Thank you very much, Steve. I'm very honoured to give this talk in front of this audience of physicists,
so I will try to date you with the current status of the explosion mechanism of massive stars,
which has been a mystery for more than 50 years, and which is to some extent still a mystery.
So we know that massive star explodes, massive stars explode as supernova.
So this is a very spectacular phenomenon.
But from the theoretical point of view, if you were to ask a theoretician,
a theoretician would guess that a massive star at the end of its life should collapse to a black hole rather than explode as a supernova.
So the evidence, the observational evidence tells you that there is something which allows matter to to bounce into an explosion,
because the theoretical part, which is very robust, is the fact that at the end of its life, the core of a massive star will collapse to the centre.
And this is the part which is related to the concept of a solar cycle, Hamas.
The fact that when you have a gas of degenerate electrons, then it cannot sustain gravity above a certain threshold, which is about 1.5 solar masses.
So this this part of theory is, is considered as very robust.
And when you have a star which is massive enough to accumulate iron at its centre, at its centre,
iron will accumulate and will not trigger new fusion reactions because iron is the most tightly bound nuclear element.
So the binding the nuclear binding energy of iron is, is, is a maximum.
So you cannot extract energy beyond the iron from the, uh, from the fusion reactions.
And so this iron coil in the massive star has to increase its mass up to the point when it will reach this, this threshold of the size of almost.
So, you know, I don't know how familiar you are in astrophysics in general,
but you know that the sun is very far from this kind of physics because the sun is
just struggling at the moment to to make the fusion of of a hydrogen into helium.
And and and during the 10 billion years of its lifetime, until the sun dies, the sun will reach maybe the fusion of carbon, but not not much more.
Whereas if you if you going to the a star, which is ten times more massive than the sun,
then gravity is strong enough to to trigger the fusion of heavier elements and very, very quickly, uh, nearly 1000 times more quickly than the sun.
So we in a few, in a few tens of million years, uh, a massive star of a of 15 solar masses is able to, to, to, to burn most of its hydrogen,
I mean a large fraction of which hydrogen and to create and create a very massive element such as this ion car,
which will collapse when it reaches the somatic elements.
So what you see here is an example of such a massive star, uh, a few hundred years after the explosion.
So what we see here is in X-rays, uh, the.
The remnants of the explosion, it's gone. It's called a supernova remnant.
The CAS, a remnant. At the centre, you have a collapsed object, which is the result of the of this,
people believe of this collapsing, uh, uh, degenerate core of ion, which forms which we call a neutron star.
So once, once there, the core of a star collapses.
What people understand is that, uh, uh, electronic capture will take place and the electronic fraction of matter will decrease.
So you will have less and less pressure support from degenerate electrons and, and the matter will be made of more and more neutrons.
And, and the, the equilibrium which you can reach in this direction is called a neutron star.
So it's the last equilibrium against gravity that you can think of before collapsing into a black hole.
So indeed, uh, indeed, we find many neutron stars here.
It's just a crust, but it's, uh, it's an object which is ten kilometres radius, about ten kilometres, which is about once 1.5 solar masses.
And those objects are, have very strange properties.
Very messy, very dense, and they are very fast.
And here you can see a recent observation by the NuStar satellite, which observes gamma ray lines in blue.
It observes the gamma ray lines of titanium, titanium 44.
And it revealed the fact that the composition of this ejecta is very ingenious and that even the distribution of these titanium blobs here,
these blue blobs, are approximately in a half plane opposite to the direction of this neutron star in the middle.
So this is the kind of observation which sets strong constraints on the explosion mechanism of of this of these objects.
So the supernova is is this moment when the the inner core collapses to a neutron star and the rest of the star,
which is typically, uh, ten solar masses or more, can be 24 masses,
is ejected and is going to feed the interstellar medium with all the elements which have
been synthesised inside the the star during its life and also during the explosion.
And so, as I said, the mystery is not the collapse, but it's really to understand how this collapse will stop and bounce into an explosion.
And sometimes people are very pessimistic about this, uh, our understanding of this process,
um, as I said, because in the, I mean, the main reason is that in one G we shoot,
if you study this problem in one dimension, uh, you realise that this, uh,
this collapse turns into not a neutron neutron star, but quickly after that, a black hole.
So I don't know if you if you're aware that neutron stars cannot afford to be more massive than a certain threshold,
there is a threshold between two and three solar masses above which these neutron matter cannot sustain the weight of of gravity.
And so if you don't manage to to trigger an explosion early enough, the mass accumulated in the centre will increase past the threshold.
And then you you will collapse the initial sign to a black hole.
And it will be even more difficult to think of a way of producing this explosion.
