1 00:00:07,370 --> 00:00:14,960 Thank you very much, Steve. I'm very honoured to give this talk in front of this audience of physicists, 2 00:00:15,320 --> 00:00:25,670 so I will try to date you with the current status of the explosion mechanism of massive stars, 3 00:00:25,670 --> 00:00:32,690 which has been a mystery for more than 50 years, and which is to some extent still a mystery. 4 00:00:33,710 --> 00:00:39,680 So we know that massive star explodes, massive stars explode as supernova. 5 00:00:39,800 --> 00:00:43,100 So this is a very spectacular phenomenon. 6 00:00:43,550 --> 00:00:48,470 But from the theoretical point of view, if you were to ask a theoretician, 7 00:00:50,180 --> 00:00:58,280 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. 8 00:00:58,670 --> 00:01:07,909 So the evidence, the observational evidence tells you that there is something which allows matter to to bounce into an explosion, 9 00:01:07,910 --> 00:01:17,420 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. 10 00:01:17,840 --> 00:01:23,690 And this is the part which is related to the concept of a solar cycle, Hamas. 11 00:01:24,050 --> 00:01:35,690 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. 12 00:01:35,990 --> 00:01:40,400 So this this part of theory is, is considered as very robust. 13 00:01:40,730 --> 00:01:48,980 And when you have a star which is massive enough to accumulate iron at its centre, at its centre, 14 00:01:51,740 --> 00:02:01,730 iron will accumulate and will not trigger new fusion reactions because iron is the most tightly bound nuclear element. 15 00:02:01,940 --> 00:02:05,930 So the binding the nuclear binding energy of iron is, is, is a maximum. 16 00:02:06,200 --> 00:02:14,210 So you cannot extract energy beyond the iron from the, uh, from the fusion reactions. 17 00:02:14,720 --> 00:02:25,500 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. 18 00:02:25,790 --> 00:02:30,019 So, you know, I don't know how familiar you are in astrophysics in general, 19 00:02:30,020 --> 00:02:35,059 but you know that the sun is very far from this kind of physics because the sun is 20 00:02:35,060 --> 00:02:41,210 just struggling at the moment to to make the fusion of of a hydrogen into helium. 21 00:02:41,390 --> 00:02:54,980 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. 22 00:02:55,100 --> 00:02:59,480 Whereas if you if you going to the a star, which is ten times more massive than the sun, 23 00:03:00,020 --> 00:03:10,969 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. 24 00:03:10,970 --> 00:03:27,140 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, 25 00:03:27,530 --> 00:03:33,559 I mean a large fraction of which hydrogen and to create and create a very massive element such as this ion car, 26 00:03:33,560 --> 00:03:37,280 which will collapse when it reaches the somatic elements. 27 00:03:37,520 --> 00:03:44,830 So what you see here is an example of such a massive star, uh, a few hundred years after the explosion. 28 00:03:45,260 --> 00:03:48,710 So what we see here is in X-rays, uh, the. 29 00:03:49,040 --> 00:03:52,310 The remnants of the explosion, it's gone. It's called a supernova remnant. 30 00:03:52,700 --> 00:03:59,930 The CAS, a remnant. At the centre, you have a collapsed object, which is the result of the of this, 31 00:04:01,070 --> 00:04:08,310 people believe of this collapsing, uh, uh, degenerate core of ion, which forms which we call a neutron star. 32 00:04:08,930 --> 00:04:12,350 So once, once there, the core of a star collapses. 33 00:04:12,350 --> 00:04:23,749 What people understand is that, uh, uh, electronic capture will take place and the electronic fraction of matter will decrease. 34 00:04:23,750 --> 00:04:34,700 So you will have less and less pressure support from degenerate electrons and, and the matter will be made of more and more neutrons. 35 00:04:35,150 --> 00:04:42,350 And, and the, the equilibrium which you can reach in this direction is called a neutron star. 36 00:04:42,350 --> 00:04:48,829 So it's the last equilibrium against gravity that you can think of before collapsing into a black hole. 37 00:04:48,830 --> 00:04:53,299 So indeed, uh, indeed, we find many neutron stars here. 38 00:04:53,300 --> 00:05:02,600 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. 39 00:05:03,110 --> 00:05:06,350 And those objects are, have very strange properties. 40 00:05:07,490 --> 00:05:10,400 Very messy, very dense, and they are very fast. 41 00:05:10,490 --> 00:05:19,970 And here you can see a recent observation by the NuStar satellite, which observes gamma ray lines in blue. 42 00:05:20,030 --> 00:05:24,170 It observes the gamma ray lines of titanium, titanium 44. 43 00:05:24,680 --> 00:05:37,980 And it revealed the fact that the composition of this ejecta is very ingenious and that even the distribution of these titanium blobs here, 44 00:05:38,000 --> 00:05:46,850 these blue blobs, are approximately in a half plane opposite to the direction of this neutron star in the middle. 45 00:05:46,880 --> 00:05:56,320 So this is the kind of observation which sets strong constraints on the explosion mechanism of of this of these objects. 46 00:05:56,660 --> 00:06:05,299 So the supernova is is this moment when the the inner core collapses to a neutron star and the rest of the star, 47 00:06:05,300 --> 00:06:11,010 which is typically, uh, ten solar masses or more, can be 24 masses, 48 00:06:11,270 --> 00:06:16,459 is ejected and is going to feed the interstellar medium with all the elements which have 49 00:06:16,460 --> 00:06:22,430 been synthesised inside the the star during its life and also during the explosion. 50 00:06:23,600 --> 00:06:32,180 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. 51 00:06:32,690 --> 00:06:39,860 And sometimes people are very pessimistic about this, uh, our understanding of this process, 52 00:06:40,280 --> 00:06:46,340 um, as I said, because in the, I mean, the main reason is that in one G we shoot, 53 00:06:46,550 --> 00:06:51,460 if you study this problem in one dimension, uh, you realise that this, uh, 54 00:06:52,160 --> 00:06:58,430 this collapse turns into not a neutron neutron star, but quickly after that, a black hole. 55 00:06:58,940 --> 00:07:05,870 So I don't know if you if you're aware that neutron stars cannot afford to be more massive than a certain threshold, 56 00:07:06,020 --> 00:07:15,620 there is a threshold between two and three solar masses above which these neutron matter cannot sustain the weight of of gravity. 57 00:07:15,920 --> 00:07:24,799 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. 58 00:07:24,800 --> 00:07:28,370 And then you you will collapse the initial sign to a black hole. 59 00:07:28,370 --> 00:07:32,420 And it will be even more difficult to think of a way of producing this explosion. 60 00:07:33,020 --> 00:07:44,450 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? 61 00:07:44,450 --> 00:07:46,130 Regions of the explosion mechanism. 62 00:07:46,520 --> 00:07:57,890 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. 63 00:07:58,220 --> 00:08:01,220 And the and the environment is endogenous. 64 00:08:01,220 --> 00:08:06,230 And so the new ingredient in supernova theory over the last, uh, 65 00:08:06,440 --> 00:08:16,610 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. 