Okay. So that's 3:00 and time to begin.
So it is a pleasure to introduce to you today Speaker Professor Gabriella Gonzalez of Louisiana State University.
Gaby has been a member of the Ligo's scientific collaboration since 1997, and in 2011 she was elected as its spokesperson.
Her group is involved in the characterisation of the noise of the like her detectors.
But the calibration of the detectors themselves. And with the analysis of the data.
On September the 14th last year. The two, like gravitational detectors in Washington State and Louisiana,
later said nearly simultaneous signals that time frequency properties consistent
with gravitational wave ignition by the merger of two massive compact objects.
Further analysis of those signals by Liger and Virgo revealed that the gravitational
waves detected by liger came from the merger of a binary black hole system.
This observation, followed by another in December of the same year,
is one of the most remarkable and significant discoveries in all of the physical
sciences in the 21st century has captured the imagination of citizens around the world,
and it marks the beginning of the new field of gravitational wave astronomy.
Asked about how she would like to be introduced today and she told me just saying,
a professor from Louisiana State who will present today a talk to you on behalf of more than 1000 colleagues and the like, a collaboration.
Please welcome Gabby Gonzalez. Thank you.
Can you hear me? Yes. Okay. Yes.
It's a pleasure to be here. Thank you for inviting me. It's my first time in Oxford and it's lovely.
And yes, I want to tell you about this beautiful observation we had, which is the first of many.
And I hope since the 21st century is still early, that it will be also the first of many significant discoveries we already had to the Higgs.
And these I'm looking for many more.
Let me remind you, maybe not all of you have studied general relativity or have learned about the basics of gravitational waves.
And we just give you a very quick tour. These are Einstein's equations, and they look very simple, but they are not.
On the left hand side, we have Einstein's stance, sort of, which is constructed from a spacetime metric.
So a spacetime metric is a sensor that tells us how to measure distances on time.
So I imagine he disagreed on rulers and clocks.
That's a spacetime metric. And what we have here is all sort of derivatives that are non-linear,
like combined multiplications of derivatives with respect to all the spacetime variables.
So that is the mass that you have on the left hand side having to do with spacetime.
The right hand side is the stress energy tensor.
That's what's telling you where the mass is and what the masses are doing, how are they moving?
And what this equation is telling you is that the metric is telling the masses how to move.
So that's why this is a theory of gravity. It tells you that the sun and the earth are this system where the earth goes around the sun,
not because there is a force of gravity that attracts them,
but because the sun curves the spacetime in such a way that for the Earth it's easier to go in a simple than to go straight.
So that is how the curvature of spacetime determines how that matters most.
But because the matter moves, then the matter is also telling the spacetime how to cope.
So the two things go together. And that is the beauty and the difficulty of Einstein's equations.
They are actually quite complicated. But even Einstein himself, after passing this in 1915.
So that if you if you said the right hand side equal to zero, and then you assume that the space time metric isn't just the regular space,
flat space and metric Minkowski metric that we use all the time to solve electromagnetic equations.
Then in other words, you assume it's a flat metric plus a small perturbation,
and small in this case means that you are measuring things that are don't have dimensions
in here because you are combining space and time or they have the same dimensions.
So this this perturbation is measured as changes in distance, over distance.
You can also transform that into changes in time.
But for our purposes, we're going to interpret that as changes in distance, fractional changes in distance.
So if you put in if you make this equal to zero and you put you put this approximation in here and you keep only terms linear in h,
what you get is a wave equation. So what that tells you is that spacetime needs Einstein's equations a neat way solutions.
And those are gravitational waves. And that he got in 1916 with some math errors in there, actually math and physics, everything down.
But those were sorted out later. Those waves would be transverse and they would have two polarisations.
The idea is that if you have a ring of death particles that are freely falling and that's not such a thought experiment.
I like to think about these people who like jumping off planes in parachutes before they open the parachutes and they are all arranged in a circle.
Sometimes they hold hands, but if they don't hold hands, what you have is particles in freefall.
So imagine that you have such a circle of this particles and there's a gravitational wave propagating in this direction.
Then distances that are going to chase particles are not necessarily going to move.
That depends on your coordinate systems, but the distances are going to change that.
That would seem to be equal distances here. Now it's longer here and shorter there, and then they are the same again.
And then this one is longer and this one is shorter. So does the distortion of distances due to the gravitational wave.
And there are two polarisation. These are quadrupole gravitational waves.
So in this polarisation, these ellipses form a plus sign in this when you have the ellipses forming a cross.
So those are the two polarisations in the theory of relativity.
Alternative theories have, of course, other assumptions. Now, how are these waves produced?
Well, in 1980 he had another paper in which he used similar approximations, but then he solved the equations,
putting some matter in here for the wave propagation, for the wave formation.
And and what he saw is what we call now the quadrupole formula that this perturbation of distance is going to be produced by your mass quadrupole.
