- il y a 2 jours
The final agony of stars is often observed across many galaxies as supernovae, but they can also die quietly in despair. In their wake, they leave behind mesmerizing and mysterious remnants, some of which even lack a physical surface. During the lectures, we will peek behind the veil of secrecy of these compact objects, where gravitational, nuclear and electroweak forces are pushed to their extremes in an exciting competition for dominance.
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TechnologieTranscription
00:00:00Finally, we can start the course of the lecture.
00:00:03Hopefully, we have some time today to learn something.
00:00:07I'm Nikolai, and I will be talking about compact objects.
00:00:12And first of all, I want to ask you to not hesitate and ask questions just during the talk.
00:00:18You can interrupt me.
00:00:19If I say some stupid things and you want to correct me, please stop me and ask all the questions during the talk.
00:00:27So, then everything will be understandable, and I will feel contact with the auditorium.
00:00:34So, we'll talk about this fascinated audience, but first, let's look in the sky.
00:00:40The typical night sky in Brussels.
00:00:43You can see usually a nice Milky Way here.
00:00:48Do I have some kind of pointer here?
00:00:50Okay, I will use my links.
00:00:54See the Milky Way here.
00:00:55And the first thing that you notice is that there is, of course, kind of a bright center.
00:01:00But then there is a lot of things that obscure it.
00:01:03So, there is a lot of actually gas and dust in the Milky Way.
00:01:07And also, the visible Milky Way consists of 85% of stars.
00:01:12It's still 15% of gas and dust, and you can see it all around.
00:01:16And this gas, it consists of hydrogen, 70%, and 28% is helium, and the other, like, astronomy is very precise science.
00:01:27So, the other, we call just metals, and don't care about them.
00:01:31So, where are stars exactly, Bond?
00:01:34If we have a zone in the sky, do you have a feeling where the new stars should be formed?
00:01:42Do you have some guess on this figure?
00:01:47What's the cloud?
00:01:49Yes, you're right.
00:01:51Just right here, new stars are born.
00:01:55I mean, it's easy, yeah?
00:01:58These are called molecular clouds.
00:02:02They contain molecular hydrogens, and they are very apart.
00:02:06So, they actually absorb all the light behind them, and this looks like a huge void, kind of nothing there.
00:02:13But actually, it's just a giant cloud.
00:02:16It's called a global, and this is Barnard 68.
00:02:20And this is actually a lot of dust, which absorbs the light.
00:02:25And there is another example of this.
00:02:27It's very famous, Eagle Nebula, and it's seen by Hubble Telescope.
00:02:31And here, as I said, that also, this cloud represents 1% by volume in the whole galaxy.
00:02:40Because they are very dense, I mean, by dense, I mean, like, 100 or 1,000 molecules per cubic centimeter in comparison with water here.
00:02:50They feel 50% of the mass of the interstellar medium.
00:02:55And here is another example with finger of gold, Nebula, obviously.
00:03:01And then, another star-forming region is F106.
00:03:05And here's a nice thing.
00:03:07You can see that the new world stars are actually in black light here in the garden realm.
00:03:12So, we can really see and probe the star formation here.
00:03:17And then, there is another famous thing that you can actually maybe look today.
00:03:23And here, you already saw it.
00:03:24You can do astronomy.
00:03:27In the Orion constellation here, there is a Travetsum cluster that is discovered by Galilei.
00:03:37Here's the location on the night sky.
00:03:39And I was very impressed when I first looked in the telescope with my own eyes and saw this very nice, beautiful nebula.
00:03:47And maybe you already did it or you could do it today or later.
00:03:52This is must to observe.
00:03:54And this is also a star-forming region.
00:03:57This is a zoom feature with Hubble telescope.
00:03:59Here, you can see the newly born stars.
00:04:02And this is kind of like a sword of Orion here.
00:04:08And then, the question is, like, how do exactly stars form?