66 00:08:17,240 --> 00:08:25,310 And in relation to this, uh, no legacy symmetric or non star recall, uh, cocktail of the explosion, 67 00:08:25,430 --> 00:08:36,890 that there are theoretical arguments to justify such a departure from this very good symmetry involving hydrodynamic instabilities. 68 00:08:37,430 --> 00:08:41,720 So this is the, the, the important ingredient which has been studied in the last ten years. 69 00:08:42,680 --> 00:08:48,100 And the hydrodynamic instabilities have some, uh, nice, uh, 70 00:08:49,220 --> 00:08:54,470 property that the laws of hydrodynamics are valid in stars, but they are also valid on earth. 71 00:08:54,470 --> 00:08:59,750 And if you choose carefully the system, you can really make some, some relevant analogies. 72 00:09:00,050 --> 00:09:09,110 And that is the kitchen sink experiment that Steve was referring to is this image that you see here, which is actually a simple, 73 00:09:09,110 --> 00:09:16,700 shallow water experiment, which happens to describe the same instability that takes place at the centre of a star. 74 00:09:17,060 --> 00:09:27,020 Uh, using the analogy between, uh, first wave surface as gravity waves in shallow water and acoustic waves in a gas. 75 00:09:27,020 --> 00:09:34,400 And this is quite surprising that you can recover with a simple experiment this, uh, this kind of physical process. 76 00:09:34,760 --> 00:09:43,960 So the, the goal of this talk is to, to try to, to show you that the simplicity that we can find in, 77 00:09:44,170 --> 00:09:51,229 in a simple water fountain, uh, is, is connected to the complexity of that explosion. 78 00:09:51,230 --> 00:09:54,860 And it can really help us understand how, how massive stars explode. 79 00:09:56,150 --> 00:10:06,620 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. 80 00:10:06,830 --> 00:10:14,600 Still not completely satisfactory, but it is also to tell you about the simplicity of some tools, some new tools. 81 00:10:14,600 --> 00:10:17,330 We have to approach this this difficult problem. 82 00:10:17,870 --> 00:10:27,049 And here there is a numerical simulation by my colleagues in Gucci, which has been published in one year before this observation, 83 00:10:27,050 --> 00:10:35,810 and which shows that, uh, so in green here you have the heavy elements which are produced during the explosion of a supernova. 84 00:10:36,110 --> 00:10:43,370 And so here you have a 3-D simulation which actually predicts that the heavy elements will be produced, uh, 85 00:10:43,370 --> 00:10:53,360 preferentially in a region opposite to the direction of the moving neutron star, uh, which is, which is just born during the explosion. 86 00:10:53,630 --> 00:11:04,850 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. 87 00:11:05,120 --> 00:11:15,590 So I put this illustration here to emphasise one important point is the question of of making of initial calculations on us. 88 00:11:15,920 --> 00:11:24,649 And this this example here is an explosion which has been triggered by putting enough energy at the centre to produce the explosion. 89 00:11:24,650 --> 00:11:29,690 And indeed in this case you have some interesting properties which resemble observations. 90 00:11:29,960 --> 00:11:40,820 But the very big difficulty is to to produce explosion without tuning parameters to to without putting the energy by hand. 91 00:11:42,080 --> 00:11:45,860 So the framework of, of all this supernova research, I mean, 92 00:11:45,860 --> 00:11:53,120 the mechanism of the explosion itself is focussed in a very small window of of space and time. 93 00:11:53,510 --> 00:12:01,070 So the size of this region, of the region, which is decisive for the explosion, for the success or the failure of the exposure, 94 00:12:01,490 --> 00:12:11,569 is a small region of 300 kilometres at the centre of a star, which is something like 600 million kilometres in radius. 95 00:12:11,570 --> 00:12:15,650 So it's very difficult to grasp this, this difference of scale, 96 00:12:15,950 --> 00:12:24,620 but you have to think of of a gravitational potential which is very deep in the centre where the, 97 00:12:24,950 --> 00:12:35,690 uh, which is where you have very extreme densities and, and, whereas the outer path of the star are very loosely bound gravitationally. 98 00:12:35,930 --> 00:12:44,360 And so this big hydrogen atmosphere of the, of the stars is very easy to, to explode, the difficult parts to explore. 99 00:12:44,360 --> 00:12:48,950 This is the in our region where the gravitational potential is deep. 100 00:12:49,310 --> 00:12:53,690 And this the timescales, of course, are very slow for this full star. 101 00:12:53,690 --> 00:12:58,819 But the very in our region evolved on a very short timescale because of the strong gravity and 102 00:12:58,820 --> 00:13:05,090 this iron core as it reaches the this classic mass collapses to a neutron star in half a second. 103 00:13:05,420 --> 00:13:08,149 So you can imagine this iron core, 104 00:13:08,150 --> 00:13:18,630 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 105 00:13:18,650 --> 00:13:29,180 whole atavistic degenerate electrons in half a second and it collapses into an object mainly made of neutrons of a few tens of kilometres, 106 00:13:29,180 --> 00:13:34,340 which later on will shrink to ten kilometres as it cools down. 107 00:13:35,480 --> 00:13:48,470 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, 108 00:13:49,250 --> 00:13:56,390 the collapse of the region is so fast that the, the outer region is losing to free falling on the, 109 00:13:56,750 --> 00:14:03,080 on this, on this collapsed iron core is going to reach supersonic velocities. 110 00:14:03,530 --> 00:14:16,939 And and unluckily the as the matter hits the surface of this very dense potential star matter is not going 111 00:14:16,940 --> 00:14:26,240 to bounce elastically but a lot of energy is going to be lost into the dissociation of iron into uh, 112 00:14:26,720 --> 00:14:36,310 protons, neutrons and electrons. So if you had an elastic bounce, then yes, you could imagine that the this could be enough to uh, 113 00:14:36,710 --> 00:14:40,970 to explode the star because you're getting a lot of gravitational energy through the collapse. 114 00:14:40,970 --> 00:14:46,580 And this, this, this energy could be transferred into the, into kinetic energy of the explosion. 115 00:14:46,580 --> 00:14:56,840 But this transfer is not efficient at all because a lot of energy is lost into, uh, uh, the binding, 116 00:14:56,840 --> 00:15:01,740 the nuclear binding energy of this iron nuclei which are dissociated into, uh, 117 00:15:01,790 --> 00:15:06,740 protons and electrons because temperatures are so high after this shockwave and. 118 00:15:06,910 --> 00:15:09,360 And this is the real difficulty. 119 00:15:09,910 --> 00:15:20,270 This bounce is not elastic and and one G simulation show that this accretion shock here, this spherical question shock starts propagating out. 120 00:15:20,320 --> 00:15:26,500 Of course, there is a shock because you you have iron elements reaching 1/10 of the speed of light. 121 00:15:27,350 --> 00:15:35,260 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. 122 00:15:35,500 --> 00:15:43,180 It's very difficult to think of a good reason to to change the direction of this rain of iron. 123 00:15:43,950 --> 00:15:53,830 But and and this generates heat, a lot of heat, which is partially absorbed into a into this oscillating iron. 124 00:15:54,400 --> 00:16:00,390 And and so unless this rain of iron is is not dense enough. 