So the the the property of this neutron star, as I said, is going to help us, uh, guess what's, what are the important things?
Regions of the explosion mechanism.
So as I said, the initial star has a, is very dense, has a very fast velocity, you know, in, in a random direction and which we try to understand.
And the and the environment is endogenous.
And so the new ingredient in supernova theory over the last, uh,
let's say ten years is to really pay attention to the non spherical cocktail of supernova explosions, of the supernova of the explosion mechanism.
And in relation to this, uh, no legacy symmetric or non star recall, uh, cocktail of the explosion,
that there are theoretical arguments to justify such a departure from this very good symmetry involving hydrodynamic instabilities.
So this is the, the, the important ingredient which has been studied in the last ten years.
And the hydrodynamic instabilities have some, uh, nice, uh,
property that the laws of hydrodynamics are valid in stars, but they are also valid on earth.
And if you choose carefully the system, you can really make some, some relevant analogies.
And that is the kitchen sink experiment that Steve was referring to is this image that you see here, which is actually a simple,
shallow water experiment, which happens to describe the same instability that takes place at the centre of a star.
Uh, using the analogy between, uh, first wave surface as gravity waves in shallow water and acoustic waves in a gas.
And this is quite surprising that you can recover with a simple experiment this, uh, this kind of physical process.
So the, the goal of this talk is to, to try to, to show you that the simplicity that we can find in,
in a simple water fountain, uh, is, is connected to the complexity of that explosion.
And it can really help us understand how, how massive stars explode.
So my, my goal in this talk is both to to tell you those are the most advanced efforts to understand that explosions which are.
Still not completely satisfactory, but it is also to tell you about the simplicity of some tools, some new tools.
We have to approach this this difficult problem.
And here there is a numerical simulation by my colleagues in Gucci, which has been published in one year before this observation,
and which shows that, uh, so in green here you have the heavy elements which are produced during the explosion of a supernova.
And so here you have a 3-D simulation which actually predicts that the heavy elements will be produced, uh,
preferentially in a region opposite to the direction of the moving neutron star, uh, which is, which is just born during the explosion.
And so this kind of 3D image would make you optimistic and believe that we understand we are able to model in 3D the supernova explosion.
So I put this illustration here to emphasise one important point is the question of of making of initial calculations on us.
And this this example here is an explosion which has been triggered by putting enough energy at the centre to produce the explosion.
And indeed in this case you have some interesting properties which resemble observations.
But the very big difficulty is to to produce explosion without tuning parameters to to without putting the energy by hand.
So the framework of, of all this supernova research, I mean,
the mechanism of the explosion itself is focussed in a very small window of of space and time.
So the size of this region, of the region, which is decisive for the explosion, for the success or the failure of the exposure,
is a small region of 300 kilometres at the centre of a star, which is something like 600 million kilometres in radius.
So it's very difficult to grasp this, this difference of scale,
but you have to think of of a gravitational potential which is very deep in the centre where the,
uh, which is where you have very extreme densities and, and, whereas the outer path of the star are very loosely bound gravitationally.
And so this big hydrogen atmosphere of the, of the stars is very easy to, to explode, the difficult parts to explore.
This is the in our region where the gravitational potential is deep.
And this the timescales, of course, are very slow for this full star.
But the very in our region evolved on a very short timescale because of the strong gravity and
this iron core as it reaches the this classic mass collapses to a neutron star in half a second.
So you can imagine this iron core,
which is about the size of the moon and in half a second changes shrinks its size due to the to the loss of the pressure support from a
whole atavistic degenerate electrons in half a second and it collapses into an object mainly made of neutrons of a few tens of kilometres,
which later on will shrink to ten kilometres as it cools down.
And so this picture proposed by a beta and we saw in the eighties, um, those people had realised that during this collapse of the region,
the collapse of the region is so fast that the, the outer region is losing to free falling on the,
on this, on this collapsed iron core is going to reach supersonic velocities.
And and unluckily the as the matter hits the surface of this very dense potential star matter is not going
to bounce elastically but a lot of energy is going to be lost into the dissociation of iron into uh,
protons, neutrons and electrons. So if you had an elastic bounce, then yes, you could imagine that the this could be enough to uh,
to explode the star because you're getting a lot of gravitational energy through the collapse.
And this, this, this energy could be transferred into the, into kinetic energy of the explosion.
But this transfer is not efficient at all because a lot of energy is lost into, uh, uh, the binding,
the nuclear binding energy of this iron nuclei which are dissociated into, uh,
protons and electrons because temperatures are so high after this shockwave and.
And this is the real difficulty.
This bounce is not elastic and and one G simulation show that this accretion shock here, this spherical question shock starts propagating out.
