Through the.
So I will continue with discussing what we actually learn from observing gravitational waves and what type of questions this this poses at present.
So this is an extremely exciting time because finally it's possible to detect gravitational waves.
And we can see in places in the universe which were originally completely hidden.
So we can now basically see through that scene the darkness and and see what's out there.
So this is very exciting because it's a completely new window on the universe.
And we can look at previous instances when this happens when different electromagnetic bands were opened up for the first time.
There was there were always very interesting new discoveries that happened.
So when the first time radio observations were made and after that actually supermassive
black holes were discovered because what was seen was at the centres of galaxies,
there were very bright radio sources and these are now known to be supermassive black holes.
As gas flows into near supermassive black holes, they shine and they can they can even outshine the whole host galaxy.
So we found something completely new and unexpected.
And similarly, for example, in the cosmic microwave background, of course, we see the light of the Big Bang, basically.
And so this was a great unexpected discovery and so on.
And so now we have the gravitational wave sky we can finally detect based on waves.
And since five years ago or than 2000 feet, so maybe now, eight years ago.
And so it's very exciting to see what is there to see.
And we don't know a priori. There are predictions that there should be black holes and maybe black holes are emerging and
neutron stars that we can finally go out and contrast the theories with the observations.
And the Nobel Prize was already awarded for the detection of gravitational waves.
But now this is a completely open field, because the explanation for why you see gravitational waves is actually completely open.
And there are there's a large range of frequencies where you can you can detect gravitational waves from nano hertz,
which Steve was just described previously up to the Hertz kilohertz regime.
So this is legal, the Earth based instrument, and this is using pulsars as the clocks.
It's basically radio telescopes or antennas.
And in between, there's going to be in the future, Lisa, which is going to be a space mission that three satellites are orbiting the sun,
trailing the earth, and they exchange laser lights and they can measure distances in space on a different scale, a much larger scale.
And so you can detect much longer gravitational wavelengths in this way.
And so here's the landscape of of different frequencies that these different instruments can detect.
And this is the characteristic strain. So this is the gravitational wave amplitude that the instruments detect.
And you can see the sensitivity of these instruments as standard procedures and different types of instruments.
And these are the source populations that are expected. So here at very low frequencies, we expect to see supermassive black hole binary in spirals.
So you have two supermassive black holes and on relatively large orbits of of order year periods or ten year periods.
So these supermassive black holes are orbiting and emitting gravitational waves and disturbing the lights of pulsars.
And these this is what we can see. And so we learn something about the abundance of supermassive black hole binaries in the universe.
Here you can detect shorter wavelengths of descent roughly the size of this instrument, or that the wavelengths between the sun and the earth.
And on these skills, you can detect the mergers of supermassive black holes collide.
And so this would be hopefully in 20, 32 or maybe sometime around that period.
And Lego is already operating and there's the European counterpart, Virgo, and also to the Japanese instrument, very similar to Lego.
And these are detecting waves between ten hertz and 1030.
So that's it's already operating.
And this can detect very short wavelengths, the gravitational waves, which are produced by stellar mass black locations or neutron stars.
Or maybe distorted balls are even. So this is what you should see.
So we can finally detect signals which are coming from places which are completely hidden in the universe.
So we have two black holes orbiting and they are distorting the background light of, of, of the of the universe.
So this is how it would look like in electromagnetic bands.
But now, of course, we can also detect directly the signal which is generated by the black list, which are gravitational waves.
And so as the black holes come closer and closer,
they are orbiting faster and faster and each other and then finally coalesce and form a stationary rotating black hole.
And so this is how the wave form looks like. Initially,
it's the two blackboards just orbiting around each other and wide orbits and but gravitational waves are carrying
the energy from the system so that the orbits shrink and eventually the black holes coalesce in this part.
And then a perturbed black hole settles, then the stationary black hole in this ring down phase.
And this is what we can measure. So we can, Steve, as Steve explained very nicely.
And so there are many signals that were already detected.
And here are some examples. They are given names based on the dates that they were detected on.
And there's now a whole array of these detections.
And just by measuring the signals of the gravitational waves, you can learn about the sources that generate these signals.
And, for example, you can then you can just measure or infer the masses of these merging objects.
And here are the different sources. In no particular order that were observed in gravitational waves.