125 00:16:00,400 --> 00:16:06,400 So for the lightest progenitors among those heavy stars which are able to produce an iron call. 126 00:16:06,610 --> 00:16:16,510 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. 127 00:16:16,810 --> 00:16:25,690 But above ten masses, you are not able in one dimension to to push out this this range of iron. 128 00:16:26,110 --> 00:16:37,120 So the the the reason why this this mechanism is called a neutrino driven delayed explosion is, is because, uh, neutrinos which, 129 00:16:37,120 --> 00:16:49,030 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, 130 00:16:49,270 --> 00:16:57,460 uh, a kind of blackbody of, uh, neutrino inside this opaque potential star, 131 00:16:57,850 --> 00:17:06,740 this neutrinos take some time to diffuse out of this yellow region, which is particularly thick. 132 00:17:07,120 --> 00:17:14,530 And so it takes nearly one second for this huge flux of neutrino to to escape of this region. 133 00:17:14,800 --> 00:17:17,380 And this is where the jet come comes from. 134 00:17:17,800 --> 00:17:26,950 And once these neutrinos escape, there was the hope proposed by between the sun that the fraction that 10% of those neutrinos would be, 135 00:17:27,340 --> 00:17:31,780 uh, would be absorbed by the neutrons. 136 00:17:32,260 --> 00:17:39,070 Following the inverse reaction here, the neutrino would be absorbed by emission and produce a potent American, 137 00:17:39,460 --> 00:17:46,660 and the absorption of neutrino would seems to be the the best way to power the explosion. 138 00:17:46,690 --> 00:17:50,380 So remember and this will not change until the end of my talk. 139 00:17:50,800 --> 00:17:58,390 The the engine of the explosion is really, uh, coming from, of course, competition in energy. 140 00:17:58,570 --> 00:18:05,170 But the competition in energy has transfer has been transferred into the kinetic energy of ion here. 141 00:18:05,170 --> 00:18:10,720 The kinetic energy of Ion has been transferred into heat as it passes with a shock. 142 00:18:11,020 --> 00:18:14,260 And this heat has generated a lot of neutrinos. 143 00:18:14,620 --> 00:18:17,410 And so the energy is in the neutrinos. 144 00:18:18,310 --> 00:18:27,190 The the the failure of the explosion corresponds to a case where neutrinos escape and matter simply shrinks to a black hole. 145 00:18:27,590 --> 00:18:33,610 The successful explosion means that sufficient neutrinos have been captured in this dense 146 00:18:33,610 --> 00:18:39,900 post-rock region so that the shock is is revived and pushed out to to generate an explosion. 147 00:18:39,910 --> 00:18:46,960 So the energy budget is is summarised here you have the gravitational energy, which is about ten to the 53 hours. 148 00:18:47,380 --> 00:18:51,670 And the observed kinetic energy of the explosion is about ten to the 51. 149 00:18:52,060 --> 00:19:04,780 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. 150 00:19:05,110 --> 00:19:14,890 In this, in this framework right here, the rotational energy of such a system, most of the theory of, of a supernova, uh, 151 00:19:15,520 --> 00:19:25,120 mechanism does not want to rely on the rotational energy because the rotational energy, as you see here, stays like ten to the 50. 152 00:19:25,720 --> 00:19:36,730 If you consider, uh, uh, 14 neutron star, which rotates with this ten millisecond period than what one sees as 5 to 10 kilometres. 153 00:19:36,970 --> 00:19:42,230 So unless you have and 10 milliseconds happens to be the typical, uh, 154 00:19:42,430 --> 00:19:51,520 I mean that happens to be the spin period of, uh, of a very fast of the fastest neutron stars. 155 00:19:52,060 --> 00:19:56,080 Uh, some neutron stars are faster than that, but they are accelerated after the birth. 156 00:19:56,380 --> 00:20:03,970 But at birth, a neutron star is, is considered to be like ten, 20 milliseconds, uh, at best. 157 00:20:04,390 --> 00:20:07,800 So you cannot really rely on. Potential energy to. 158 00:20:08,130 --> 00:20:14,250 To power the explosion. So people have tried to develop models without rotation. 159 00:20:14,340 --> 00:20:22,830 Neglecting this rotational effect. And. And the recent ideas rely on hydro dynamical instabilities. 160 00:20:22,920 --> 00:20:33,290 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. 161 00:20:33,810 --> 00:20:37,140 It's so this is in blue. The colour scale is unhappy. 162 00:20:37,740 --> 00:20:47,490 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, 163 00:20:47,550 --> 00:20:53,110 symmetric and perfectly original, this accretion structure starts to wobble along this axis. 164 00:20:53,150 --> 00:21:01,020 So by hypothesis, this simulation is actually symmetric so that it looks three, but it's actually a actually symmetric hypothesis. 165 00:21:01,410 --> 00:21:09,630 And there is a symmetry axis here and you see that the shockwave u which measures something like 150 or 200 kilometres here, 166 00:21:10,050 --> 00:21:17,160 this shockwave moves, uh, moves around in what is called a sloshing motion. 167 00:21:17,580 --> 00:21:26,340 And you have on smaller scales, uh, bubbles, bubbles of material heated up by, by neutrinos. 168 00:21:26,550 --> 00:21:29,400 And in this case, this was in 2009. 169 00:21:29,760 --> 00:21:38,510 This was one of the I was the first of initial numerical simulation, which produced an explosion without tuning parameters. 170 00:21:38,520 --> 00:21:47,520 So they in this simulation, they had solved neutrino transport in a in the best way they could. 171 00:21:47,520 --> 00:21:53,190 It was not perfectly accurate, but it was it was not biased to produce an exposure. 172 00:21:53,580 --> 00:21:59,160 And and you see that after some wobbling, uh, the explosion, the shock starts to move out. 173 00:21:59,580 --> 00:22:03,959 The full simulation you've just seen here is 800 milliseconds. 174 00:22:03,960 --> 00:22:13,070 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. 175 00:22:13,860 --> 00:22:21,030 So at this point, it's not necessary to continue the simulation because once you go out of the of 400 enough kilometres, 176 00:22:21,690 --> 00:22:25,169 you know that the shockwave has enough energy to propagate across the star. 177 00:22:25,170 --> 00:22:33,510 The star is, it will take several days, uh, to, to reach the, uh, to reach the, the outer edge of the star. 178 00:22:33,900 --> 00:22:38,220 Um, but there is enough energy to, to, to do that. 179 00:22:38,910 --> 00:22:46,649 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. 180 00:22:46,650 --> 00:22:51,210 So it's not fully satisfactory. But it was a big, uh, a big success. 181 00:22:53,130 --> 00:23:01,800 The two instabilities that you see in this, uh, in that you saw in this movie have been well identified over the years. 182 00:23:02,190 --> 00:23:05,250 One is called neutrino driven convection. 183 00:23:05,310 --> 00:23:06,990 It's due to the fact, as I said, 184 00:23:06,990 --> 00:23:14,819 that some neutrinos are going to be absorbed by the material which passes with a shock and which is attracted outward. 185 00:23:14,820 --> 00:23:23,370 So if you want to go into detail, there are two regions depending on the dominant direction of this reaction of electron capture. 