00:04:13I know, after me, there's going to be a whole cycle of lectures about this.
00:04:17But this is kind of necessary for us.
00:04:20I will give you some introduction.
00:04:22But then, the really detailed information will be after me.
00:04:27So, then, there was Sir James James.
00:04:31And in the end of 19th century, he kind of analyzed how can we form stars from the moon.
00:04:38Just these dense clouds.
00:04:39So, we have a dense cloud, this self-gravitating object.
00:04:43And he actually, by solving equations of gas-dynamics, he saw that if we insert some perturbation,
00:04:52sun clouds will be unstable and they start to collapse under its own gravity.
00:04:59And the criterion he derived was about if this cloud has more than two solar masses.
00:05:04In astronomy, you measure everything in solar masses.
00:05:08There is a scale of 10 to the power of 33 grams, if it tells you something.
00:05:14So, if it is more than this, then the cloud starts to collapse under its own gravity.
00:05:20And you can see its collapse, it's kind of like spherical fate.
00:05:24But then, because of the movements here and there, the cloud has kind of net angular momentum.
00:05:31And then, it starts to spin around and there forms accretion disk.
00:05:35Here, some of the gas is expelled here.
00:05:38Here, it's ejected.
00:05:40These are called jets.
00:05:42And then, you can see also here, the accretion disk, some jets.
00:05:48And then, in this accretion disk, the planning system can transform.
00:05:52And here's the usual timescape of it.
00:05:56The interesting thing that if you consider this collapse of the cloud,
00:06:01at some point in the part of the cloud, starts to be unstable against collapse itself.
00:06:08So, there can be some fragmentation.
00:06:10And actually, more than 50% of the stars are in binary system, exactly because of this.
00:06:15Because this cloud fragmented into small pieces.
00:06:19And it can be double systems, like binary system, or system of three stars, or system of four stars, and so on.
00:06:29Here's some examples.
00:06:31Here's again, a couple of space telescopes.
00:06:34The feature of disk, again, in Orion Nebula.
00:06:38And this is artist-centric, and how planets are formed in all this, in the disk.
00:06:46So, then we question how these gas will resist to the gravitation.
00:06:52So, what is formed then is kind of like a giant ball of cloud gas,
00:06:57because when you start to compress the matter, it heats up.
00:07:01And there is a so-called hydrostatic polygram,
00:07:03and it basically says that you have pressure of gravity as you go.
00:07:08to pressure of gas, and this compression goes as a matter to heat up.
00:07:12And then you heat up the matter, you have kind of gas particles,
00:07:16and they move all around, like chaotic movements.
00:07:19And then, if you kind of put the ball there, it will feel some kind of momentum that is transferred to it,
00:07:27this kind of a pressure.
00:07:28And with this gas, and here's the equation for the pressure, which depends on the density and on the temperature.
00:07:38And this is how gas resists to the gravity.
00:07:42So, actually, can we call it already the star?
00:07:47This will be the question.
00:07:49Another thing, that we also have radiation, and radiation also can create pressure.
00:07:56So, if you have some source of light, and you put it, I don't know, if you're trying to light some kind of a list,
00:08:03it will also feel pressure, but of course, kind of negligible.
00:08:07But it can be used, and was used, for solar sails in our system.
00:08:13Actually, the Japanese Aerospace Agency, they created a large kind of solar sail that was traveled in the solar system,
00:08:23and it was operating there.
00:08:24So, this is kind of a future, and there are some projects kind of going to light with a laser on the sail,
00:08:32and then, with a laser, you can have some kind of space, a small spaceship that will travel to large distances.
00:08:41And this radiation pressure also is important in the start, but it actually is more important for massive aspects,
00:08:51like time with solar masses, and today we'll be more talking about from 0.1 to 10 solar masses.
00:09:00Okay, so, can we call this a star?
00:09:04This is a question.