So you need the non vertical distribution you need to have it must quadrupole, you need to have time derivatives.
In fact, we want three time derivatives because to just give you a constant H and what you want is a periodic H or two time dependent H,
so you want three derivatives of come here and there are very unfortunate constants in here.
This is Newton's constant because this is a theory of gravity. This is a speed of light,
because this is a relativistic theory of gravity and you have distance to the source
non distance squared because this is the field effect we had calculating the field,
the field and not the not the energy. And this is unfortunate because if you think about experiment,
so now if you think about I do not do very heavy masses in a ring rotating at some kilohertz frequencies.
The Hertz experiment that this aid is just negligible.
And Einstein had in that paper this was a tournament which they were calculating observational effects of this theory to to to prove it,
to see whether there were experiments that could prove it.
He said this was never going to be measured, and that's what we thought for a very, very long time.
Now we know better. We know that this could be you have large quadrupole.
So if you have on time dependent if you have for example to masses moving around the centre of mass like the earth and the sun.
But if you have compact objects like neutron stars, then not only they are going to rotate,
but they're going to be losing energy to these gravitational waves.
So they're going to get closer and closer than the if they are compact, they can get very close and then move very fast.
So that's the way to get a large quadrupole and we know that exists.
You probably remember that in the seventies, the first binary system of neutron stars was discovered.
That was a wholesaler system and it was in our galaxy not that far away.
And they had the stars were quite close. This was an eight hour period.
Imagine you have each star, the mass of the sun they had rotating with an eight hour period.
The earth rotates with a one year period around the sun.
And here you have these two copied stars a lot closer to it.
It's actually, to me, mind boggling to think about this system.
It was the first binary system discovered since then.
There's been quite a few more, but because they were close, if you want, then the laws of energy could be seen.
And that was the first proof that gravitational waves exist because they take energy of the system, just like the theory predicts.
So that was absurd. And then we knew that those gravitational waves would have this form.
As the stars get closer and closer, then the period gets shorter, the frequency gets higher.
You can use an approximation. And then this dimensionless quantity is more or less proportional to the product of the radio of the stars.
It's about ten kilometres for neutron stars divided by the distance between the stars.
So the closer they get, the larger the gravitational wave. Divided by the distance to the source.
So how far can these sources be? Well, these are in our galaxy, so they're not that far, but they're very far apart.
So this actually the number for this particular system on earth is about ten to the -26.
Fractional reserve. And that's way too small for any instrument we know, even space instruments.
And this is, again, a very low, very long period, low frequency.
So let's think about and this would be stronger if they had close to coalescence, but that wouldn't happen for about 300 million years.
We don't want to wait that long. So let's imagine that we're looking at the larger volume of space.
Let's imagine that we are sensitive to the Virgo cluster in the Virgo cluster.
Systems like these are probably coalescing not once every 10,000 years, like on let go in our galaxy, but once every 50 years.
And that's getting reasonable, especially taking astronomy errors into account.
So let's imagine we have a detector that's sensitive to that distance.
How strong would have detected have to be? And the answer is ten to the -21.
So a binary system of neutron stars at about 26 produce a fractional change.
And this is near the earth of it. But in ten to the 21.
How small is that? Well, very small. And of course, let's put some numbers in there.
If we are thinking about the baseline of the distance between the earth and the sun, a part in terms of the 21 is about an atomic diameter.
So we have looking at the wave that's moving the earth from the sun closer and farther away by an atomic diameter.
That's not suitable. Can we make it shorter?
Well, if we make it shorter, then we need to make it more sensitive.
We can measure on that much better than an atomic diameter.
Right. How much better can we measure?
Well, that's what people in the seventies have begun trying to calculate how small it could be, and they'll hold the suspense until a bit later.
But, you know, now that this number we can measure.
So let's get to the sensitivity of it just a bit later.
Let me tell you now about another calculation that was also not done until about ten years ago, only ten years ago.
And that is the solution for the amplitude of gravitational waves on the form of gravitational waves produced by black holes.
If you really want to calculate how spacetime, how gravitational waves that form, the simplest system you can think of is black holes.
Because then you don't have matter, you don't have radiation, you don't have atoms, you only have space.
That sounds easy. It wasn't that easy, actually.
You cannot get analytical solutions. You can only get numerical solutions.
And that's what people need. Again, not more than ten years ago.
Now they are done regularly, but they take a lot of computer time.
And I'm showing you I'm going to show you here the movie of just just because two black holes that have about 30 solar masses.
And what I am going to show you is a colour representing curvature near the black holes.
And then the solution to the gravitational wave that you would measured far away from the black holes in the radiation zone.
So this is going to be the gravitational wave measure, let's say universe, and this is going to be the curvature near the black holes.
And let me show you.
It's actually quite nice. I know how to make that thing go away.
There are. Notice that the black holes are relatively far away.
This is half a second before coalescence. There's a very large curvature near each black hole.