You can see that some of these have masses up to 20 or 30 solar masses merging with each other and producing a merger remnant,
which is higher than 50 solar masses in many cases.
There are some where you have lower mass black holes of a few solar masses merging with others, and you also have neutron stars merging,
which are have masses of 1.4 solar masses, roughly speaking, and they produce something which we don't know exactly what they are.
But in future, in the future versions of these instruments,
you can see whether or not they are black holes or it's some kind of a of a exotic neutron star.
For example, there are these other points in this in this slide,
which would show actually the electromagnetic previous electromagnetic observations of both neutron stars and black holes.
It turns out if a black hole is orbiting around the star it studies orbiting around the black hole, the star can can see the black hole.
And so the gas flowing into the black or shines. And you can detect it with electromagnetic radiation and infer the presence of the black hole.
So this was this was done before these gravitational wave detection were made, but they found lower masses.
As you can see, these black holes often have much higher masses.
So this is already something interesting. A new. And so by measuring these signals, you can learn about the parameters describing.
So here's a long list of all of these signals and some of the parameters that you can measure.
So you can measure the masses, as I said, of both objects. But it's not a very accurate measurement.
There are some error bars, and this is showing the confidence like distribution function of the inferred mass for the two objects.
So in some cases they are narrow and in others they are quite poorly constrained.
You can also infer the mass ratio from these parameters, which are often poorly constrained, as you can see.
But you can also measure the spins. So the black holes are spinning.
They have angular momentum. This progenitor star has angular momentum.
So you expect the black holes to perhaps they're spinning.
And you can measure one component of the spin, which is the component.
So spin is normally a vector, but the component along the angular momentum to the direction of the orbital axis,
you can measure the spins along that in that direction relatively accurately, as you can see with some large error bars.
But you can see a magnet and you can detect the distance to the source.
So this is basically all you know. And so then you can look at these distributions, what comes out, but what did the instruments show?
And so this is, for example, you can plug the mass distribution of these detections and you can see that this is what they get.
And so this is based on 100 events that were detected or 90 events that.
You can see that there are lots of events with masses between, you know, up to ten stolen masses.
But this distribution extends all the way to 70 and actually beyond.
Now they're newer detections extending to even beyond the 100 similar masses.
As I will show you, this is somewhat surprising already.
So they are somehow very massive black holes in the universe, which we didn't know of previously, which are actually merging, which is interesting.
And so you can you can also plot the mass distribution of the primary black hole mass as a function of like the density of them in the universe,
the merger density in the universe. And again, you see that this is peak that there and then but the distribution extends to the larger masses.
So the heavier ones are easier to see because they they produce stronger signals.
So that's why the mass distribution I showed you here extended to two higher masses.
So we see more of the massive ones. And you can also see that spins.
So how quickly the black was spinning and there's a maximum spin that the black horse can have.
So this is this is so the spins are usually normalised to the maximum.
And so this is if they are, they have spin one that means they are maximally spinning in that case and that the geometry
is basically swirling around the black hole at almost the speed of light at the horizon.
And if the black holes were spinning even more rapidly than you would see a naked singularity.
And there's a conjecture that that these types of blackness does not exist.
And if you collapse a star into a black hole, you never form anything above unity, spin in this in these units.
And so so you can you can see what the observations show.
And they seem to cluster and zero.
So the so the spin component in along the orbital axis seems to be close to zero, which is somewhat surprising, as I will show you.
And you can look at possible the correlations between these these parameters.
Is there correlation between mass spins for individual sources? But there is no clear trend that you see.
You can also look at the rate of at which the black was merged in the universe.
You can you could already measure this with the first two detections that were announced in 2016.
And the merger rates at that point were quite poorly constrained.
It was between two and 600 per gigabyte. Q Per year in the universe.
But there's more and more detections came along. The error bars shrunk.
And so at the at present, and it's even better known now, it's around 30 gigabytes per year.
And there's there were also detections of neutron star neutron star mergers.
So there are now three detections, as you can see.
And that and the merger rate is quite poorly known.
But it's it's it seems to be much higher than the rate of black hole backflip mergers.
This is not surprising because there are more neutron stars in the universe than black holes.
But they are only more by a factor of three.
So it's somewhat possibly somewhat surprising if if this number is much higher than if you compare to the or black or.
There's also examples of black hole neutron star coalescence is that you can see in the future.