00:09:06So, we have a gravitation energy, which is released, and it powers the stars,
00:09:11and Lord Kelvin calculated what is the sun's age.
00:09:16If you just take the luminosity of the sun, and we divide it by gravitational energy,
00:09:22and he obtained that the sun is 30 million years old.
00:09:25Is it true?
00:09:27Yes, of course, it's not true.
00:09:31And from radio-islet of dating, already at his life, he already knew that Earth is actually 4.5 billion years old.
00:09:42So, this is not the correct age of the sun, and the question is, what powers the sun?
00:09:48What is the source of the energy in the sun?
00:09:51For this, we need to dive a bit deeper into physics.
00:09:56So, here's kind of like particles and matter, right here, we have kind of normal matter,
00:10:02this is here, the table, everything around.
00:10:06And then it is composed of molecules, as you know, these are composed from atoms.
00:10:12Atoms are composed of nucleus with electrons.
00:10:15It usually is shown by this, but actually it's kind of huge empty space here.
00:10:20If you imagine that the nucleus is kind of like, but the scale just is one centimeter,
00:10:26then the electron that orbits its nucleus will be one kilometer away.
00:10:30So, you just imagine how it's all empty.
00:10:34This is not true about the nucleus itself.
00:10:38It consists of protons and neutrons, which are nucleons, and it's a very dense system.
00:10:43And we can, I mean, we will not go further.
00:10:46This is kind of enough for us.
00:10:48And then, there are kind of four fundamental forces.
00:10:52First is gravity.
00:10:53And we know that all the bodies are attracted to each other.
00:10:56It's always attractive.
00:10:58And it scales proportionally to inverse distance between the object square.
00:11:07And this is what governs the evolution of large distances, like galaxies evolution,
00:11:13and then also what allows me to stay here, or Louis Armstrong to stay on the moon.
00:11:20And then there is electrostatic force equation, or electromagnetic force, which also scales closer as gravity,
00:11:33but it can be both repulsive and attractive.
00:11:36Attractive, you can feel it if you wrap the air balloon in the air,
00:11:40and then you can do some attraction and repulsion,
00:11:43and then you can have some magnets that repulse and so on.
00:11:46And this will be abundant later.
00:11:48But this is not the source of energy that powers the star.
00:11:52Then we have strong nuclear force, which binds the nuclei,
00:11:56and pulls all the nucleons together.
00:11:59And we have big interaction, which just converts Newton to Bratons and back.
00:12:05So, I think you already know the answer.
00:12:08This is the strong interaction, actually, which powers our sun.
00:12:14This is kind of like the sketch of all fundamental forces together.
00:12:20You can see it kind of like it's strong.
00:12:22The strength is, let's say, one.
00:12:24There is electromagnetic force, which is not as strong.
00:12:27And there is big interaction, which is much, much weaker.
00:12:31And gravity, this is kind of a scale.
00:12:33It's very small.
00:12:35But just because it acts everywhere under all distances,
00:12:39and it's always attractive, this is very important for evolution of galaxies.
00:12:45So, then we go to what is nuclear-abandoned energy.
00:12:51So, if you have the system of nucleons here, this kind of fundamental bridge that forms our nucleus.
00:13:00And measured masses of each nucleon, you will have, for example, the system.
00:13:05And you will have the energy of the system with just number of protons or mass of protons,
00:13:11number of neutrons or mass of neutrons.
00:13:14And you then can measure separately the mass of the nucleus.
00:13:19So, there are so-called time of flight measurements.
00:13:22So, you have an accelerator, and your particles will move here in the accelerator.
00:13:28And just by their speed and by the frequency of the movement back and forth,
00:13:35you can measure their mass.
00:13:37It's very simple.
00:13:38And the funny thing is that with this, you can measure the masses in the nucleus,
00:13:45and it turns out to be smaller than the mass of the separated nucleons.
00:13:50separate, like, taken here.