186 00:23:23,760 --> 00:23:35,010 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. 187 00:23:35,460 --> 00:23:41,520 Whereas if you are in this outer region, which is dense enough, uh, behind the shock, 188 00:23:42,150 --> 00:23:49,100 it's the opposite reaction of neutrino capture, which is so, which is a region where the entropy increases in. 189 00:23:49,230 --> 00:23:55,260 Also where you are prone to some negative will be vigilant against gravity. 190 00:23:55,260 --> 00:24:00,570 So you are prone to, uh, to, to develop buoyancy. 191 00:24:01,890 --> 00:24:11,490 And so this is what people observe here. All these people both are, is, it corresponds to material which is heated up by neutrinos. 192 00:24:11,850 --> 00:24:14,940 And there is a second instability, which is called a accretion. 193 00:24:14,940 --> 00:24:18,780 So I can say ETA and it's this one which we are going to, to, 194 00:24:19,170 --> 00:24:25,650 to see more details in this, uh, in the simple setup of the, of this fountain experiment, 195 00:24:26,070 --> 00:24:31,610 it's a global instability of the shock which is shown here in this particular simulation in a, 196 00:24:31,620 --> 00:24:38,309 in a case where there is no, uh, known a dramatic process due to heating or cooling. 197 00:24:38,310 --> 00:24:46,350 So in this particular simulation, there is no possibility of, uh, of, of cold convective instability. 198 00:24:46,500 --> 00:24:56,250 It's just the motion of the shock which, uh, which generates entropy, uh, in which an eighties and the studying, 199 00:24:56,250 --> 00:25:04,860 the, the mechanism identifying the mechanism of this instability has been my task of, uh, several years. 200 00:25:05,190 --> 00:25:14,630 And the can be. Summarised in this very simple sketch where behind the shock wave you all you have a subsonic flow. 201 00:25:15,110 --> 00:25:18,830 In a subsonic flow, acoustic waves kind of propagates in every direction. 202 00:25:19,280 --> 00:25:22,390 And so you have in blue here some acoustic wave. 203 00:25:22,850 --> 00:25:33,679 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. 204 00:25:33,680 --> 00:25:36,050 So here this vorticity perturbation is shown in red. 205 00:25:36,530 --> 00:25:42,920 And so that's one step of the instability is this generation of of entropy and vorticity at the shock. 206 00:25:43,640 --> 00:25:53,780 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, 207 00:25:54,770 --> 00:25:58,430 it's going to produce some sound. So this is not intuitive at all. 208 00:25:58,580 --> 00:26:06,110 Usually when you think of a of a of a perturbation, which I can generate here with my hand, you don't hear anything. 209 00:26:07,550 --> 00:26:15,080 And, but if, if you have a vertical motion attracted into a endogenous flow, 210 00:26:15,260 --> 00:26:21,470 then then it will produce it will break the hydrostatic equilibrium and produce some sound. 211 00:26:21,800 --> 00:26:24,590 And the same is true for all topic attribution. 212 00:26:24,980 --> 00:26:34,459 So you have this generation here of acoustic waves, uh, which are going to propagate again, which to shock and generate new distribution. 213 00:26:34,460 --> 00:26:39,260 So this cycle is, is a key to, to the, this global instability. 214 00:26:39,620 --> 00:26:44,269 And it's this global instability is not a small scale one like on this hedge, 215 00:26:44,270 --> 00:26:50,030 but it's a global instability because it relies on the regions of the flow which are on the large scale. 216 00:26:50,600 --> 00:26:58,459 This coupling process here is more efficient when the when there when the wavelength 217 00:26:58,460 --> 00:27:03,560 of the distribution is bigger than the size of the of the individualities, 218 00:27:03,560 --> 00:27:13,850 of the flow. And so this is this slide summarises all the the hydrodynamic dynamical instabilities that we need for the moment. 219 00:27:14,360 --> 00:27:26,450 And this simple formula here is also an important ingredient to consider is reminds you that this convective instability which 220 00:27:26,450 --> 00:27:33,420 takes place in this outer region is not exactly the same as the convective instability taking place in a hydrostatic I mean, 221 00:27:33,530 --> 00:27:38,479 initially hydrostatic atmosphere. But this is not really an atmosphere. 222 00:27:38,480 --> 00:27:45,110 It's it's a flow of of gas from the shock to the initial subsurface. 223 00:27:45,110 --> 00:27:49,669 There is really a flow of matter. And so matter spends only a finite time in this region. 224 00:27:49,670 --> 00:27:58,160 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. 225 00:27:58,550 --> 00:28:02,870 And so this is really this ratio, the meaning of this ratio here you compare the balloon vessel, 226 00:28:02,870 --> 00:28:08,780 our frequency of growth rate with extra growth rates related to the B region, 227 00:28:09,350 --> 00:28:17,210 unstable region to the geography is the time we spent to cross this region. 228 00:28:17,530 --> 00:28:23,419 And these two crossing time is too short compared to the to the growth time. 229 00:28:23,420 --> 00:28:30,680 Then the flow. This flow is linearly stable. So this instability can be really stabilised. 230 00:28:31,070 --> 00:28:37,130 If the size of this region or is the velocity across this region makes the advection time short enough. 231 00:28:38,540 --> 00:28:42,950 So having understood that, you can for clarification, 232 00:28:43,250 --> 00:28:50,450 you say there's a gravitational wave between our signature gravitational wave and two things that GMO or gravitational radiation. 233 00:28:50,540 --> 00:28:54,620 Did I say gravitational wave? No, you haven't said anything on your slide. 234 00:28:55,340 --> 00:29:00,889 So the question. So acoustic. No, here, it's what I hear. 235 00:29:00,890 --> 00:29:10,220 Oh, sorry. Okay. You know, he. I wrote gravitational waves because when you have this and this large scale motion here, 236 00:29:10,610 --> 00:29:17,630 you move around a mass, uh, significant mass, like maybe three solar masses. 237 00:29:18,020 --> 00:29:25,489 And so you move, uh, you move around the, you change the gravitational field and you generate gravitational waves. 238 00:29:25,490 --> 00:29:30,060 The gravitational radiation. Yes. No. Yeah, yeah. 239 00:29:30,110 --> 00:29:39,770 No, no, no, no. Here, it's really gravitation. Yeah, this really the pressure gravity does the fashionable gravitational waves and also a neutrino. 240 00:29:39,800 --> 00:29:43,700 Uh, you know what you need is which are these two? 241 00:29:44,000 --> 00:29:45,950 This is very, very important point. 242 00:29:46,460 --> 00:29:57,410 Computational waves and neutrinos are the only two signals which can bring information directly from this very embedded region, 243 00:29:58,370 --> 00:30:06,110 whereas the what we call the piece of cake, which will be the final velocity of the pulsar years after the explosion. 244 00:30:06,770 --> 00:30:11,930 This one is some very important agnostic, but it's more indirect. 245 00:30:13,280 --> 00:30:16,429 And also for the information it's in nucleosynthesis, 246 00:30:16,430 --> 00:30:25,040 it's it's more in direct question with the velocities in the inner parts of the host as we talk about 247 00:30:25,700 --> 00:30:31,270 velocities of the neutron star of the gas No of is in a region with a large masses moving around. 