You can also make plots of the merger rate how it evolves with Redshift so the distance from us.
So Redshift as the universe expands, describes the distance to the sources and the cosmological scale.
And you can you can basically measure how the merger rate changed in time as the universe evolved.
And you can contrast that theories and try to learn about the sources.
And they are future extensions of the present instruments.
And so currently we have legal, but in the future we will have like or A-plus is a advanced version of the advanced legal instrument.
And and there are different instruments being planned on earth.
And this will reduce the noise in these instruments so you can increase the sensitivity to larger and larger redshifts.
So when these future instruments come along, maybe in ten years you will see basically all of the mergers to do almost 100 redshift,
which is even beyond the time at which the first stars formed.
So you can see and most of the mergers in the universe, at least at these mass in the in these massive changes.
And so based on the rate of mergers that we already know,
we can calculate how many mergers there are in the universe in a in this volume that we can detect.
So at the moment, we are limited to redshift of 0.5.
So there are one, two, three mergers per day, but we don't see all of them because the instruments are not sensitive to all directions equally.
And but this is the order that we see there, rates that we see it at present.
But when we see it shifts up to two and we will see a couple of mergers per hour.
Based on this rate. So we can we can start asking questions about the sources.
So what what are we seeing? So the big questions are how the black hole has form and how did the binary form?
Why are black holes in binaries and why do they merge? Why do they come so close that gravitational waves can actually merge them?
Turns out this is this is this is an interesting question because you need to put the black was very,
very close such that the gravitational waves actually merge the black hole is otherwise it takes too long.
So if if the the black holes are at the typical separation where we see stars to be in binaries,
they will only merge in much larger time than the than the age of the universe.
So in order for them to merge, you have to put them at a distance, which is less than the earth from the sun.
You have to put two black holes, the masses of tens or 30 solar masses at on the scale of the mercury through the sun such that they actually merge.
But what is the process which takes them to such small distances so that they can merge the two gravitational waves?
And so the big question is what are the most likely environments for mergers?
Do mergers happen in the in the galaxy, in the galactic disk?
Do they happen in the galactic bulge,
the central regions of the galaxy or star clusters like globular clusters or the halo which surrounds the galaxy, as I recall.
So these are some of the possibilities and let me just take you through some
of them and the big problems that each of these areas are face at the moment.
So first question is how do black holes form a binary?
So, so the simplest idea is that we already see stars to be in binaries, often especially massive stars.
And we know that black holes form from massive stars, lower mass stars form white dwarfs typically,
and higher mass stars form neutron stars, and only the highest mass stars form black holes.
But these higher, highest mass stars are often observed in binaries.
And so this is these are observed. And and so you can you can you can you can ask what happens with these binaries at late banks.
So eventually the stars run out of hydrogen and they expand, they become red giants.
And at that point they can transfer mass to the other star.
And ultimately the star explodes in a supernova explosion and turns into a black hole.
So then you have a black hole and another star surrounding it.
And this black hole can actually suck matter from the other star and shine in X-rays.
So this gas, which is flowing in the direction of the black hole, is observable.
So you can observe this stage of the evolution. And then there's this star also explodes as a supernova.
It forms another black hole. And so you have a black hole. Black hole binary.
But there are open questions. So but let me just show you some some of this in more detail.
So this is an example for what happens if you start with the black holes,
the water mass of 100 or 90 and 60 stories is then ultimately this one of the
stars expands and stands for some mass and then it turns into a black hole.
And and then the other star expands.
And there's a phase when this star is actually engulfing the black hole.
So it expands. Red giant becomes so large that it actually engulfs the other objects that the black hole is now moving inside the other star.
And ultimately the star turns into a black hole.
And and then you have two black holes at short distances, which then merge into gravitational waves.
And so you see that there are many stars in each galaxy.
Then for the 11 stars, let's say, and we know what fraction of them are massive.
And so all of them turn into black holes. And so we have an estimate of how many black holes we should have in each galaxy.
And it's quite a large number, 10 million to 100 million black holes in each galaxy.
But the question is how many of them are in binaries? Let's say most of them because massive stars are in binaries.
But how how many of them are actually in such a closed binary that they have these
carbon envelope phase that they can actually go so close that they can eventually,
which is an open question. And and most massive stars are in wide binaries.