This is a cat on a plane, of course. Could virtually anything in all four dimensions, not just three.
But this is just on a plane. But the solution is calculated all over space time.
So they're getting closer and closer. Now we are 250 milliseconds before coalescence.
We see that as they get closer, they have rotating faster.
The amplitude of gravitational waves is larger. Now the curvatures are beginning to mix up and we knew these that it was going
to get very messy here and how it is now that the horizon's got together.
That's in order to look at all the detail in there. But now look at how simple life form is here.
This relativity, this numerical relativity simulation tells you what happens near the black hole and far from the black hole.
This is what we will measure. We can infer from what we measured what happened pretty near the black hole.
But what we need to measure is relatively simple. It's a way forward that shows increasing amplitude and frequency.
The frequency depends on the masses of the black holes.
And then a ring down. So in the seventies, people thought that ten to the -21 was something that was achievable with an interferometer.
They had to calculate what their sources of noise could be in an interferometer if you didn't to see how long it could be down.
And they calculated that rate wise, it's one of the first ones that put not just that concept of any that phenomena that had appeared earlier,
but also the noises, sensitivity of a detector.
So he imagined kilometre sized detectors for kilometres.
So that means that you would have to measure about ten to the -18 metres.
1810 to the -18, an atom is sent to the minus two as a proton is sent to the -15 metres.
We are talking about ten to the -18, a part in a thousand of a proton diameter in the difference between this length and that length.
Each of these lands four kilometres long. And he put some noise.
Kirsten down, made some estimates with some other people that hurt him.
He said it's possible. Took some time to convince.
So this was the idea is detectors four kilometres long.
It took some time to convince the National Science Foundation, but that was done.
It was done in a very special way.
It said that if you build it four kilometres long and you installed the technology we have now, that's in the nineties.
I was starting my to that. Then you can measure ten to the -21, but that would probably not be enough to detect gravitational waves.
You would have to install technology to do ten times better.
And they from the beginning, this was thought to face experiment.
So the funding in the nineties was to build these two facilities to put in their what
was called the initial legal detectors that would have noise at about ten to the -21.
Oh, that was a facility in Livingston, Louisiana.
That's near Baton Rouge, where they live. Again, you can go to Google Maps.
I love doing that. If you go to the Google Maps, you see the real thing and then you can fly 3000 kilometres.
If you go straight 10 milliseconds, if you travel at the speed of light to Hanford and that's in the middle of the desert,
you go from the swamp, from a logging forest to the middle of the desert.
And those are the to lie detectors. That was in the early nineties.
In the 2000, we began measuring noise in those detectors.
It took about five years to get to the noise sensitivity to the design sensitivity that those detectors had been built for.
And that is about this. So this is a way in which we represent the noise in the detectors, not the signal, but the noise.
But the noise is what determines the sensitivity. So we have we call this a noise, spectral density,
because it tells us about the noise measured us through a fractional distance measurement as a function of frequency.
So it's the noise that we have at each frequency because this is noise.
Low is good. So this is our sweet spot.
This was this was our sweet spot. The initial liger at low frequencies, we are limited by seismic noise and high frequencies.
We were limited by the quantum noise in the laser.
We are measuring photons. So the uncertainty, that number of photons, that is short noise, we call that quantum noise, but that is just show noise.
And in the middle, we don't quite know what the actual noise was, but it was consistent or very close to the Brownian motion of the mirrors.
The mirrors are in vacuum, so they're not pushed around by air molecules, but they are made of atoms that you had at warm temperatures.
They are vibrating. And we measured the position of the front face of the mirrors.
So we do have some sensitivity to that.
We have to calculate the frequency dependence of that of that thermal noise.
And that is this one. Notice that these numbers are ten to the -22, ten to the -23.
You would say, well, that's ten, 100 times better than ten to the -21.
So much better. We worded because when we say ten to the -21, what we are thinking is a rude, mean square.
If you have a noisy time series.
But when you have a time series, what you have to think is you have a time series that is filtered through some frequency band.
So the rudiments of that time series, let's say filter between 102 hundred hertz would be the integral of this keyword,
of this good versus frequency, and then taking the square root.
And then you see here that this is two or 310 to the -23.
You multiply by ten because you're integrating over frequency.
So that gives you ten to the -20. But it would have been better than that, but only near these frequencies.
That was initial logo. It took a while to get it done.
This was what we had in 2010. That was enough to see this binary neutron start coalescence, this individual cluster at 1520 megabytes six.
We didn't see any. But they told you that we expect those to happen once every 50 years.
So it wasn't a surprise. We would hoping to be lucky, but we didn't.
But we had this plan. We had this plan for advanced legal for that we do better seismic isolation so that we have lower seismic noise.
We have a different way. We have lowered sources of energy dissipation.
And in the question period, you can ask me why that reduces the brown noise, but that's what it does.
Let me see bezel less brown and noise at these frequencies and we can use more for those higher laser power and that reduces the quantum noise.