Of course, there is a shock because you you have iron elements reaching 1/10 of the speed of light.
Imagine 1/10 of the speed of light. You have something like 4.5 solar masses per second falling at 1/10 of the speed of light.
It's very difficult to think of a good reason to to change the direction of this rain of iron.
But and and this generates heat, a lot of heat, which is partially absorbed into a into this oscillating iron.
And and so unless this rain of iron is is not dense enough.
So for the lightest progenitors among those heavy stars which are able to produce an iron call.
So unless you are in the range of 8 to 10 solar masses, in this case, a11 dimensional scenario like this is is good enough to produce an explosion.
But above ten masses, you are not able in one dimension to to push out this this range of iron.
So the the the reason why this this mechanism is called a neutrino driven delayed explosion is, is because, uh, neutrinos which,
which were produced by the, which were produced by the electrons capture of electron on protons and which are also produced by the very warm,
uh, a kind of blackbody of, uh, neutrino inside this opaque potential star,
this neutrinos take some time to diffuse out of this yellow region, which is particularly thick.
And so it takes nearly one second for this huge flux of neutrino to to escape of this region.
And this is where the jet come comes from.
And once these neutrinos escape, there was the hope proposed by between the sun that the fraction that 10% of those neutrinos would be,
uh, would be absorbed by the neutrons.
Following the inverse reaction here, the neutrino would be absorbed by emission and produce a potent American,
and the absorption of neutrino would seems to be the the best way to power the explosion.
So remember and this will not change until the end of my talk.
The the engine of the explosion is really, uh, coming from, of course, competition in energy.
But the competition in energy has transfer has been transferred into the kinetic energy of ion here.
The kinetic energy of Ion has been transferred into heat as it passes with a shock.
And this heat has generated a lot of neutrinos.
And so the energy is in the neutrinos.
The the the failure of the explosion corresponds to a case where neutrinos escape and matter simply shrinks to a black hole.
The successful explosion means that sufficient neutrinos have been captured in this dense
post-rock region so that the shock is is revived and pushed out to to generate an explosion.
So the energy budget is is summarised here you have the gravitational energy, which is about ten to the 53 hours.
And the observed kinetic energy of the explosion is about ten to the 51.
And so you just need to make sure that, uh, at least 1% of the collapse energy is, uh, is transferred into, uh, kinetic energy of an explosion.
In this, in this framework right here, the rotational energy of such a system, most of the theory of, of a supernova, uh,
mechanism does not want to rely on the rotational energy because the rotational energy, as you see here, stays like ten to the 50.
If you consider, uh, uh, 14 neutron star, which rotates with this ten millisecond period than what one sees as 5 to 10 kilometres.
So unless you have and 10 milliseconds happens to be the typical, uh,
I mean that happens to be the spin period of, uh, of a very fast of the fastest neutron stars.
Uh, some neutron stars are faster than that, but they are accelerated after the birth.
But at birth, a neutron star is, is considered to be like ten, 20 milliseconds, uh, at best.
So you cannot really rely on. Potential energy to.
To power the explosion. So people have tried to develop models without rotation.
Neglecting this rotational effect. And. And the recent ideas rely on hydro dynamical instabilities.
So to to illustrate that with a with a numerical simulation by the Russian group in Germany, you see here in blue matter falling gradually.
It's so this is in blue. The colour scale is unhappy.
Here is the shock, a stationary shock. And you see that this spherical stroke, uh, even though the accretion flow here is, is a perfectly spherical,
symmetric and perfectly original, this accretion structure starts to wobble along this axis.
So by hypothesis, this simulation is actually symmetric so that it looks three, but it's actually a actually symmetric hypothesis.
And there is a symmetry axis here and you see that the shockwave u which measures something like 150 or 200 kilometres here,
this shockwave moves, uh, moves around in what is called a sloshing motion.
And you have on smaller scales, uh, bubbles, bubbles of material heated up by, by neutrinos.
And in this case, this was in 2009.
This was one of the I was the first of initial numerical simulation, which produced an explosion without tuning parameters.
So they in this simulation, they had solved neutrino transport in a in the best way they could.
It was not perfectly accurate, but it was it was not biased to produce an exposure.
And and you see that after some wobbling, uh, the explosion, the shock starts to move out.
The full simulation you've just seen here is 800 milliseconds.
So that's very fast. That's less than a second. And and it was a big success to see this explosion start, even though the.
So at this point, it's not necessary to continue the simulation because once you go out of the of 400 enough kilometres,
you know that the shockwave has enough energy to propagate across the star.
The star is, it will take several days, uh, to, to reach the, uh, to reach the, the outer edge of the star.
Um, but there is enough energy to, to, to do that.