00:13:54So, there exists some binding energy, this kind of additional thing,
00:13:58which is the difference of masses of all nucleons minus mass of the nucleus itself.
00:14:07Which can be considered as the energy cost to break the nucleus,
00:14:12or you can consider it as the energy gain when the nucleus is created.
00:14:18So, in other words, by fusing the particles like hydrogen, which is just one proton,
00:14:26by fusing them together and building heavier elements, like you have hydrogen,
00:14:31you build helium, which is two protons and two neutrons.
00:14:36And you have some energy gained from this.
00:14:39And then you go further, and you have carbon and then oxygen.
00:14:44And you fuse. You see that there is a fusion line.
00:14:46And in all of these processes, you gain the energy.
00:14:49There is a huge energy release, actually.
00:14:51And then you go until iron. Iron is the most bound nucleate.
00:14:55That's why there are a lot of iron everywhere.
00:14:58And then if you try to go further, like, to create some energy,
00:15:02to have some energy gained from iron, you cannot do it.
00:15:05That's right. And then there is only fission.
00:15:08So, you kind of break the nucleus from there.
00:15:12But here it wasn't for us that we can have some energy from converting hydrogen
00:15:18to heavy elements, or helium.
00:15:20But then the problem is, like, why don't we do it everywhere?
00:15:26Why don't we just take one protein, another protein, and then we fuse them,
00:15:31and we have a lot of energy?
00:15:32This would solve a lot of problems.
00:15:34The problem is pull-on potential, because they are both positively charged.
00:15:39And if you try to move them closer and closer together,
00:15:43they will feel a lot of repulsive force.
00:15:45And this is, as I said before, inverse proportional to the distance squared.
00:15:52So, you close and closer, the force raise.
00:15:55And then people thought, okay, this idea doesn't work in this stuff.
00:15:59We cannot fuse two positively charged particles together.
00:16:04But then people discovered or developed quantum physics.
00:16:08That allowed for a lot of magic things.
00:16:11One of them is quantum tunneling.
00:16:13That actually particles can penetrate this barrier and in the end fuse.
00:16:18Because, as I will talk later, actually particles can be also considered as waves.
00:16:24And this wave is kind of like smeared here, and then another one, and actually then they can be fused together.
00:16:33This is what happens in the star.
00:16:36But you need quite high temperature, like 5 million Kelvin and high density to start hydrogen fusion.
00:16:44So, what will happen if you have some gravitationally bound object, which does not fulfill this condition, which doesn't have a lot of temperature?
00:16:57Yes.
00:16:58Excuse me.
00:16:59Excuse me.
00:17:00So, it gets like, harder and harder to, like, the cosine and cosine we all, it gets harder and harder.
00:17:07And then suddenly drops, like the, yeah, like the recursion suddenly drops and they just bound it?
00:17:15Yes.
00:17:16I will discuss in the big details, but in the, indeed if you have, for example, two fields, then they just become bound.
00:17:22Because then strong force, it acts only on the short distances.
00:17:27So, here you have a lot of repulsion.
00:17:30And then at some point you will have, like, a huge repulsion.
00:17:34As we discovered before, it's here.
00:17:38It has much larger strength, strength 1, in contrast to 1 divided by 137.
00:17:45So, it's much stronger.
00:17:46Coulomb is important in the nuclei.
00:17:50And actually here in the binding energy, if you go through really large guys, they have a lot of protons.
00:17:57And at some point, some of them become unstable.
00:17:59Exactly what it is, because Coulomb kind of is repulsive.
00:18:02It kind of leads to fission.
00:18:04But for us now, for example, for Helium, it works quite well.
00:18:11Because of the very strong interaction afterwards.
00:18:19Someone didn't like my explanation.
00:18:22No, I'm joking.
00:18:24I'm joking.
00:18:25Yeah, you're free to be for sure.
00:18:26And then, what happens if these conditions are not fulfilled?