So that was a plan for the advanced liger. Of course, that plan takes a lot of technology, a lot of time, a lot of money.
Let me just show you some pictures. It's all in a vacuum.
So these lasers are travelling for kilometres in a vacuum tube that has to be big so that you don't have scads of light bouncing on the walls.
These are emitted and a half in diameter. You have the laser, which is an amplified laser of 200 watts, and we had only 24 now.
The mirrors are state of the art mirrors, both for the polishing and the coding of the mirrors.
The laser is an infrared, so our mirrors are made reflective or transmission when they need to be in the infrared and also at twice the frequency,
because we also use three lasers to align. So they are two frequencies and we have them for seismic isolation.
We have them hanging from a quadruple pendulum.
So this mass, which is a full silica mass, is hanging from this mass.
It's hugging from blades is coming from blades. We have four horizontal pendulums.
We have three a couple system of blades for vertical seismic isolation.
And we have all of that hanging from a seismic isolation platform,
which is a triple platform in which we measure the noise, the relative noise between the stages and we can select.
And all of that is standing on hydraulic actuators that also have ways to measure this is that helps the hundred.
Oh, 00i see. I've been talking for too long.
I think that's what it's telling me that is all hanging from.
Yes. Okay. This is the seismic isolation platform.
I said this is a hydraulic actuators. These can be moved by hundreds of microns to compensate for earth tides.
And all of that is in vacuum chambers. Yes.
All of that all of these hanging from the are hanging from that is is inside vacuum chambers.
And then it all has to work together. The topology has these quadruple pendulums.
We have two we need to arm because we make the line go back and forth.
Many times what we actually have is an optical resonant cavity in each arm, fabricated cavity.
We keep the interference of the output destructive, which means that the interference going back to the input is constructive.
So this is acting like a mirror. So we have another mirror in here that we call a powered resulting metre that makes
the light go back and forth that it has more photons circulating in the system.
The quantum noise. We have a signal recycling mirror to the output and with all of that we have a noisy time series
and the end that has about anonymous of ten to the -22 foot advance like Putin to the -22.
Now with that, I'm serious. We need to search for gravitational waves and we search for several kinds of gravitational waves.
We look for cross correlation between the two, nor is it time series in the ligo's detectors.
And that's because then we can we can measure the unknown.
We don't need to have a template. We don't need to know what we are looking for.
We just cross correlate Hanford with Livingston.
We see whether there's something there. If there is, then we can find anything in there that very sensitive.
That would be the case, for example, for the supernova explosion. What wave forms are very complicated and not very well known.
We look for periodic signals. Those would be produced by neutron stars rotating if they are not perfectly symmetric.
That's another amazing thing about neutron stars. They have the mass of the sun concentrated in the size of a small city, about ten kilometres.
We, as Felicity said, that the highest mountain is a couple of centimetres.
It's a pothole. I know it's in Baton Rouge.
Isn't that larger than that? So but they cannot be perfect.
If they are not perfect spheres, then they will produce gravitational waves and those will be periodic.
So we know how to look for those.
We have way for four binary systems, whether they are black holes or do we have the full waveform or neutron stars where it gets messy at the end.
But then we know that at the end neutron stars would produce a black hole.
So we would see a black hole getting born, just produce perhaps with the supernova too.
And we could even look for cross correlations of stochastic background between
the detectors we looked at using cross correlation between the detectors.
This would be the case for gravitational waves from the early universe which exist in our frequency band, but they're very, very small.
So so far we've put the best upper limits in those frequencies,
but we don't expect to see those because they yet they are predicted to be way, way below the noise.
But we could see many of these signals or many of these signals if they are small and all mixed together.
We call that the astrophysical bug.
So we need to build the detectors, develop the technology, build the detectors, operate the detectors, look for the data.
That's what we've been doing for years and that takes a lot of people.
So when I say a thousand people, it's really true. The League of Collaboration was formed in 97.
It has now about 1100 members. We are in 15 countries and since 2007 we actually take the data and jointly
analyse data with a video collaboration that has about 250 people in Europe.
So it takes a lot of people a lot of time to do that.
But we are very proud. And I just want to show you that there's about 235 people in the UK doing this too in several different universities.
And there's everything from hardware development, data analysis, future detectors, upgrades, optics, technology for future detectors.
We have a very nice Life magazine. One of the main editors and magazine is in Birmingham.
There's a lot of outreach, so a lot of this is the main design for the these quadruple suspensions was done in the University of Glasgow.
So we are very good friends of the UK.
In 2015, we had the Liger, the advance liger detector's working at a sensitivity that we thought it was quite good.
It was about three times better to be better, three times better.
Initial Liger. In initial liger we had this reached the binary neutral stars of 26 with this noise level that we had in September 2015,
we had to reach to neutron stars of about 70, make up us six.
So we had decided in advance of this that at that level it was good to take data
for a few months and then stop and keep tweaking the detector to get to the 246,
which is the potential of the advanced liger detectors. So that's what we had.