The, the only problem here is that the, the final energy of this explosion is still weak compared to the observed into the 51,000 in kinetic energy.
So it's not fully satisfactory. But it was a big, uh, a big success.
The two instabilities that you see in this, uh, in that you saw in this movie have been well identified over the years.
One is called neutrino driven convection.
It's due to the fact, as I said,
that some neutrinos are going to be absorbed by the material which passes with a shock and which is attracted outward.
So if you want to go into detail, there are two regions depending on the dominant direction of this reaction of electron capture.
So if you if you emit neutrinos close to the neutron star, it's a region of heat, of a cooling, where the ultimately gradient is going to be stable.
Whereas if you are in this outer region, which is dense enough, uh, behind the shock,
it's the opposite reaction of neutrino capture, which is so, which is a region where the entropy increases in.
Also where you are prone to some negative will be vigilant against gravity.
So you are prone to, uh, to, to develop buoyancy.
And so this is what people observe here. All these people both are, is, it corresponds to material which is heated up by neutrinos.
And there is a second instability, which is called a accretion.
So I can say ETA and it's this one which we are going to, to,
to see more details in this, uh, in the simple setup of the, of this fountain experiment,
it's a global instability of the shock which is shown here in this particular simulation in a,
in a case where there is no, uh, known a dramatic process due to heating or cooling.
So in this particular simulation, there is no possibility of, uh, of, of cold convective instability.
It's just the motion of the shock which, uh, which generates entropy, uh, in which an eighties and the studying,
the, the mechanism identifying the mechanism of this instability has been my task of, uh, several years.
And the can be. Summarised in this very simple sketch where behind the shock wave you all you have a subsonic flow.
In a subsonic flow, acoustic waves kind of propagates in every direction.
And so you have in blue here some acoustic wave.
And when an acoustic wave reaches a shock wave, then it will push a little bit the shock wave and generate entropy and vorticity activation.
So here this vorticity perturbation is shown in red.
And so that's one step of the instability is this generation of of entropy and vorticity at the shock.
And the second step is corresponds to the fact that some ultrapure vorticity way maturation as it is evicted towards the surface of the star,
it's going to produce some sound. So this is not intuitive at all.
Usually when you think of a of a of a perturbation, which I can generate here with my hand, you don't hear anything.
And, but if, if you have a vertical motion attracted into a endogenous flow,
then then it will produce it will break the hydrostatic equilibrium and produce some sound.
And the same is true for all topic attribution.
So you have this generation here of acoustic waves, uh, which are going to propagate again, which to shock and generate new distribution.
So this cycle is, is a key to, to the, this global instability.
And it's this global instability is not a small scale one like on this hedge,
but it's a global instability because it relies on the regions of the flow which are on the large scale.
This coupling process here is more efficient when the when there when the wavelength
of the distribution is bigger than the size of the of the individualities,
of the flow. And so this is this slide summarises all the the hydrodynamic dynamical instabilities that we need for the moment.
And this simple formula here is also an important ingredient to consider is reminds you that this convective instability which
takes place in this outer region is not exactly the same as the convective instability taking place in a hydrostatic I mean,
initially hydrostatic atmosphere. But this is not really an atmosphere.
It's it's a flow of of gas from the shock to the initial subsurface.
There is really a flow of matter. And so matter spends only a finite time in this region.
So you must be careful when you think of buoyancy times K to compare this buoyancy time scale to the time you spend in this region.
And so this is really this ratio, the meaning of this ratio here you compare the balloon vessel,
our frequency of growth rate with extra growth rates related to the B region,
unstable region to the geography is the time we spent to cross this region.
And these two crossing time is too short compared to the to the growth time.
Then the flow. This flow is linearly stable. So this instability can be really stabilised.
If the size of this region or is the velocity across this region makes the advection time short enough.
So having understood that, you can for clarification,
you say there's a gravitational wave between our signature gravitational wave and two things that GMO or gravitational radiation.
Did I say gravitational wave? No, you haven't said anything on your slide.
So the question. So acoustic. No, here, it's what I hear.
Oh, sorry. Okay. You know, he. I wrote gravitational waves because when you have this and this large scale motion here,
you move around a mass, uh, significant mass, like maybe three solar masses.
And so you move, uh, you move around the, you change the gravitational field and you generate gravitational waves.
The gravitational radiation. Yes. No. Yeah, yeah.
No, no, no, no. Here, it's really gravitation. Yeah, this really the pressure gravity does the fashionable gravitational waves and also a neutrino.
Uh, you know what you need is which are these two?
This is very, very important point.
Computational waves and neutrinos are the only two signals which can bring information directly from this very embedded region,
whereas the what we call the piece of cake, which will be the final velocity of the pulsar years after the explosion.