248 00:30:31,280 --> 00:30:40,730 Yeah. So so the in blue here, the, the incident velocity of free falling material is 1/10 of the speed of light. 249 00:30:40,850 --> 00:30:43,280 Yes, but I was talking about this with the rate in the turbulent regions. 250 00:30:43,460 --> 00:30:52,940 So the turbulence region, uh, so the, let's say the, the sound speed in this region is uh, 251 00:30:53,570 --> 00:31:04,640 comparable to this 10th of the speed of light and the, and the motion point mark points three at best close to the shock. 252 00:31:05,090 --> 00:31:09,530 So it would be one third of 1/10 of the speed of light at best. 253 00:31:09,530 --> 00:31:16,070 But it's actually this is what you would obtain if you if you're a diabetic relative, it's relatively relativistic. 254 00:31:16,610 --> 00:31:23,900 Yeah, yeah, you can neglected. But it would be more like one manoeuvre would be more like one. 255 00:31:24,230 --> 00:31:29,930 So it would be 100th of the speed of light. Yeah. So that is a signal that that's pretty low relativistic. 256 00:31:30,020 --> 00:31:33,590 Yeah. That's a way production that really suppresses it quite, quite a lot. 257 00:31:33,770 --> 00:31:41,120 No, no, no, uh, no, no. The, uh, uh, y no, no. 258 00:31:41,120 --> 00:31:45,530 You can, you don't need, do you? Yeah. That's a high power. 259 00:31:45,740 --> 00:31:49,760 Yeah, yeah, yeah. But yeah, it's a chronic stress tensor, right? 260 00:31:49,850 --> 00:31:55,459 Yes. Okay. Yeah, no. Okay. But still, uh, still this does generate. 261 00:31:55,460 --> 00:31:58,520 Uh oh, of course it does. Yeah. Okay. 262 00:31:59,080 --> 00:32:05,149 Yeah, you're right. Yeah, you're right. This is an important factor to to to scale this computational wave. 263 00:32:05,150 --> 00:32:14,230 So you're right. Yeah. But it's a big amount of mass which compensates those the smaller velocities. 264 00:32:15,670 --> 00:32:24,640 Um, so to illustrate quickly what I've just said, there's a short movie which shows these two steps of coupling. 265 00:32:24,820 --> 00:32:29,900 So in blue you have acoustic waves travelling towards a stationary shock. 266 00:32:30,110 --> 00:32:35,260 It's like a talking with anywhere you have a stationary shock and and the infrared. 267 00:32:35,270 --> 00:32:46,840 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. 268 00:32:46,850 --> 00:32:51,190 So the blue one is propagating, the red one is simply attracted with the flow. 269 00:32:51,550 --> 00:33:00,160 And then in the second half of the movie, this vorticity wave, uh, simply attracted in a uniform flow, 270 00:33:00,430 --> 00:33:07,630 suddenly meets a region of this, of some external potential, which produces some deceleration. 271 00:33:07,690 --> 00:33:13,480 This is just a talking with that and you will see how the disintegration of a shear wave in red I. 272 00:33:13,720 --> 00:33:17,590 I say vorticity wave as a synonym of shear wave. 273 00:33:18,130 --> 00:33:21,340 Uh, this is simply a linear wave I'm talking here of linear coupling. 274 00:33:22,210 --> 00:33:27,880 This will generate a pressure wave. So to illustrate that, you just see this. 275 00:33:31,180 --> 00:33:34,570 So you see here the vorticity wave. This is a shock wave here. 276 00:33:34,840 --> 00:33:43,780 And this is the dislocation of region. As soon as you enter this this dislocation region, you generate this this acoustic wave, 277 00:33:43,780 --> 00:33:48,670 acoustic wave, you generate upwards and also downwards, uh, with different amplitude. 278 00:33:48,680 --> 00:33:58,960 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. 279 00:33:59,320 --> 00:34:09,160 So these are the two steps which allow you to think of this global, attractive acoustic cycle to explain this as instability. 280 00:34:09,760 --> 00:34:14,319 So I am sorry if this was a bit fast. 281 00:34:14,320 --> 00:34:16,750 I don't know if it was fast or not, but if you understand this, 282 00:34:16,750 --> 00:34:22,899 you can really understand that there will be some diversity of explosion forces because depending 283 00:34:22,900 --> 00:34:28,240 on the those relative timescales will be dominated by one or the other of these two instabilities. 284 00:34:28,720 --> 00:34:37,629 And and indeed, over the years I mean, recent years since 2012, because I showed you in 2009, 285 00:34:37,630 --> 00:34:43,930 this 15 hour massive explosion, which was successful at that time, people believe that explosions would be genetic. 286 00:34:43,930 --> 00:34:47,950 One explosion would be the same for any kind of progenitor. 287 00:34:48,310 --> 00:34:57,350 But over the years, people realised that the explosions were not all the same when they consider different masses of the progenitor. 288 00:34:57,360 --> 00:35:04,389 Also, from the 8 to 27 from masses, you would have different successful explosion. 289 00:35:04,390 --> 00:35:11,740 So it was many successful explosions, but some showed oscillations on a large scale and some didn't. 290 00:35:11,860 --> 00:35:17,740 And this was related to the relative importance of those of those two instabilities. 291 00:35:18,880 --> 00:35:27,130 I don't want to go into details, but people who've been in this field know that that there is there are many, 292 00:35:27,130 --> 00:35:31,900 many discrepancies between the different groups who perform this new simulations. 293 00:35:32,680 --> 00:35:35,799 Very few groups were able to do such simulations at the beginning. 294 00:35:35,800 --> 00:35:39,790 And there was the group of of Adam Burrows in Arizona and in Princeton, 295 00:35:39,790 --> 00:35:45,490 there was the group of Tomas Young kind gushing in the group of 20 minutes that combined Oak Ridge. 296 00:35:46,030 --> 00:35:51,939 And now there are more groups, but still a lot of discrepancies between these groups because all of these groups 297 00:35:51,940 --> 00:35:57,010 have to rely on different approximations to approximate neutrino transport. 298 00:35:57,550 --> 00:36:05,140 Neutrino transport, like radiation transport in multi GS is very difficult, these very time consuming for computer. 299 00:36:05,530 --> 00:36:13,390 And so you have to rely on approximations which don't give converging results from one group to another. 300 00:36:15,100 --> 00:36:24,460 So over more recent years there has been some progress, uh, on the side of nuclear physics. 301 00:36:24,520 --> 00:36:30,790 The uncertainties of the nuclear question of states have have been not completely sorted, 302 00:36:30,790 --> 00:36:43,750 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, 303 00:36:44,140 --> 00:36:53,830 of equations of state which could not produce such large masses with around the parameter space was smaller due to these nice observations, 304 00:36:54,550 --> 00:37:07,930 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. 305 00:37:08,070 --> 00:37:11,550 1.5 star mass is collapsing. But depending on the structure of the stock, 306 00:37:12,300 --> 00:37:22,140 you could be influenced by perturbations coming from the convective burning of all the 307 00:37:22,140 --> 00:37:30,000 turbulence in the last stages of oxygen and silicon burning before just above the iron core. 308 00:37:30,180 --> 00:37:34,050 So this is the effect of the collapse. 