We would using 20 volts. That's why one of the reasons we are not so good everywhere.
But we had a sensitivity that was very decent. Look at this, ten to the -23 there.
And before we started taking data into 24, seven before we started officially this observing run while we were running tests, diagnosing,
calibrating the data in the detectors, analysing the data whenever that was time for the two detectors to take the data jointly.
We saw this on September 14 of 2058.
That must have been the busiest Monday well I've had in my life.
But most of the people in collaboration have had probably some people went on vacation where he was, for example, was in vacation.
And he knew he suspected about this not because he was reading it, but because he was reading the electronic logs.
To use this, we have something in space and he saw that we had cancelled maintenance and say so he could that say what happened this attack.
So I'm telling you, you probably know this already, but in blue is the data with some minimal filtering in living still in red,
there's the data again with minimal filtering in a frequency band and taking away some some power lines in Hanford 3000 kilometres away.
And here we have shifted the Hanford data 7 milliseconds so that it lines up with Livingstone
and we saw something that looked larger than the noise in both detectors the same.
So that was a gravitational wave. It was larger than the noise, it was the same in both detectors.
We couldn't find any other explanation. It was the gravitational wave.
And on top of that you could see the signature of a sine wave that got higher in frequency,
higher in amplitude, and then smoothly settled down to that noise.
That's what you expect from black holes. And then when you calculated the black hole masses, these were so distorted it must black holes.
I mean, this is all incredible. We were not expecting gravitational waves.
And here we had a gravitational wave. We were not expecting black holes.
And had we had black holes, we would not expect them through the black hole.
Nobody was. And here they were. We couldn't believe it.
It took us months to convince ourselves that this was real and there was no other explanation for this.
But you know that now we did discover gravitational waves on September 14, 2050, but that wasn't the only one.
We had planned to take data for three months. We decided to take that for four months.
We had a lot to do on the detector, so we had decided to stop in January and on December,
December 26 in Europe, but it was still December 25, it was still Christmas in the US.
We saw another signal. It wasn't as big.
I cannot. I'll show you some drawings. It wasn't as clear as that.
First detection. That's because these are smaller black holes.
These are 30 solar mass black holes each 29 and 36, this at eight than 14.
So they're quite a bit smaller even though they are different in mass.
So the signal was smaller in amplitude, but it was longer and that's why we could detect it with very, very high confidence.
And we even had a third candidate. We call this a candidate not a detection because it's much lower amplitude.
It has it is consistent with binary black hole system with masses in between these two.
It depends who you ask whether this is a detection or not.
If you ask me, it has a 15% chance of not being a detection of not being an astrophysical signal.
So for me that's not quite enough. But as a member of a family, it's a very reasonable candidate if we didn't have this.
We wouldn't pay any attention to that. But now we have this debate, and this is the beginning of gravitational wave astronomy.
We do know from X-ray astronomy that there are black holes of stellar masses.
We know that that's how they start from supernova explosions with a few solid masses, but hot ten solar masses.
These are big stars, but they need to get compressed. We do know that when two neutron stars merge, they form a black hole.
But those would be two black holes. We have seen black holes from X-ray studies, from X-rays emitted from either the stellar companion,
which is not a black hole, or from the jets of the black hole itself.
But they are all relatively low mass.
And here it was our first detection and the two largest black holes known in this range, forming another black hole.
This is 29. This was 36 solar masses and this was 62.
And for those people who can do algebra in their heads, which is not me, I always make mistakes.
But 29 to 36, it's not 62.
There are three solid masses missing, though. Those are three solid masses that went away in energy in the gravitational waves.
Energy and mass are the same. Equal, empty square.
That's Einstein's formula. That would be three solid masses in energy of gravitational waves.
If that had been visible energy in a fraction of a second, that's us.
All the galaxies in the visible together, exploding in a fraction of a second.
That's how much power that was indeed. It was incredible.
No wonder it took us months to convince ourselves the December the December event was more normal, we say.
It was similar, consistent with these masses. The candidate is in between.
Again, we said we sent a member of the family. This is actually a few more details about that detection.
This is what they showed you before. Just the raw data minimally filtered.
This is the numerical simulation I showed you before medical relativity simulation for
two black holes compared with the template that we used to find it an approximate,
approximate template and with a reconstructed template that we can use just by cross correlating the date that without using any assumption.
So you can recover the template if even if you don't know anything about the wafer.
That only happened because this is such a strong signal in general, you can not do that.
If you subtract the signal from the data, then you get noise.
So this is the Time series I was telling you about before that you can reconstruct an amplitude from their spectral density.
This is another way we like to plot it. This is the colour plot that shows the normalised amplitude of the wave.
So blue in here is normal noise. And this is time.
This is frequency. So this is a time frequency plot.
And this is showing you in Hanford that the signal gets brighter, larger amplitude,
higher in frequency, and then it gets the node at the highest frequency and it disappears.