This one is some very important agnostic, but it's more indirect.
And also for the information it's in nucleosynthesis,
it's it's more in direct question with the velocities in the inner parts of the host as we talk about
velocities of the neutron star of the gas No of is in a region with a large masses moving around.
Yeah. So so the in blue here, the, the incident velocity of free falling material is 1/10 of the speed of light.
Yes, but I was talking about this with the rate in the turbulent regions.
So the turbulence region, uh, so the, let's say the, the sound speed in this region is uh,
comparable to this 10th of the speed of light and the, and the motion point mark points three at best close to the shock.
So it would be one third of 1/10 of the speed of light at best.
But it's actually this is what you would obtain if you if you're a diabetic relative, it's relatively relativistic.
Yeah, yeah, you can neglected. But it would be more like one manoeuvre would be more like one.
So it would be 100th of the speed of light. Yeah. So that is a signal that that's pretty low relativistic.
Yeah. That's a way production that really suppresses it quite, quite a lot.
No, no, no, uh, no, no. The, uh, uh, y no, no.
You can, you don't need, do you? Yeah. That's a high power.
Yeah, yeah, yeah. But yeah, it's a chronic stress tensor, right?
Yes. Okay. Yeah, no. Okay. But still, uh, still this does generate.
Uh oh, of course it does. Yeah. Okay.
Yeah, you're right. Yeah, you're right. This is an important factor to to to scale this computational wave.
So you're right. Yeah. But it's a big amount of mass which compensates those the smaller velocities.
Um, so to illustrate quickly what I've just said, there's a short movie which shows these two steps of coupling.
So in blue you have acoustic waves travelling towards a stationary shock.
It's like a talking with anywhere you have a stationary shock and and the infrared.
I show the vorticity which is in the flow and you will see how the voltage, the acoustic wave generates the vorticity wave which is evicted.
So the blue one is propagating, the red one is simply attracted with the flow.
And then in the second half of the movie, this vorticity wave, uh, simply attracted in a uniform flow,
suddenly meets a region of this, of some external potential, which produces some deceleration.
This is just a talking with that and you will see how the disintegration of a shear wave in red I.
I say vorticity wave as a synonym of shear wave.
Uh, this is simply a linear wave I'm talking here of linear coupling.
This will generate a pressure wave. So to illustrate that, you just see this.
So you see here the vorticity wave. This is a shock wave here.
And this is the dislocation of region. As soon as you enter this this dislocation region, you generate this this acoustic wave,
acoustic wave, you generate upwards and also downwards, uh, with different amplitude.
So I just show it again. The acoustic wave generates vorticity and the vorticity way, as soon as it enters a visitation region, generates electricity.
So these are the two steps which allow you to think of this global, attractive acoustic cycle to explain this as instability.
So I am sorry if this was a bit fast.
I don't know if it was fast or not, but if you understand this,
you can really understand that there will be some diversity of explosion forces because depending
on the those relative timescales will be dominated by one or the other of these two instabilities.
And and indeed, over the years I mean, recent years since 2012, because I showed you in 2009,
this 15 hour massive explosion, which was successful at that time, people believe that explosions would be genetic.
One explosion would be the same for any kind of progenitor.
But over the years, people realised that the explosions were not all the same when they consider different masses of the progenitor.
Also, from the 8 to 27 from masses, you would have different successful explosion.
So it was many successful explosions, but some showed oscillations on a large scale and some didn't.
And this was related to the relative importance of those of those two instabilities.
I don't want to go into details, but people who've been in this field know that that there is there are many,
many discrepancies between the different groups who perform this new simulations.
Very few groups were able to do such simulations at the beginning.
And there was the group of of Adam Burrows in Arizona and in Princeton,
there was the group of Tomas Young kind gushing in the group of 20 minutes that combined Oak Ridge.
And now there are more groups, but still a lot of discrepancies between these groups because all of these groups
have to rely on different approximations to approximate neutrino transport.
Neutrino transport, like radiation transport in multi GS is very difficult, these very time consuming for computer.
And so you have to rely on approximations which don't give converging results from one group to another.
So over more recent years there has been some progress, uh, on the side of nuclear physics.
The uncertainties of the nuclear question of states have have been not completely sorted,
but the fact that people observe neutron stars of two solar masses, uh, in a reliable manner show that excluded, uh, uh, uh, category of, uh,
of equations of state which could not produce such large masses with around the parameter space was smaller due to these nice observations,
but at the same time the parameter space became larger because people realised that the problem was not simply, uh, a problem of this inner core of.
1.5 star mass is collapsing. But depending on the structure of the stock,
you could be influenced by perturbations coming from the convective burning of all the
turbulence in the last stages of oxygen and silicon burning before just above the iron core.