So that that that helps. And some of them are in theatres so that there may be a third star which is which helps the merge the intervening.
But so there are some open questions with this theory.
And here are some of them. So basically, all of the all of the points I've laid out here.
Are poorly known. So there are so many open questions.
There are basically three parameters in all of these theories.
And and you're constraining these three free parameters with observations.
But then the question is, if you have so many free parameters, what can you actually learn from these types of observations?
And so you can see that the biggest question is what happens during the common envelope evolution?
This is poorly understood. What happens to an object inside another star, for example?
And the only point where you don't have question marks is the last point that we have two black holes.
It's move, you know, in response to Einstein's equations, and they emerge because of gravitational waves.
We only know this part. But so what can what can we do?
How can we make progress? And we can look at the observations.
So as I told you, you can observe the part of this evolution when there's a star and a black hole next to it.
And so these are X-ray binaries, and you can measure the masses of these X-ray binaries and they turn out to be clustered into two categories.
One is around 1.4 solar masses. These are believed to be neutron stars and others are around ten solar masses.
These are believed to be black holes. And so what we see is the gas flowing into them.
And based on the spectra, you can infer that these masses and you can also look at the spins.
And so but here so the big question is, why are the merging black holes that Ligo's see so massive?
It's unclear. Especially if you think about stellar evolution.
It turns out that the prediction, the theoretical prediction is that you should not see any black holes with mass
higher than 50 solar masses because they just cannot form from stellar evolution.
If you have a very, very massive star, it will typically shed most of its mass and so it will just lose its mass in vain.
So there's a solar wind coming out of these massive stars and they they lose so much mass that the remnant is typically smaller than 50 solar masses.
If it if it was bigger and there's an explosion as instability and an explosion which just pushes the star apart.
And there's this these pairs form these particle antiparticle pairs form and and you expect to see no, no black hole left back with higher mass.
So so this is an open question why we see black holes with so high mass in in the observations.
And the other question is, why are the black holes not spinning?
Because, first of all, theoretically, you expect them to be spinning because if you have a star in a black hole next to it,
mass is flowing into the black hole which spins up in the black hole.
And the other thing is that the black hole is orbiting the star, which spins of the Star.
These objects are very, very close. So they have strong tidal interactions.
And so you expect to see very highly spinning stars, which should conserve their angular momentum as they collapse through a black hole.
And so you expect to have very highly spinning black holes in the end.
And indeed, the X-ray observations have shown that there are only three objects which have each are progenitors of black hole, black hole mergers.
So these are the so-called high mass X-ray binaries where the donor star will turn into a black hole and not a neutron star.
And all of these observations indicate that the spin is large for these for these black holes,
but the gravitational waves so that the merging black holes are actually not spinning highly.
So this is another indication that maybe this is not the possibly not the correct theory explaining the sources.
Okay. So is there anything, any other idea around?
Well, there are. There's a very famous one called the Dynamical Merger Channel.
And here the idea is that you have globular clusters or galactic nuclei which host very large population of stars in a very small region.
So you have these globular clusters where you have roughly a million stars in a very small region of one parsec, one light, a few light years.
And so you have a million stars, whereas in the galaxy,
the closest are through to earth and to the sun is the next one is is the same is a few light years away.
But here you have a million stars in that region. And so in this case, you have a possibility of close encounters between these stars.
So you can form binaries dynamically as stars approach each other, or three stars come by.
They have a complicated gravitational interaction,
and one of the stars is ejected and the leftover stars form as a stellar binary, which can then merge.
And there are further interactions with other stars, and this can reduce their separations to the scale we need for gravitational waves to merge them.
And then galactic nuclei are even denser environments so that these very centres of galaxies,
you have supermassive black holes and in that region you have the density up to 1000000 to 1000000000 times larger than indigo in the field.
And so the possibly the rate of merger will be higher in that region.
And so you can calculate what is the encounter rate between objects and which which come close and which can shrink the binary.
Once you have a binary and this turns out to be a scattering process which is proportional to the square of the density.
And in this region, the scale of the density is ten to the 12 to 10 to the 20 times higher than in the galactic sphere.
So here this process can actually happen and you can simulate that.
So this is a theoretically clean problem. Not, not, not like stellar evolution that I showed you,
because here you just have point masses moving around that you can put on a computer and see what happens.
And so here is a simulation. And.