This is what we call a took and this is in Hanford, this is in Livingston.
You see that it's demoed in Livingston and Hanford.
So you would say you saw it. It was Lanzarote in Hanford and in Livingston.
But here you show the the same amplitude, they are the same calibrated amplitude.
But Livingston had a bit higher noise at these frequencies than Hanford did.
So the signal to noise ratio was higher in Hanford, the Livingston.
That's why this is brighter than that. But they have the same calibrated amplitude.
So there's a lot of information in these plots thing more than people usually assume.
But this is not how we found the signal. We are not plotting this time series on the screen to see all of this.
The gravitational body would have to be too many graduate students to do this in parallel.
So what we actually do is we use something called smart filtering, which is a cross correlation,
but it's a cross correlation of a template that we suspect this in the data with the data itself.
So in this example, the red is the data out of the detector that may or may not have a gravitational wave in this simulation.
We have injected the gravitational wave into there, but you cannot see it's hiding in the data.
So we show it to you in blue. This is a gravitational wave hiding in the data.
So if you know you are looking for this kind of wave form, then what you do is you take the wave form of any amplitude.
It doesn't have to be the same when you take a white form of any amplitude and then you cross correlated with the data as a function of time.
And that is what this movie is showing.
So that cross correlation gives you a random number that has some distribution.
Until it finds something in the data.
So if there is something similar to the way from your looking forward,
then that will be a peak in this time series, which is a signal to noise ratio time series.
And then if that peak is larger than what you expect from the statistics in the noise, you call this a candidate.
Now this is a candidate in one detector. You do this, you do this for tens of thousands of templates in one detector.
And then you do the same thing with tens of thousands of templates in the other detector.
And you have a list of candidates. And now you look for candidates that within a ten millisecond window that slide through that window,
we actually use a bit wide that window to account for possible errors, 20 milliseconds.
So you look for coincidences within a time window.
And if there are coincidences, then you check that the template that produced this big is consistent with a template that produced this big.
And only then you call that a coincidence.
Now. How many coincidences do you think we found in that in those four months of data which weighed about 50 times of coincident data?
We found about 2000 of those concerns as.
But we know that most of those are not astrophysical.
Sometimes you find that coincidences off a peak just by chance.
And you would think that these things are easy to pick. But our data is not as clean as this at all.
Our data has a lot of glitches that even in the raw data you can pick up.
So this picks up even more. So you have lots of spikes and sometimes they had a quality to by chance.
So we have to be careful and differentiate a real astrophysical coincidence from one that is not.
Tell you a bit more about that statistic. But let me show you now what this looks like for the second detection, the December detection.
So I am plotting here in red. The Hanford data is in blue.
The Livingston data. I have mistakenly deleted the time scale, but this is a second in here, one full second or the fraction of a second.
And you don't see that way for just don't see it in the filter data.
There's no way to filter the data, but in a reasonable way that shows it as obvious as for the first one.
So I have to superimpose in the template that we used to find the data.
So that's just like in the example I showed you before, I have to plot it in there to show you that it said, but that's not how we found it.
We found it in this signal, the Noise Time series, because it produced a big, big in Hanford, a bit smaller peak in Livingston.
And it was because the same template views these large amplitude peaks within one millisecond in this time.
In this case, it wasn't seven millisecond. It was just one millisecond time difference that we knew that this was a detection to.
This is a statistic that we found. This is how we say this coincidence is not just any coincidence.
It's very significant. I told you that we calculate the signal to noise ratio in one detector, a signal to noise ratio and the other detector.
We make some weighting in those with chi squared and then we combine those two numbers.
So we have a number that we call a detection statistic that measures the loudness of the signal.
This is a number of events that we found, a histogram of the number of events we found number of coincidences versus this loudness.
So this was one our loudest event.
This is one we found one event that had the loudness of about 23.
We had another event that had the loudness of 13.
We had another one that had 11 and something, but we had like a thousand coincidences all together of smaller loudness.
The statistic of a we had like a thousand in these 50 days of data.
So there are lots and lots of coincidences, but we know those are not all events,
because if we calculate how many coincidences we expect as a function of loudness,
we can say that some number is, is, is significant and some other not some other number is just consistent with not.
It's the way we do that.
The way we would like to do that is see our experiment and say there are no gravitational waves in the experiment, but we could not do that.
The nice thing about gravitational waves is that they bring very beauty information because they go through everything,
but that's why we cannot see them.
So what we actually do is we fake the data one detector, we add to the clock, one detector to 10.32 one 6 seconds, some arbitrary number of seconds,
such that when we do the analysis and find the coincidence, we know it's a coincidence in a non physical time window.
So we know it's not that it's a coincidence, but it's Northern Astrophysical signal and we can do this time.
Shifting a million times. 10 million times depends on how much that we have.
The more that we have, the more time shifts we can have in both directions.