309 00:37:34,060 --> 00:37:41,670 Asymmetries can can be significant and contribute to two to help the explosion. 310 00:37:42,300 --> 00:37:57,090 And also the stellar evolution showed us that it's a very bad idea to to to label progenitors with a mass at birth. 311 00:37:57,090 --> 00:38:02,970 This zero age mini sequence must form a 10 to 40 or 100 years of very bad labelling, 312 00:38:03,480 --> 00:38:08,220 because the history of the star can be very different from one star to another. 313 00:38:08,670 --> 00:38:14,280 And and some have lost a lot of wind or a lot of mass wind. 314 00:38:14,290 --> 00:38:20,520 Some have, and some have binary companions which change their evolution. 315 00:38:20,790 --> 00:38:32,340 So all all those different histories and the complexity of burning in the stars made a very different style structure just before the collapse. 316 00:38:32,620 --> 00:38:35,100 Here. This parameter is the compactness parameter. 317 00:38:35,850 --> 00:38:51,210 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, 318 00:38:51,450 --> 00:38:56,490 how compact this this star is. 319 00:38:56,760 --> 00:39:05,000 And you can see the there was one hope at the moment that in this series of simplified models in Grey, 320 00:39:05,790 --> 00:39:14,880 uh, you can see the other stars which produce which don't explode and publish a black hole and in red, 321 00:39:15,210 --> 00:39:21,480 those which explode according to a simple prescription in one G, which is far from being an initial calculation. 322 00:39:21,810 --> 00:39:30,959 And people realise that the more compact, the the core of a star of the star, the more difficult it is to to explode. 323 00:39:30,960 --> 00:39:36,570 So there is a correlation between the production of black holes and the compactness of the core. 324 00:39:37,110 --> 00:39:47,270 So this is one complexity and, and a very interesting recent paper pushed this method to, to, to explore the parameter space and, 325 00:39:47,760 --> 00:39:57,270 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. 326 00:39:57,270 --> 00:40:07,250 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. 327 00:40:07,410 --> 00:40:10,260 But if you take these forces for our mass at the moment of collapse, 328 00:40:11,080 --> 00:40:19,950 the the the star has lost a lot of mass here in the grey and it's about 15 at our mass, 329 00:40:19,950 --> 00:40:25,320 whereas this one or 24 hour mass is heavier because it has lost less mass. 330 00:40:25,590 --> 00:40:33,780 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. 331 00:40:34,200 --> 00:40:44,340 And people realise that the distribution of neutron star masses in green here when when you manage to produce an explosion, 332 00:40:44,580 --> 00:40:48,209 the neutron star mass is somewhere between one and two solar masses. 333 00:40:48,210 --> 00:40:56,100 And the distribution you obtain from this simplified model matches the distribution of neutron star masses in here, 334 00:40:56,100 --> 00:41:01,950 in the dashed lines which are observed and the distribution of black holes you obtain, 335 00:41:02,340 --> 00:41:10,530 uh, here in these models matches the black hole distribution masses observed. 336 00:41:10,800 --> 00:41:17,760 If you assume that the hydrogen layer has been ejected during the before the collapse, just some observation. 337 00:41:17,760 --> 00:41:20,130 But that is you. That may be the DA. 338 00:41:20,580 --> 00:41:28,810 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, 339 00:41:29,100 --> 00:41:37,770 layer of the hydrogen, because this black distribution here, masses of black hole masses, much is more or less the observed distribution. 340 00:41:37,770 --> 00:41:44,400 So this is appealing as a possibility to to gain confidence in our simplified models. 341 00:41:44,880 --> 00:41:55,380 But still it's very, uh, very preliminary and very insufficient because we know that such models ignore the binary history of stars, 342 00:41:55,380 --> 00:42:06,180 which is, which is well established. And you have here in Oxford the specialist Philip opposite of he is specialist of this binary effect. 343 00:42:08,020 --> 00:42:19,540 Should not be neglected. And also all these one D models which describe all these series of of explosions, all are calibrated. 344 00:42:20,080 --> 00:42:26,890 There is some recipes which calibrate the evolution on a very specific, uh, 345 00:42:26,920 --> 00:42:33,070 supernova explosion, which is, uh, which is around 84 masses, which is a 1987, 346 00:42:33,230 --> 00:42:34,840 which is the supernova, which, 347 00:42:35,080 --> 00:42:42,790 for which we observed the neutrinos in 1987 because it exploded close enough to our galaxy in the large Magellanic Cloud. 348 00:42:43,360 --> 00:42:51,830 So it's it's a bit dangerous to calibrate all those models on the single explosion, because this particular explosion, 349 00:42:51,850 --> 00:42:58,270 1987 eight, was known to be a very particular star, which was actually a binary system. 350 00:42:58,600 --> 00:43:07,570 And so it's dangerous to to think that all the, all the models will follow the behaviour of the 1987. 351 00:43:08,260 --> 00:43:19,630 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, 352 00:43:19,900 --> 00:43:33,190 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, 353 00:43:33,190 --> 00:43:38,200 on the deep physical understanding to, to finish with this overview. 354 00:43:38,520 --> 00:43:51,179 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, 355 00:43:51,180 --> 00:44:02,169 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. 356 00:44:02,170 --> 00:44:13,470 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, 357 00:44:13,750 --> 00:44:22,469 then they added a very small ingredient to the computation, which was the strangeness content of, of neutrons. 358 00:44:22,470 --> 00:44:33,370 So the, uh, the diffusion of uh, uh, neutrinos on neutrons, uh, depends on the small parameter, which is the strangeness. 359 00:44:33,850 --> 00:44:37,570 Neutron does not contain any strain that does not contain any strange quark. 360 00:44:37,870 --> 00:44:45,399 But there is still strangeness, uh, content, which is not exactly zero and which is constrained by, 361 00:44:45,400 --> 00:44:52,180 uh, experiments to be in a certain range around zero and very few. 362 00:44:52,240 --> 00:44:56,910 During this lifetime. It was enough to change this non exploding model into an explosion. 363 00:44:56,920 --> 00:45:00,460 Not, not that this strangeness content is is crucial. 364 00:45:00,910 --> 00:45:09,010 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. 365 00:45:09,910 --> 00:45:18,069 So this is how it looks like when it did not explode. Uh, so again, you have this, uh, shockwave in black. 366 00:45:18,070 --> 00:45:26,020 It's not empty ion falling towards the centre and, uh, and in the middle you will have the portal neutron star. 367 00:45:26,410 --> 00:45:30,200 So you the symmetry is broken by instabilities again. 368 00:45:30,200 --> 00:45:36,400 And you on the smaller scale, you have the buoyancy driven instabilities due to neutrino absorption. 369 00:45:36,970 --> 00:45:47,890 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. 370 00:45:48,130 --> 00:45:50,530 And so the two instabilities here coexist. 