So this is the effect of the collapse.
Asymmetries can can be significant and contribute to two to help the explosion.
And also the stellar evolution showed us that it's a very bad idea to to to label progenitors with a mass at birth.
This zero age mini sequence must form a 10 to 40 or 100 years of very bad labelling,
because the history of the star can be very different from one star to another.
And and some have lost a lot of wind or a lot of mass wind.
Some have, and some have binary companions which change their evolution.
So all all those different histories and the complexity of burning in the stars made a very different style structure just before the collapse.
Here. This parameter is the compactness parameter.
Which measures which which measures the it's like the comparing the radius to which the radius of a of the inner core to its function is radius how,
how compact this this star is.
And you can see the there was one hope at the moment that in this series of simplified models in Grey,
uh, you can see the other stars which produce which don't explode and publish a black hole and in red,
those which explode according to a simple prescription in one G, which is far from being an initial calculation.
And people realise that the more compact, the the core of a star of the star, the more difficult it is to to explode.
So there is a correlation between the production of black holes and the compactness of the core.
So this is one complexity and, and a very interesting recent paper pushed this method to, to, to explore the parameter space and,
and show that, uh, here again, you see the, the zero age mini sequence mass and here you have the mass just before the collapse.
So one important thing to remember is that the most massive stars can be at the moment of collapse can be less massive than the Phantom.
But if you take these forces for our mass at the moment of collapse,
the the the star has lost a lot of mass here in the grey and it's about 15 at our mass,
whereas this one or 24 hour mass is heavier because it has lost less mass.
So there is this mass of us which is important and there is the mass of the hydrogen layer and in black the mass of the helium core.
And people realise that the distribution of neutron star masses in green here when when you manage to produce an explosion,
the neutron star mass is somewhere between one and two solar masses.
And the distribution you obtain from this simplified model matches the distribution of neutron star masses in here,
in the dashed lines which are observed and the distribution of black holes you obtain,
uh, here in these models matches the black hole distribution masses observed.
If you assume that the hydrogen layer has been ejected during the before the collapse, just some observation.
But that is you. That may be the DA.
There are some processes which are able to eject to get rid in addition to the wind, to get rid of this yellow uh, uh,
layer of the hydrogen, because this black distribution here, masses of black hole masses, much is more or less the observed distribution.
So this is appealing as a possibility to to gain confidence in our simplified models.
But still it's very, uh, very preliminary and very insufficient because we know that such models ignore the binary history of stars,
which is, which is well established. And you have here in Oxford the specialist Philip opposite of he is specialist of this binary effect.
Should not be neglected. And also all these one D models which describe all these series of of explosions, all are calibrated.
There is some recipes which calibrate the evolution on a very specific, uh,
supernova explosion, which is, uh, which is around 84 masses, which is a 1987,
which is the supernova, which,
for which we observed the neutrinos in 1987 because it exploded close enough to our galaxy in the large Magellanic Cloud.
So it's it's a bit dangerous to calibrate all those models on the single explosion, because this particular explosion,
1987 eight, was known to be a very particular star, which was actually a binary system.
And so it's dangerous to to think that all the, all the models will follow the behaviour of the 1987.
So it's because of this difficulty that we, we, we at the same time as we try to generalise and make broad landscapes of explosion,
we have to go back to the detailed physics to, to assess our understanding and to, to, to, to be sure that we can generalise processes based on,
on the deep physical understanding to, to finish with this overview.
I will show you the most advanced 3D simulations by the Russian group where, um, where, uh, the used, uh, some uh, insane number of, uh,
of processors and compute, uh, uh, I was suppose to finally find that this progenitor, which was exploding in 2D, actually did not explode in 3D.
So there is a kind of crisis now in this field of research where people realise that 3D is more complicated than 2D and but uh,
then they added a very small ingredient to the computation, which was the strangeness content of, of neutrons.
So the, uh, the diffusion of uh, uh, neutrinos on neutrons, uh, depends on the small parameter, which is the strangeness.
Neutron does not contain any strain that does not contain any strange quark.
But there is still strangeness, uh, content, which is not exactly zero and which is constrained by,
uh, experiments to be in a certain range around zero and very few.
During this lifetime. It was enough to change this non exploding model into an explosion.
Not, not that this strangeness content is is crucial.
But this is more to to to show that these these explosion this are not exploding model was very close to the threshold of explosion.
So this is how it looks like when it did not explode. Uh, so again, you have this, uh, shockwave in black.
It's not empty ion falling towards the centre and, uh, and in the middle you will have the portal neutron star.
So you the symmetry is broken by instabilities again.
And you on the smaller scale, you have the buoyancy driven instabilities due to neutrino absorption.