And so this shows that black holes are moving around and stars actually in simulations.
I think they are only stars, but in others they are black holes.
And it turns out that the central parts at the centre, the massive stars segregate in the centre,
they form binaries and they start ejecting other stars that they encounter.
And ultimately the cluster loses a lot of many stars because of this.
And, and eventually in the in the simulations, the cluster disperses completely.
So these star clusters are a transient phenomena.
They should not last forever, but luckily and deliver the early time in the age of the universe that these are still around.
So you can still use them as probes of of of of astrophysics and and they provide a channel for gravitational wave sources.
So there are many processes that happen. So there's a dense population.
There's a possibility for three objects to come close.
And so there's a scattering encounter which forms the binary.
And then there are these binary single interactions and binary interactions, the massive objects seen through the centre.
And eventually you have memories which come so close that they emerge because of gravitational waves.
So this is the ADF and you can use these theories and simulations to make predictions for what should be the rate of mergers,
what should be the mass distribution of mergers, that spinning the distributions, and you can then check with the observations.
And. It turns out there are some problems.
But let me just show you how this may look like in nature if you just looked at it.
So this here at the very centre, there's a there are black holes flying around at the centre of the globular cluster.
They seem to, because they are more massive than stars and they distort the light from,
from the background, stars and arrows of stars flying around this region.
And then and so it's quite a dynamic environment and you form binaries and eventually they merge and by
studying gravitational waves you finally can look in this region and see and detect signals from these.
These are highly dynamic, dark regions of spacetime.
Okay, So. So what is the prediction for spins? So the implication is that it should be centred.
Well, this is the observation. So there. So the prediction is that if you have an isotropic distributed cluster, so it's based on the assumption,
but you assume for the initial spin distributions, but if the spins say it's a spherical cluster,
you can assume that it's a isotropic distributed cluster and that there's no particular
reason why you should expect this things to be in any particular direction.
So it's the assumption is that in globular clusters,
the spins of these black holes may be arbitrarily isotropic and you form binaries back there in close encounters,
which do not synchronise these spins.
So you can have these black or black or binaries, and there are these exchange interactions when black holes can pick out stars from an
existing binary and sit in their place and then another black can kick out the other star.
So you can form black or black or binary with an arbitrary spin direction.
And in this case the component along the orbital angular axis, which is the component that is measured, will be distributed around zero.
So this is the prediction and it matches the observations.
So that's so far so good. But the rate of mergers is the prediction is too low.
So if you look at the simulations and so they are Monte Carlo Markov chain and
direct and but it's information that I just showed you and these simulations
is a complicated simulations run run them on a supercomputer and get that the rate of mergers in the universe should be around six per gigabyte.
You pretty? But the observed rate is between 15 and 39 gigabytes 60 per year, so it's a bit lower.
So why is that? Is it is it possible that you just made some error in the numerical code?
This is the first thing that comes to mind. But actually, this number makes sense.
So you can you can understand this. So if you assume that each black hole merges at most once.
So this is an upper limit. Let's say all of the black was merged in the cluster.
And you can calculate how many black holes you have in the cluster because you see how many stars you have and you know,
what is the mass distribution of stars and you know, how many of them will turn into black holes.
So you know how many black you should have in a cluster and you see how many globular clusters you have in the universe.
And if each of them merges once in the age of the universe, the present stage of the universe, you get a rate.
And this rate turns out to be 40. So this is an upper limit for the past couple years.
So if all of them are but the simulations show that only 20% of them merge and only about 10 to 20% of them actually form binaries.
So most of them are single and only half of the banks merge.
So the rate of merger is a factor of ten lower, so you get from 49 to 4.
But this is just the rough estimate. So actually it's around six, but you understand where this comes from.
And still so this is an upper upper limit type estimate.
So so it's not clear If so, you might be missing most of the mergers here.
This is the bottom line. And you can make the for the mass distributions.
It turns out that more massive black holes emerge more easily in these systems.
And you can plot to the expectations as a function of mass ratio and total mass.
And most of them will be merging at high masses.
So those are the ones which sink to the centre and have the most encounters with other objects.
And there's interestingly a small population here with even higher masses.
So so you form black holes with masses lower than 50 solar masses.
And let's say these merge over here. So they have a mass ratio of around 1 to 50 smaller mass that holes the total mass 100 at maximum.