371 00:45:51,070 --> 00:46:01,809 And after a while, uh, none of them is enough to, to, uh, to change the degree of a symmetry sufficiently to, 372 00:46:01,810 --> 00:46:08,500 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 373 00:46:08,500 --> 00:46:12,700 helpful to the explosion in the sense that they are able to push matter on one side. 374 00:46:13,090 --> 00:46:22,250 And on this side, the, the matter is dense enough to absorb more neutrinos than, uh, than when matter was distributed historically. 375 00:46:22,630 --> 00:46:26,890 So in this case, the explosion doesn't seem to proceed. 376 00:46:28,270 --> 00:46:33,700 So this is annoying, but this is just one simulation and parameter space is gigantic. 377 00:46:33,700 --> 00:46:39,760 So we should not, uh, rely too much on this particular case, and we should rely on the physics. 378 00:46:40,870 --> 00:46:44,859 So the physics is what you see in your kitchen sink, for example. 379 00:46:44,860 --> 00:46:47,640 This is how you built your physical intuition. 380 00:46:47,650 --> 00:46:55,990 This is a hydraulic jump in your kitchen sink, and you know that the hydrogen jump is a transition between a fast flow, 381 00:46:55,990 --> 00:47:02,139 which is very thin layer, a thin layer of water, and the fast which becomes slower and thicker. 382 00:47:02,140 --> 00:47:07,840 So you have converted kinetic energy into potential energy across this hydraulic. 383 00:47:08,350 --> 00:47:18,160 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. 384 00:47:19,180 --> 00:47:22,410 I mean, the opposite of a kitchen sink, hydrogen. 385 00:47:22,430 --> 00:47:28,990 So we would like to inject water from the outside towards the centre and produce this transition. 386 00:47:29,110 --> 00:47:33,700 You know, such a domino in the same way as we have a spherical shock wave. 387 00:47:33,910 --> 00:47:36,050 When we approached the neutron star in the middle. 388 00:47:36,070 --> 00:47:46,210 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, 389 00:47:46,690 --> 00:47:52,000 of the cylinder by splitting over here and the, and the, 390 00:47:52,040 --> 00:48:03,370 and this and the slope of this surface is meant to mimic the Newtonian potential, uh, uh, governed by the neutron star. 391 00:48:03,400 --> 00:48:12,310 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. 392 00:48:12,610 --> 00:48:17,920 So you have this analogy even though you are dealing with a, with a incompressible fluid, 393 00:48:18,190 --> 00:48:26,350 the variations of depth in this incompressible fluid mimic the variations of density in a compressible gas. 394 00:48:27,490 --> 00:48:34,660 So instead of acoustic waves in the gas, you have your first gravity waves in a in a in this flow. 395 00:48:35,020 --> 00:48:41,340 And you have this analogy between the seven equations describing the shallow water. 396 00:48:41,350 --> 00:48:43,010 So here's the continuity equation. 397 00:48:43,030 --> 00:48:53,050 H is the depth, and here is the only equation which you can compare to the continuity equation, your gas and the earlier equation. 398 00:48:53,440 --> 00:48:57,210 Well, I have slightly transformed the equation. 399 00:48:57,220 --> 00:49:06,160 I mean, the pressure source has been separated into a ontology and I turn to to show the boundary constant. 400 00:49:06,160 --> 00:49:10,030 But this is really an equation, a geometric case and a isothermal case. 401 00:49:10,030 --> 00:49:19,000 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, 402 00:49:19,180 --> 00:49:25,840 but it resembles the Da Vinci case in the sense that the until P looks like gamma equal to gas. 403 00:49:26,410 --> 00:49:32,680 So we call it the isotropic gas law, non-stop equations with gamma equal to. 404 00:49:32,770 --> 00:49:39,500 And when you accept this kind of a intermediate analogy between these two type of gases, uh, 405 00:49:39,550 --> 00:49:45,850 you, you expect the same physical processes to take place, the same coupling processes. 406 00:49:46,210 --> 00:49:58,190 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, 407 00:49:58,440 --> 00:50:02,910 and you expect to have the same instability and on a different scale. 408 00:50:02,920 --> 00:50:09,909 So you the ratio of timescales is given by this ratio of of gravitational forces. 409 00:50:09,910 --> 00:50:14,710 And in the case of this level, you have to experiment you you expect to have a process, 410 00:50:15,280 --> 00:50:22,080 an instability taking place on a timescale 100 times slower than the value. 411 00:50:22,450 --> 00:50:26,950 But in astrophysics, in astrophysics, we had 30 milliseconds oscillations. 412 00:50:26,950 --> 00:50:30,820 So here we expect 3 seconds, uh, oscillations. 413 00:50:31,660 --> 00:50:36,490 And the size of course is smaller. It's 1 million times, about 1 million times smaller. 414 00:50:37,960 --> 00:50:46,300 So Steve mentioned the fact that this is as simple as a garden kitchen sink physics, and it's simple as a garden experiment. 415 00:50:46,660 --> 00:50:51,620 So I built this experiment in, in a few months in my garden and, uh, 416 00:50:51,820 --> 00:50:59,770 and I show this to encourage any, uh, any physicist, any young physicist, young or old, 417 00:50:59,770 --> 00:51:07,210 to try things yourself if you don't, if you haven't done it yet because it's, it can be rewarding, 418 00:51:07,870 --> 00:51:16,810 since this very simple experiment in the end made the the front cover of people in, in 2012. 419 00:51:17,290 --> 00:51:21,220 So all the results were obtained in this very simple device. 420 00:51:21,460 --> 00:51:27,970 My institute, after a few years, uh, helped me build a much more sophisticated one. 421 00:51:28,180 --> 00:51:33,069 But the results were obtained in the, in the, in the very basic one. 422 00:51:33,070 --> 00:51:37,690 And this is what you observe in the, in the experiment. So you inject water through a slit. 423 00:51:38,290 --> 00:51:41,860 The hydraulic jump is more or less shattered off. 424 00:51:42,700 --> 00:51:47,710 The injection is as stationary as possible, as homogeneous as possible. 425 00:51:48,010 --> 00:51:50,649 And the hydrogen and the water is able to escape. 426 00:51:50,650 --> 00:51:59,020 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. 427 00:51:59,020 --> 00:52:06,850 The no region here is there's no transverse motion yet. And, and you see that, uh, the instability develops. 428 00:52:07,900 --> 00:52:13,150 On the three with a three second, uh, oscillation period. 429 00:52:13,540 --> 00:52:16,600 So this oscillation gets amplified. 430 00:52:17,350 --> 00:52:24,250 And after breaking the symmetry, the symmetry is going to be broken again because this, 431 00:52:24,580 --> 00:52:30,340 this axis, this random axis of oscillation is going to to change into a rotation. 432 00:52:30,730 --> 00:52:37,750 And you see, now that the the hydrogen starts rotating and the as the hydrogen rotates in one direction, 433 00:52:38,020 --> 00:52:42,490 the inner regions of the flow start rotating in the opposite direction. 434 00:52:43,090 --> 00:52:46,900 Since there is no angular momentum injected in the experiment, 435 00:52:47,230 --> 00:52:56,380 you you expect that some some rotational motion appearing in one region should be compensated by some rotational motion, 436 00:52:56,590 --> 00:53:01,200 some opposite rotational motion in some other region. 