And on a large scale you have this sloshing motion of the, of the wave of the shock wave, which is, uh, associated to this instability.
And so the two instabilities here coexist.
And after a while, uh, none of them is enough to, to, uh, to change the degree of a symmetry sufficiently to,
to be able to absorb enough entry those to produce an explosion. This is this is actually the maybe I should have said that those instabilities are
helpful to the explosion in the sense that they are able to push matter on one side.
And on this side, the, the matter is dense enough to absorb more neutrinos than, uh, than when matter was distributed historically.
So in this case, the explosion doesn't seem to proceed.
So this is annoying, but this is just one simulation and parameter space is gigantic.
So we should not, uh, rely too much on this particular case, and we should rely on the physics.
So the physics is what you see in your kitchen sink, for example.
This is how you built your physical intuition.
This is a hydraulic jump in your kitchen sink, and you know that the hydrogen jump is a transition between a fast flow,
which is very thin layer, a thin layer of water, and the fast which becomes slower and thicker.
So you have converted kinetic energy into potential energy across this hydraulic.
So it's, and it's a good analogue of the shock wave. Uh, and the shock wave range we see in is the exactly the, the opposite of a hydraulic jump.
I mean, the opposite of a kitchen sink, hydrogen.
So we would like to inject water from the outside towards the centre and produce this transition.
You know, such a domino in the same way as we have a spherical shock wave.
When we approached the neutron star in the middle.
So instead of a neutron star, we put a cylinder in the middle which allows water to, to escape only through the upper edge of this, uh,
of the cylinder by splitting over here and the, and the,
and this and the slope of this surface is meant to mimic the Newtonian potential, uh, uh, governed by the neutron star.
So if you put a marble here, it will roll towards the centre as if it were attracted by the, uh, by the neutron star.
So you have this analogy even though you are dealing with a, with a incompressible fluid,
the variations of depth in this incompressible fluid mimic the variations of density in a compressible gas.
So instead of acoustic waves in the gas, you have your first gravity waves in a in a in this flow.
And you have this analogy between the seven equations describing the shallow water.
So here's the continuity equation.
H is the depth, and here is the only equation which you can compare to the continuity equation, your gas and the earlier equation.
Well, I have slightly transformed the equation.
I mean, the pressure source has been separated into a ontology and I turn to to show the boundary constant.
But this is really an equation, a geometric case and a isothermal case.
And the shallow water case corresponds to I mean, it resembles the isothermal case in the sense that you don't have any entropy effect,
but it resembles the Da Vinci case in the sense that the until P looks like gamma equal to gas.
So we call it the isotropic gas law, non-stop equations with gamma equal to.
And when you accept this kind of a intermediate analogy between these two type of gases, uh,
you, you expect the same physical processes to take place, the same coupling processes.
So you will not have until about to be shown. But along the hydraulic trunk you expect stuff as gravity wave to couple to vertical motions and,
and you expect to have the same instability and on a different scale.
So you the ratio of timescales is given by this ratio of of gravitational forces.
And in the case of this level, you have to experiment you you expect to have a process,
an instability taking place on a timescale 100 times slower than the value.
But in astrophysics, in astrophysics, we had 30 milliseconds oscillations.
So here we expect 3 seconds, uh, oscillations.
And the size of course is smaller. It's 1 million times, about 1 million times smaller.
So Steve mentioned the fact that this is as simple as a garden kitchen sink physics, and it's simple as a garden experiment.
So I built this experiment in, in a few months in my garden and, uh,
and I show this to encourage any, uh, any physicist, any young physicist, young or old,
to try things yourself if you don't, if you haven't done it yet because it's, it can be rewarding,
since this very simple experiment in the end made the the front cover of people in, in 2012.
So all the results were obtained in this very simple device.
My institute, after a few years, uh, helped me build a much more sophisticated one.
But the results were obtained in the, in the, in the very basic one.
And this is what you observe in the, in the experiment. So you inject water through a slit.
The hydraulic jump is more or less shattered off.
The injection is as stationary as possible, as homogeneous as possible.
And the hydrogen and the water is able to escape.
This thing in the middle is just a passive piece of metal to to illustrate or to visualise the the transverse motion of the throwing.
The no region here is there's no transverse motion yet. And, and you see that, uh, the instability develops.
On the three with a three second, uh, oscillation period.
So this oscillation gets amplified.
And after breaking the symmetry, the symmetry is going to be broken again because this,
this axis, this random axis of oscillation is going to to change into a rotation.
And you see, now that the the hydrogen starts rotating and the as the hydrogen rotates in one direction,
the inner regions of the flow start rotating in the opposite direction.