So that's what we do. For this signal.
It was so loud that we did.
This time shifts more than 10 million times and we didn't find anything that got the loudest things we find were out of about 20.
And it turns out that most of those non astrophysical coincidences was the signal in one detector with something else in the other detector.
So if we cut out the fraction of a second that had this astrophysical signal in both detectors,
then the number of events with this this blue thing, we didn't find anything louder than 13 up.
So. So this is huge. This was more than Five Sigma.
This one is also heute after.
Even if you don't take this one out, you have to do about 200,000 shifts.
So that gives you the probability, 100,000 of these being an artificial noise.
Coincidence, a false alarm. But if you take it away again, you don't see anything like that.
And the ones you see are more lost. But not all the coins.
Is this signalling one detected coincidence with something else?
So this one was also a very strong detection. This one not so much for this one.
You only have to do the equivalent of two years of data to see coincidences are just as loud.
So that means that once every two years you expect a coincidence by chance.
Like this one, we saw one in 50 days. To me, that's not the detection, but that's how you do the statistic.
The templates that that found these signals are shown in here.
The one for the largest one is a short template, large black holes.
The one for the December one is no one has a longer signal, one second signal there than one in between.
So this is all we found for binary black holes. Now my favourite part and I'm running late so I begin to go fast.
But I want to do this. My favourite part and I hope this works, is to play what they call gravity music.
This I showed you the frequencies they had near 100 hertz.
They start at 40 hertz. They they coalesce at about 220 hertz.
They bring down at 250 hertz. Those are frequencies we can hear.
They're not very musical, though. So you might remember having heard these.
But let me let me see if I'm going to have you here.
If the sound works first, what we call the natural beat, that is the minimally filtered signal.
Put in a speaker. I said wipe us waves sound.
That's a December one. This is the September glut.
One is long. The other is short, but they're not very musical.
So we added 400 hertz, and that's what you probably heard on YouTube.
We like that. We call it gravity's music.
Okay. Let me quickly give you some more details and then you can ask me a lot of questions.
First of all, the first one was so loud that the way we sounded is not looking at the Time series, but with an online system.
We had testing. We were testing on that day looking for bursts.
This is cross correlating the signal between the two detectors and looking for cross cross correlations without templates.
Actually, they divide their their coincidences, their cross correlations in three classes.
One that we know it's mostly noise, one that has increasing frequency.
So it has some pattern to the frequency and another that it has increasing frequency, but also a bit of noise.
So on the key on what we call the clean sector, this one that has increasing signal, then there is this very significant detection.
Notice that the second one did not appear. The second one and the candidate were not found with this method.
But this could be found if you bought this second class of sources in there.
We do find some other coincidences. So the probability of this one is not as high as with much filtering.
And that's because we do have transients in the signals we call these little glitches.
We don't know where they come from. There are glitches in the detectors.
In both detectors. About once an hour, they're not coincident.
So we know they're not gravitational waves, but we don't know where they come from.
We don't know how to eliminate them. And we can calculate that there is by chance they could be coincident.
And that's points of which sensitivity to these transients, if they are of that form.
But this is another powerful method. We have to find gravitational waves using templates.
However you can find parameters. We have tens of thousands of templates, each of which has several parameters.
It has the two masses, the mass and the spin of the final black hole.
We know that the final black hole will be spinning because it has the system has angular momentum from the beginning,
from the to it from the two black holes. Even if the black holes are not spinning, there is angular momentum in the system.
We can get the distance, but the distances coupled with the all the inclination of the orbit, we are more sensitive if this signal,
if they orbit is parallel to the plane of the detector, we are almost insensitive if it is at all.
So we have a scatterplot of the match of all these templates in all these planes.
This is the mass must play. This is the largest mass, the smaller mass.
And then we draw a 50% contour and then 95% goes to this line.
And here is a diagonal line because these we this is always the heavier mass.
So when I say 29 and 36 solid masses, well, it's 36 plus minus the feel.
This is a 90% confidence protection, 36 and 29 plus minus a few more.
So that's how we measure the error in. I would put out metres too.
This is the 62 solid mass, the final mass of the black hole on the speed.
The speed is all of this being calculated as a fraction of the maximum spin is the black hole cannot be more than
a certain amount and that certain amount is when the points in the horizon are moving at the speed of light.
The black hole cannot move, cannot spin any faster than that.
So we call that speed one, and then any other speed is going to be less than one.
This final huge black hole was spinning at about 70% of that maximum spin.
This is the distance is about 400 megabytes, six.
That's 1.3 billion light years away.
This event happened 1.3 billion years ago when on earth that would just multicellular organisms getting organised.
Imagine everything that happened when this gravitational wave was travelling and that's the way I like to think about it.
So that's how far it is, but that has about the 50% error in there.
And notice that this is this has a strange shape.
It's most likely that the system was face off meaning.
Then the angular momentum was pointing away from the from the earth, from the line of sight.