00:18:33If the star cannot fuse hydrogen?
00:18:36So, then it becomes, let's go, the ground force.
00:18:40The object that has less than 08 solar masses, or 13 to 18 masses of Jupiter.
00:18:48They can fuse a little bit of Deterium, so there is kind of some reactions going on.
00:18:55It's not like the planet.
00:18:56The planet doesn't have any reactions.
00:18:58It has some burning, but it doesn't become a real star.
00:19:04And here's kind of observation of brown dwarf in the system, GLEAS 229.
00:19:16And then, we go to the normal stars.
00:19:21And there, there is a process of fusion of hydrogen.
00:19:25But then it's a bit more complicated, actually, process.
00:19:28Because you cannot form, like in the nucleons, in Helium, you have two neutrons and two protons.
00:19:36You cannot create the system just for protons.
00:19:39Because it will be all repulsive.
00:19:41So, actually, the first reaction is called proton-proton cycle.
00:19:46The first reaction is actually proton decay in the field of another proton to positron and Nincino.
00:19:54So, actually, it is governed by V-interaction.
00:19:57And that's why it's very, very slow process.
00:20:00And it takes like billion of years.
00:20:03While the second reaction, if you have just Deterium and hydrogen, they fuse very fast in one set.
00:20:10So, this reaction is super, super slow.
00:20:13And that's why our sun and other stars, like Loma stars, they live very, very long.
00:20:20And they're like more than eight of the universe, some of them.
00:20:23And then, there is an energy release in this reaction that maybe doesn't tell you about.
00:20:29We'll discuss later.
00:20:32There is another cycle which is active in the, a bit larger stars, but okay.
00:20:40Here, we also have kind of hydrogen.
00:20:43This is kind of a catalyst reaction with carbon and oxygen in there.
00:20:48I mean, what do you do is to convert in the hydrogen here, hydrogen here, here, and here to create helium in there.
00:20:55Then, the question is like, how do we know about this?
00:21:02So, here, this reaction, for example, produces photons and they all go into the heat.
00:21:07Actually, this photon shows really only one centimeter in the star.
00:21:12How, I mean, how do we really know that there is nuclear reactions going on there?
00:21:17Like, you can see that it takes like 200,000 years for a photon to move from the core to the surface.
00:21:23And it will be here absorbed and then emitted, and it will be not the same photon anymore.
00:21:28So, the information is lost.
00:21:32Do you know the answer?
00:21:35What are the particles that freely escape the sun?
00:21:42Yes, you are right.
00:21:44There is a nice particle, clear-produced neutrino.
00:21:48It just travels directly from the sun.
00:21:51It doesn't kill it.
00:21:52It goes out, and then it goes to the earth.
00:21:54Wonderful, you would say.
00:21:56Let's detect it.
00:21:57But then, if neutrino escapes the sun, how can it be trapped on Earth?
00:22:06And we need huge detectors.
00:22:08And it was done in, it is called Olmstead experiment by Raymond Davis in South Dakota.
00:22:16He filled a huge tap with the chlorine.
00:22:19You all know, you use it, I don't know, in the pool or to clean something and so on.
00:22:23A huge tank of chlorine.
00:22:26And then, there is like a little, like a few atoms in all this huge tank react with neutrinos.
00:22:33And then they create argon.
00:22:35And then you need, I mean, it's a very precise experiment.
00:22:38Then you need to collect all of them.
00:22:40And then you can count how many these atoms were produced.
00:22:44Or how many neutrinos did you observe.
00:22:47Or how you can actually calculate and compare your experiment to the theory.
00:22:52How many neutrinos from the sun was emitted.
00:22:54And it was done.
00:22:55And what people obtained is that they obtained only one third of the theoretical value.
00:23:03And then theoreticians say, okay, you have a problem with your experiment.
00:23:07It cannot be one third.
00:23:09And then maybe, I don't know if you've heard of this or not.