But once they merge, they form a remnant. And this remnant, if it's not kicked out from the cluster, can merge again.
And so you can predict what is the fraction of population which merges again.
So these are the second generation mergers, and these are possible in globular clusters if the progenitor blackhole does not seem rapidly.
And in this case, 5 to 10% would be second generation mergers.
Third generation mergers are difficult to produce in globular clusters because that would that merge.
They experience a gravitational wave kick.
So the emission of gravitational waves is not isotropic and there's a lot of energy carried away by gravitational waves.
As Steve mentioned, there's three solar masses, M.C. Squared energy carried away in in not exactly isotropic.
If some of it is carried a is is ejected in one direction is emitted in my direction.
Then the black hole will be kicked in the opposite direction. And so there's this kick that the remnant experiences.
And in these environments, then the gravitational veil is relatively shallow.
You ask the escape velocity from these globular clusters is relatively low.
So you expect some of these black was to be objective. And if the black hole is actually merge, they produce highly spinning black holes.
And the this if you have a highly spinning black hole, then this kick velocity will be much larger.
So in that case, we expect all of them to be ejected and not merge again in this cluster.
And so this is the question how can Black was merge multiple times and not get ejected?
So it turns out that the measurements indicate that 83 events are one G plus first generation mergers.
So they are consistent with ordinary theory. But five of the events are of this type one G plus two G,
meaning that a second generation black hole is was not ejected and is merging again with another black hole in the cluster.
And this is consistent with the rate being 5% for these ones.
But you also see two G plus two G mergers, two events which are not clear if that happens or higher than the recent events in in globular clusters.
And also, by the way, done. Some of the murderers have eccentricity.
It turns out that the eccentricity distribution should have three peaks for these types of black holes,
which are binaries which form in globular clusters. So there are binaries which which are merging outside of the globular cluster.
They are binaries which merge in the globular cluster and F due to gravitational waves,
and they are binaries which merge during the encounter of three objects.
So that also happens. And it turns out that those are those mergers.
So the ones which which happened during the three by encounter three black holes encountering each other are 5% of all of them.
And and these ones should be eccentric. In that case, they they form binaries.
The merging binary is such a small separation that there's not enough time for the signal for the orbit disaccharides before they merge.
So these should be eccentric. And so this would detect 5% of these globular cluster mergers to be eccentric.
At the moment there's only one detection which is even controversial, which may possibly be eccentric out of 100.
So but in the near future you will have many more sources so you can test this paradigm with eccentricity observations.
And finally, there's the question about the dark matter halo.
So you have the galaxy surrounded by this mysterious massive dark component, which you can infer based on the motion of stars in the galaxy.
And the interesting idea, which came up after the first discovery was if there is dark matter was actually made of black holes,
then it would be nice if if, if this was the case, because then if black holes merge, if these dark matter black holes merge,
then you can actually see them with gravitational waves. They're not dark anymore.
And so there were some observational probes earlier with electromagnetic observations.
So if you have lots of these black holes in the dark matter, then you should see lensing variable light from from different sources.
And this puts a constraint on the masses of these types of black holes.
You also see binaries in the binaries in the galaxy.
It would be disruptive if you would have these massive dark matter particles, black holes flying around in the in the galaxy.
But we see these binaries, so that also puts a limit on of black holes.
But there's a range which is still allowed, which could be the ones that losses.
So that's very interesting that maybe this is just dark matter, but this you.
And in fact, there was a paper which claimed that if 100% of the dark matter is made up, 30 cylinders,
single black holes, and they should produce exactly the same rates that we see that Lagos is.
So this is a coincidence, which is very interesting.
But there are other studies which showed that that there was a miscalculation.
And if you make it make a more accurate estimate, then only 1% of the dark matter is sufficient to explain all of the detections.
And if 100% of the dark matter is made of black holes, then you overproduce the mergers that you see.
And you can also have black holes in principal in the early universe that no one knows if primordial black holes existed,
that there after shortly after the Big bang. But you can prove them with gravitational waves now.
And if only 0.1% of dark matter is in primordial binary black holes after inflation in the early universe,
then those then only those will explain all of the mergers.
So that's very interesting. Of course, it's a little bit speculative.
So I think it's still basically an open question.
So this is the summary. So these are the possible ideas and possible problems that there are.
And so there are some other ideas that I didn't have time to go into.