437 00:53:01,210 --> 00:53:12,270 And so we checked the validity of this experiment by doing a shallow water simulations, and we compared it to the gas simulation. 438 00:53:12,280 --> 00:53:18,759 So here is shallow water. And here is, uh, astrophysical gas simulation. 439 00:53:18,760 --> 00:53:28,809 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, 440 00:53:28,810 --> 00:53:33,880 nonlinear symmetry breaking and uh, and rotation with this kind of angular point here. 441 00:53:34,450 --> 00:53:45,729 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. 442 00:53:45,730 --> 00:53:45,880 And, 443 00:53:46,240 --> 00:53:56,770 and this is the agreement which we obtained between the oscillation periods of the experiment and the oscillation period of the numerical simulation, 444 00:53:56,770 --> 00:54:02,290 and also the selective analysis of the secondary positions for different sizes of the hydraulic jump. 445 00:54:02,320 --> 00:54:07,780 We can we can choose this the initial size of the hydrogen by, uh, 446 00:54:08,170 --> 00:54:14,440 by choosing the height of the cylinder and immediately see if we want to have a large hydrogen jump. 447 00:54:14,440 --> 00:54:20,680 We have a high, uh, uh, uh, high cylinder in the middle. 448 00:54:22,120 --> 00:54:26,139 And so it's quite, uh, I should, uh, hurry up. 449 00:54:26,140 --> 00:54:35,880 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, 450 00:54:36,220 --> 00:54:44,580 the discourse which is affecting water and all sorts of uh, differences, as I said, between the lack of buoyancy. 451 00:54:44,590 --> 00:54:49,570 And so it's that's we didn't expect to have such a good agreement. 452 00:54:50,080 --> 00:54:55,150 But, uh, and actually the agreement is very good on the oscillation timescale, but there is, 453 00:54:55,600 --> 00:55:00,610 there is some disagreement, slight disagreement on their growth rates, which we, we think we understand now. 454 00:55:01,450 --> 00:55:07,810 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. 455 00:55:08,230 --> 00:55:15,250 And so we have now this experiment in the museum in Paris for to explain supernova physics to to the public. 456 00:55:15,250 --> 00:55:22,990 After a period of two months where we showed ourselves this to the public of the the museum is showing this, uh, themselves. 457 00:55:23,440 --> 00:55:24,760 We are very happy about that. 458 00:55:25,030 --> 00:55:35,340 And I would like to spend a few less few minutes talking about floatation effects because now we have a new experiment which uh, 459 00:55:35,810 --> 00:55:39,190 uh, allows the full experiment to rotate. 460 00:55:39,580 --> 00:55:45,940 And what's happening now is that water is injected with some elemental, 461 00:55:46,660 --> 00:55:54,620 and the instability always develop in the same direction as the rotation of the progeny just on its own. 462 00:55:55,360 --> 00:56:01,690 And what's happening is that in our region, try to rotate in the opposite direction compared to the progenitor star. 463 00:56:02,200 --> 00:56:08,620 And indeed you can end up with inner regions rotating opposite. 464 00:56:08,950 --> 00:56:13,599 We're going to see that now. They are going to rotate in the direction opposite to the progenitor. 465 00:56:13,600 --> 00:56:20,530 So you can think of neutron star rotating opposite to the direction of rotation of the opportunity to because 466 00:56:21,130 --> 00:56:29,050 this instability has has produced shockwaves rotating in the same direction as the as topological star. 467 00:56:29,260 --> 00:56:34,360 You see, the motion is chaotic, but you see that this region rotates opposite. 468 00:56:34,480 --> 00:56:39,270 Now to the to the progenitor star. 469 00:56:39,280 --> 00:56:46,510 So this was predicted actually by numerical simulations by my, my colleague John Blondin in uh, in the US. 470 00:56:46,690 --> 00:56:49,840 But this is the experimental analogue of it. 471 00:56:50,650 --> 00:57:00,610 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, 472 00:57:00,970 --> 00:57:07,600 uh, surprising development of this experiment is what's what's hot, what's happening when the rotation rate increases. 473 00:57:08,220 --> 00:57:12,350 To even higher overall mental. 474 00:57:12,690 --> 00:57:22,380 Then you have another type of instability which is called the which is called accommodation instability and political instability, 475 00:57:23,310 --> 00:57:27,720 which is not related to the instability that I've mentioned so far, 476 00:57:28,110 --> 00:57:35,969 but is related to the distribution of angular momentum in the in the fluid, in the differential, your rotating fluids. 477 00:57:35,970 --> 00:57:44,280 So this is something that Steve is very familiar with when magnetic fields are in, especially when magnetic fields are included. 478 00:57:44,640 --> 00:57:48,210 But here it's a it's an instability, which is purely hydro. 479 00:57:48,540 --> 00:57:57,000 And of course, when you when you have strong rotation rates, you you need to worry about the possible generation of magnetic fields. 480 00:57:57,600 --> 00:58:01,440 So this is a new direction of the of this field of research, 481 00:58:01,440 --> 00:58:06,839 where this the mechanism of this is that it is a kind of has been interpreted in the 482 00:58:06,840 --> 00:58:12,629 eighties as a kind of overt reflection of acoustic waves across the rotation region. 483 00:58:12,630 --> 00:58:26,100 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. 484 00:58:26,100 --> 00:58:32,850 What you see, it's called low shareholder value t being the kinetic energy and w the gravitational energy. 485 00:58:33,450 --> 00:58:42,569 It gives this kind of a spiralling pattern, your simulations and, and, and the existence of this quotation region. 486 00:58:42,570 --> 00:58:49,830 In the very region, you have a region of the flow which rotates faster than the, than the spiral pattern. 487 00:58:49,830 --> 00:58:54,630 And this is a key and region to to identify this instability. 488 00:58:54,870 --> 00:58:59,910 The Phoenician is not trivial, despite the small sketch show I showed before. 489 00:59:00,450 --> 00:59:04,259 So I, I don't have time to, to elaborate more on this. 490 00:59:04,260 --> 00:59:15,570 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, 491 00:59:15,600 --> 00:59:27,540 is able to decelerate the, uh, the pulsar compared to the velocity it would have due to simple actually symmetric, uh, uh, collapse. 492 00:59:28,080 --> 00:59:37,080 But so we, we need now to, uh, it's just ongoing research which we need to investigate, including related fields now. 493 00:59:37,410 --> 00:59:40,049 So I leave you with my conclusions. 494 00:59:40,050 --> 00:59:47,760 My, my main point is to say that hydrodynamic instabilities are king region to the collapse, to the mechanism of supernova explosions. 495 00:59:48,270 --> 00:59:54,389 And this my other point is to say that with very simple tools like this, simple something, 496 00:59:54,390 --> 01:00:00,960 we are able to capture at least two of these uh, um, uh, unstable processes. 497 01:00:01,320 --> 01:00:05,940 And this is a good way to, to build up our physical intuition about this, uh, physics. 498 01:00:06,450 --> 01:00:06,780 Okay.