00:23:14Then people did another experiment.
00:23:17And they detected not only electron neutrinos.
00:23:20Because actually neutrinos have three species.
00:23:23And they detected the other species of neutrinos.
00:23:27And they found out that actually neutrinos oscillate.
00:23:32Because they have masses.
00:23:33I don't know.
00:23:34Yeah.
00:23:35Why do you choose chlorine to fill the tank?
00:23:42Does it interact in a specific way with neutrinos?
00:23:47Okay.
00:23:48It's one of the things that interact.
00:23:50And I think it's also cheap.
00:23:52You can have a huge tank of this chlorine.
00:23:57It's not like other precious gases and so on.
00:24:01But actually you can do it.
00:24:03Like I think it was gallium.
00:24:05There was an experiment also in Soviet Union.
00:24:08And they took it from all the huge Soviet Union.
00:24:11And this time they collected it.
00:24:12Also built it some tank with another thing.
00:24:14So it was a whole thing.
00:24:15It was very expensive.
00:24:17But the Soviet Union liked to spend money on something like this.
00:24:24Then later, I mean with a more precise technique.
00:24:29In the Super-Kameakande facility in Japan.
00:24:33We already have a neutrino telescope now.
00:24:36And we can see our sun in the neutrino spectrum.
00:24:39So this is a huge tank already.
00:24:42So this is another technique in another lecture.
00:24:44So anyway, it's nice that we really can prove that we see these reactions in the sun.
00:24:52Here's kind of like the comparison of the energy scale.
00:24:56The sun gives like 100 billion megatons per second.
00:25:01Compared to like a huge like Tsar Bomba or Hiroshima strike.
00:25:09That of course had much lower.
00:25:13But also was based on the nuclear reactions.
00:25:16And here trying to match the sun on Earth.
00:25:21People are trying to do their nuclear fusion for many, many like years.
00:25:26And here's kind of the most developed now project with ETHER in France.
00:25:31which is supposed to generate 500 megawatts.
00:25:35But only for 500 seconds.
00:25:38While sun can generate like 10 to the power 20 megawatts.
00:25:42And it works for 9, 10 years.
00:25:45So should we really like spend money on these facilities and so on when we already have the sun?
00:25:52Would it be easier to build Dyson sphere kind of like to cover the sun with some shoes and collect all the energy?
00:26:02We don't know.
00:26:03Maybe this is a signature of other civilization that we could see.
00:26:08Yeah.
00:26:10So then we will talk about like smaller stars which are called white bars.
00:26:16that falls in this mass range.
00:26:18And they actually represent like 75% of stars in the nuclear.
00:26:23And the closest star to us is frozen in Centauri.
00:26:26It's only 4.2 light years away.
00:26:29It has mass of 4.1 solar masses.
00:26:32But unfortunately because it's small, it's not visible by a naked eye.
00:26:37And here's kind of like how many stars we have in different beings.
00:26:45with stellar masses.
00:26:47And the most of the stars fall here with a red bar.
00:26:52So kind of yellow.
00:26:54And here's what I told you that the smaller the star, the longer it leaves.
00:27:02Because the time scale of burning hydrogen is not proportional to the mass of the star cube.
00:27:07So you have very low mass stars.
00:27:10It can be like 6 trillion years.
00:27:13Why?
00:27:14It's much larger than the age of the universe.
00:27:16It's only like 13 billion years.
00:27:19And here's what's the most favorable exercise of astronomers like in the 19th and the beginning of 20th century.
00:27:31So this diagram shows you the luminosity of the star on this scale.
00:27:40And here's the surface temperature of the star in Kelvin.
00:27:44And that's why the stars have different colors.
00:27:47Kind of like with the surface temperature of 3000 Kelvin, you will see it as red.
00:27:53If you hit it up to 5000 Kelvin, it will be kind of like yellow or maybe a bit white.