So, for example, the third, third star around the binary can have merged this binary.
But again, the problem here is maybe there is not enough of them in the right configuration for them to merge.
And the other idea is that maybe in galactic nuclei you have a supermassive black hole.
In that case, supermassive black hole helps to to increase the escape velocity.
So in that case, it's much harder to eject the object. So you will have multiple generations of mergers more easily.
So maybe, maybe, maybe this will be the the answer.
But it's at the moment it's not clear. And dark matter Halo is another possibility, but it's somewhat of an exotic possibility.
And I think I'm out of time. I just want to highlight another idea that we've been pursuing here at Oxford with some brilliant students.
So here we are investigating if there's a supermassive black hole at the centre of the galaxy.
In some cases there's a gas disk surrounding the black hole and the gas can help to merge the stellar mass black holes in this environment.
So you have a star cluster which is observed a supermassive black hole.
Again, you can calculate how many of them will turn into into black holes and you expect something like 10000 to 20000 stellar mass black holes,
small black holes to, you know, orbit around a big supermassive black hole.
In this big supermassive black hole. Keeps these small that close in there in its vicinity.
And there's also gas flowing into the supermassive black hole,
which shines brilliantly and spectacularly that we can see from the other side of the universe.
So this is observed. And so the prediction is that there should be stellar mass black, which then interacts with the gas cloud.
And so you expect to see black holes get captured in this gas clouds in relatively short time.
Within ten years, you can calculate this and you can calculate what happens with objects in gas and they emerge relatively quickly because of gas.
So then you solve this problem of how do you bring the black holes close with the gas dissipation.
And and so the interesting thing here is that you have the possibility of having an electromagnetic counterpart,
the signal, because the object is not just in in darkness, but there's gas around.
So you might excite the gas and produce some kind of a flare.
In fact, one of the events that we observed had an energy and flare in the same region of the sky at the same time and 34 days after the event.
And so there was some speculation that maybe this is related to the observation.
And of course, this is complicated to calculate because there are lots of different processes to include in the calculation.
But we have done some simulations. So this is simulation by congruence.
So we're simulating an annulus of gas. Just the the part of this this supermassive black hole of gas is where you have
two stellar mass black holes embedded in the gas disk and and see what happens.
And so the so the black holes get closer and as they orbit and different radiate different velocities.
And we're just now zooming in to see to see what happens.
Let me just. Sorry. Okay.
Sorry. I can advance it. So the black hole is just come close.
And eventually they form tight binaries. And.
And you can see that perhaps they. They've emerged.
You could not run these simulations all the way to merger, but.
But it's very promising that this is these. In these. In this case, you can form binaries just by single single encounters.
You don't need the third object to form a binary. So it's much more likely to form binaries in these cases.
And so if you zoom in, you see that we have it changing the, the colours, the colours to show it more clearly what happens,
you know, these dense spiral streams and, and the black holes combine and get stuck in a binary.
If you, if you neglect the gas effects you run the same simulations without gas then the objects are just scattered away from each other.
So gas is helping them to form a binary. And here's another student, student Henry Whitehead,
using a different kind of simulation where you actually zoom in and now you take into account the thermodynamic effects,
which are it must make the calculations much more complicated.
And this is what we get.
So it's really, really awesome that you you get basically merging black holes and in this case, you produce these shock shockwaves in the gas disk.
It's just potentially observable. If you look in, if you search for these types of signals.
Okay. So I think I'm out of time. So let me just summarise. So you you have now something like 90 black or black hole mergers.
These were detected by like one year ago and there are many astrophysical pathways, but there are some problems with all of these batteries.
So now it's a completely new field.
It's going to be interesting to see if someone can come along and suggest a completely different avenue to merge these objects,
and maybe that will be the correct one.
But gravitational waves can already probe astrophysical systems in new ways so we can detect globular clusters.
And we can we cannot see globular clusters in electromagnetic bands because they are faint, only the closest ones.
But these ones you can see all the way to the edge of the universe, basically the observable universe.
And so that's very exciting and new type of observation that is possible with these types of instruments.
Also, you can detect active galactic nuclei, new ways and and processes in them.
And so there's a very bright future for gravitational wave astronomy because there are new instruments coming along.
And and so I think it's going to be really exciting for the next decade or so and beyond.
So thank you very much.