Since there is no angular momentum injected in the experiment,
you you expect that some some rotational motion appearing in one region should be compensated by some rotational motion,
some opposite rotational motion in some other region.
And so we checked the validity of this experiment by doing a shallow water simulations, and we compared it to the gas simulation.
So here is shallow water. And here is, uh, astrophysical gas simulation.
And you, you see that the, uh, in the three cases, you, you have the same type of, uh, oscillation and then symmetry breaking new symmetry,
nonlinear symmetry breaking and uh, and rotation with this kind of angular point here.
In the industry, three cases. So the, the experiment was confirmed by the very simple two equations of over seven of these sort of water equations.
And,
and this is the agreement which we obtained between the oscillation periods of the experiment and the oscillation period of the numerical simulation,
and also the selective analysis of the secondary positions for different sizes of the hydraulic jump.
We can we can choose this the initial size of the hydrogen by, uh,
by choosing the height of the cylinder and immediately see if we want to have a large hydrogen jump.
We have a high, uh, uh, uh, high cylinder in the middle.
And so it's quite, uh, I should, uh, hurry up.
Maybe now, uh, if you have 5 minutes or even a few minutes, uh, it's quite surprising that the equipment is that good given the,
the discourse which is affecting water and all sorts of uh, differences, as I said, between the lack of buoyancy.
And so it's that's we didn't expect to have such a good agreement.
But, uh, and actually the agreement is very good on the oscillation timescale, but there is,
there is some disagreement, slight disagreement on their growth rates, which we, we think we understand now.
Uh, I will, I will pass on this. I mean, I will not pass on this because it's, it's a very good tool for public outreach.
And so we have now this experiment in the museum in Paris for to explain supernova physics to to the public.
After a period of two months where we showed ourselves this to the public of the the museum is showing this, uh, themselves.
We are very happy about that.
And I would like to spend a few less few minutes talking about floatation effects because now we have a new experiment which uh,
uh, allows the full experiment to rotate.
And what's happening now is that water is injected with some elemental,
and the instability always develop in the same direction as the rotation of the progeny just on its own.
And what's happening is that in our region, try to rotate in the opposite direction compared to the progenitor star.
And indeed you can end up with inner regions rotating opposite.
We're going to see that now. They are going to rotate in the direction opposite to the progenitor.
So you can think of neutron star rotating opposite to the direction of rotation of the opportunity to because
this instability has has produced shockwaves rotating in the same direction as the as topological star.
You see, the motion is chaotic, but you see that this region rotates opposite.
Now to the to the progenitor star.
So this was predicted actually by numerical simulations by my, my colleague John Blondin in uh, in the US.
But this is the experimental analogue of it.
I will not, uh, say more about the comparison of growth rates, but I want to, to go jump immediately to faster rotation rates to show you a new,
uh, surprising development of this experiment is what's what's hot, what's happening when the rotation rate increases.
To even higher overall mental.
Then you have another type of instability which is called the which is called accommodation instability and political instability,
which is not related to the instability that I've mentioned so far,
but is related to the distribution of angular momentum in the in the fluid, in the differential, your rotating fluids.
So this is something that Steve is very familiar with when magnetic fields are in, especially when magnetic fields are included.
But here it's a it's an instability, which is purely hydro.
And of course, when you when you have strong rotation rates, you you need to worry about the possible generation of magnetic fields.
So this is a new direction of the of this field of research,
where this the mechanism of this is that it is a kind of has been interpreted in the
eighties as a kind of overt reflection of acoustic waves across the rotation region.
But I will, I will, uh, I will jump to, to the conclusion to, to say that this kind of instability has now been observed in astrophysical simulation.
What you see, it's called low shareholder value t being the kinetic energy and w the gravitational energy.
It gives this kind of a spiralling pattern, your simulations and, and, and the existence of this quotation region.
In the very region, you have a region of the flow which rotates faster than the, than the spiral pattern.
And this is a key and region to to identify this instability.
The Phoenician is not trivial, despite the small sketch show I showed before.
So I, I don't have time to, to elaborate more on this.
But but the current conclusion is that this kind of fast rotation is, is able to to have an impact on the physics of the explosion,
is able to decelerate the, uh, the pulsar compared to the velocity it would have due to simple actually symmetric, uh, uh, collapse.
But so we, we need now to, uh, it's just ongoing research which we need to investigate, including related fields now.
So I leave you with my conclusions.
My, my main point is to say that hydrodynamic instabilities are king region to the collapse, to the mechanism of supernova explosions.
And this my other point is to say that with very simple tools like this, simple something,
we are able to capture at least two of these uh, um, uh, unstable processes.
And this is a good way to, to build up our physical intuition about this, uh, physics.
Okay.