This would be face on and this would be edge on.
So it is probably because it was face on that was so strong.
And this is a localisation. Localisation is mostly from these seven millisecond time difference.
The time difference between two detectors gives you a circle in the sky.
If it is zero, if you have no time difference, then you know it's halfway between the between the detectors, and that is simply in the sky.
In this case, it came first to Livingston, then to Hanford. So it was in the South Hemisphere, but it's still a circle.
And you can tell that some points are more likely than others because of the amplitude and phase comparison between the two.
The thing that's similar to detectors, but that's not very good localisation because these are the same plots for the three three years I
was telling you about the first detection and getting the mass must play in the December detection.
Notice they said this is longer, so it's that much thinner release that doesn't give you better mass, especially in this direction,
but it gives you a better but a better combination of parameters that is called the two mass of the system.
That is that we can measure the best. Again, these are two final buzzes and final spins around similar.
This is the spin, the initial spin of the black holes projected over on the angular momentum, the direction of the angular momentum system.
So it's a next being so good. It's zero. Is it two?
If the black holes are not spinning or one is spinning up and the other is spinning down on,
we can tell only for the longer signal, for the December signal that at least one of the black holes was spinning.
The nets being projected in that direction is about point two.
So we can tell quite a bit from this thing that we can also test general relativity.
This is a test on different pulse, Newtonian parameters, and this is the fractional accuracy,
the the limit that you can put in that fractional accuracy of general relativity.
So that's a fractional deviation from g r on for the theorem for the lowest Newtonian, but you get the best and that's about the 10% test.
But that's not very good. 10% test. We have much, much better tests of general relativity from binary pole sets, for example,
we have like a thousand now, so this is not as good, but we have this off order of magnitude in here.
So that's about the fact that of two or three on these higher Newtonian orders and these are the first kind of tests
and these are strong field effects and that's because we are shooting a very different with them than other systems.
We looked for Biden and it was suddenly close. We didn't find any.
I can go back to this to tell you that we will find this later on.
This is showing that even in Initial Largo, it took us years to get to that sensitivity I showed you in the beginning,
saying we think it's going to happen with Advanced Largo.
A few years ago, we had made this plan that was just a guess on what sensitivity we would have in 2015.
It was somebody with Bloomberg in 2016 and 2017.
We would actually spot on. We would in the lower part of this, but 2015 and that's when we got our first detection.
But we haven't made a lot much of a dent in this green band yet.
So this is next science, the next upsetting one.
But we think that we will be progressing. So this will be will start to run.
That will be somewhat on the upper side of this green band this year.
We start that in December would take about six months.
Ron Virgo will join early next year. Then we will be here and then sometime, maybe 2000, 1919 will be on the design sensitivity.
And all this time now we know we will be detecting black holes, but we are going to be detecting other signals too.
So that's very exciting. This is how in the press, this is the sensitivity that was with very preliminary calibration measured at Livingstone.
Oh, this blue was what we had in in February, just after the run.
That was 80 megaparsec until the green is what we had just after the run.
The blue is what we had October 11th and that was 95 make up out of six.
So we had to be better than we were. We wanted to be at the hundred.
Not quite good. But we you get good. And life is not the only story.
I told you that we will be joining next year with some lower sensitivity, but then they will catch up.
Khadra is a Japanese detector's underground cryogenic that would probably begin operating 2000, 18, 19 or so.
India is going to be building the new side, the new observatory next year.
So we'll probably have a detector, reliable detector there, 2024 or so.
So there's going to be a network. You all are going to be hearing about more and more black holes and then neutron
stars and then other gravitational waves from this network and from future upgrades.
It's a very bright future and we are also hoping to see gravitational waves in coincidence with other kinds of ways with electromagnetic waves.
That's what we expect from merging of mutual stuff. But even with black holes, we look.
I mean, people, astronomers, not we, but astronomers look for those neutrinos.
We also look for causes as we extend those if these are supernova.
So this is going to be multi messenger astronomy.
And this is coming. This is going to happen. It's going to take time.
But this is happening. And this is just one window that we have opened in the gravitational wave spectrum.
But there's a whole spectrum of gravitational waves.
We know that small, smallest black holes and neutron stars produce gravitational waves in this frequency band.
Massive black holes and white dwarf binaries.
And the galaxy will produce gravitational waves in the frequency band of a space detector, which has been approved by a European space agency.
We know that supermassive black holes and perhaps the inflationary background
produces gravitational waves of wavelengths that are appropriate for bolster timing.
This is like having an interferometer using the radio beams from neutron stars.
It's like having a galactic interferometer. That's the way I like to think about this.
And early universe. Gravitational waves can be measured through the polarisation of the cosmic microwave background.
And we saw this as thing that it wasn't quite.
But it's coming. These detection textures are getting better and better.
So this is just the beginning. We're going to have more and more of these and all of these in the next decade.
This is a great beginning. Thank you.