabel, for your complete answer. Welcome. Okay, are there any more questions from the audience? Okay, I have one question. So you've been able to get a lot of information from only one event, basically, right? So I don't know how often do you are expecting to get such events per year. I would like to know, Marles, how much data do you think that you'll be able to acquire over the lifetime of LIGO and Vergo. What sort of information will we be able to ultimately obtain at the end of this life? Okay, about the first question, I think we were very lucky, very lucky. I mean, we had a lot of luck. We were only observing for weeks. Now, both LIGO and Vergo are advanced, Virgo and Advanced LIGO, which means that they have been improved from previous observing runs. The detection rate, I will not give you a very precise number, because it's one of the things that was not very well known. I would say a priori. It depends on a lot of things. For example, the sensibility curve of a detector is something a little other life, in the sense that you don't have the perfect curve all the time. But let's say, so very general number, and now we have one per year, okay, more or less, or a little more, but I will not say very precise number. But we are now both LIGO and Virgo, we are in commissioning period. They are improving a lot the sensibility, well, a lot, they are improving the sensibility of the detector. Only a factor two of improvement in distance because of the volume means eight times more of a detection. I would say that where we expect that ending of next year, we will have another observing period, but I don't know exactly one month or something like that, but let's say. So, and we expect a few ones. What means a few? A few means more than one, but maybe I would not say a hundred, no? A few, a few ones. And that will depend a lot on how good are we decreasing the noise in the observatories. So, I would say for the next year, I would expect a few detections. A few more than this year, but a few detections. I don't want to be very, very optimistic. I would like to be more realistic because this is really technologically, it's amazing the things that are included in these instruments. But if you think in token that Kagra is being, well now the people in Japan, they are constructing Kagra and they are constructing it very, very quickly. There are also a strong steps done in the construction of LIGO India, not the observatory itself, but the technology, the compromise of the government. So, I think we will have a few more observatories soon, which also enhance a lot possible detections because, well, I have shown the spectrogram of some of the detections and in some of them, I think by eye, you can see where is the signal. But in general, we were very lucky and in general, maybe we will have more noise or the source is further, so the amplitude of the gravitational wave that we observed is small. For this point, templates are critical, are very, very important. And if you have not only one or two or three detectors, but four or five detectors, that can be very, very important. So I would say for next year, a few ones and a few more than now, but I don't know. And then if you take into account, well, Lisa and future, I would say maybe something one per day. I hope to be able to see one per day soon, but soon means in a few years, no? Maybe Alejandro, who is in Virgo Observatory, can say more than me, but this is the number I can remember now. So you're referring to the other Alejandro, not the one that asked the question. Yes, Alejandro Torres is a member of our group here in Valencia too. Okay. I don't know if he wants to say something more, but... No, I don't have more things to say. I think you are right or less. I don't remember them. Okay. Yeah, and also I would like to say that this is, this is technologically, this is amazing. So who knows if they can improve? For example, they are now, they are installing the squeezer in the laser, they are including more and more elements, more observatories, less noise, better technology, who knows? Super. So it's a little bit late. Let's see if there's any other questions in the audience. Sorry, I almost took it a lot. Oh no, no, it's okay, this is what it's about. I don't know if there's any other final questions from the audience. Okay, so we're good. And from the YouTube live chat, there's, okay, there's just a comment from Felipe Gomez, who's saying that it's been a very nice talk. Thank you. So there we go. Okay, so that's it. This has been the last webinar of the year. We are restarting next year in January, around the 15th, after the 15th of January, by the webinar by Bradley Kavanaugh, who will be talking about Dark Matter. So we hope to see you all there. Before we sign out, thanks again, Issa, for the wonderful seminar. Thanks for all the viewers this year, and we hope that you have a very nice end of the year. Okay, so we'll see you around. Goodbye. Bye. Thank you.