00:28:19And then if you hit it more, you will have blue stars.
00:28:23That's why the stars are the spectral.
00:28:27They have a spectral glass going from red here to kind of violet.
00:28:33And this is all like NKG.
00:28:37So you can remember it's like O, B, F, A, fine girl, T, swing.
00:28:43This is how astronomers, you can remember this.
00:28:47And for some historical reason, I don't know actually exactly why.
00:28:52It's floated from low temperature to high temperature, right?
00:28:56And this is how stars go like when there is a collapse of this cloud.
00:29:02And it takes, for example, 150 million years to sun to fall on the main sequence.
00:29:09And here where the star spends almost all of its life on this sequence,
00:29:14you have small stars like red ones with low luminosity and low temperatures.
00:29:20Here you have sun, here in the middle, and then you have more massive stars than that.
00:29:26More luminous, and they are like blue and so on, but they also live shorter.
00:29:33Yes.
00:29:39The beginning, where they start at the beginning depends on how big that cloud was at the beginning.
00:29:46Yes, you're right.
00:29:48So there is actually, thank you for your question.
00:29:50There is actually a theorem of Russell Watt,
00:29:53that the evolution of the star is basically almost fully determined by its initial mass.
00:30:00So it depends only on mass of this cloud on the, it depends also on the composition,
00:30:06but we will not dive into these details.
00:30:09Yeah.
00:30:11Then we have next massive stars is G type stars.
00:30:15So G works like our sun and it's like, has solar mass.
00:30:21And it's around 700,000 kilometers.
00:30:26It lives for about 9 billion years.
00:30:29Now we're in the middle.
00:30:31And it's not very special, except that we know that it creates habitable worlds.
00:30:38And yeah, this is why I'm here giving this lecture.
00:30:43So this is the future evolution of the sun.
00:30:48So, so it started from right here.
00:30:51It's like prime, uh, main sequence.
00:30:54And then it arrives, uh, in the, in the main sequence where it spends like 10 billion years here.
00:31:00And then at some point when it will exhaust its hydrogen, uh, in the core, it's, it will start to burn hydrogen in the, in the shell.
00:31:09And then it will start to expand here, uh, on this line.
00:31:14Uh, and I will show you here.
00:31:17Then it starts to expand.
00:31:19And at some point you will see this kind of scale.
00:31:23Then the sun, the size of the sun now.
00:31:25And then at some point it even will reach the orbits of Mercury and Venus and we will then call them.
00:31:31And then at some point it even will smaller Earth.
00:31:35But it will happen only in like 7 billion years.
00:31:40Don't worry.
00:31:41We will die earlier.
00:31:43Uh, because in 1 billion years, Sun Luke will bury all the oceans.
00:31:49Excuse me.
00:31:50On your first diagram, um, it showed the, the visible spectrum compared to like, um, with all the stars.
00:31:59Does that mean that, that other stars don't emit light in the visible spectrum?
00:32:04No, no, they, they, they, they, they emit.
00:32:07Because, just.
00:32:08Yeah.
00:32:09Because I mean, it shows them out of the spectrum.
00:32:11Would that mean that it would be, like some would emit in ultraviolet?
00:32:16This one?
00:32:17Yeah.
00:32:18I mean, if you, well, that usually we don't have this, this star.
00:32:21But for example, we could have the star here.
00:32:25And then there is a tail, it will go down, but it will emit a little bit.
00:32:29Yeah.
00:32:30Into the red.
00:32:31Yeah.
00:32:32I mean.
00:32:33At some point it would emit in non-visible light.
00:32:35In the infrared.
00:32:36Yeah.
00:32:37Yeah.
00:32:38But there is always going to be kind of some, some tail going here.
00:32:41So.
00:32:42This is what we usually see.
00:32:45Yeah.
00:32:46Thanks for the question.
00:32:48Yeah.
00:32:49Evaporate all the oceans.
00:32:51This is how it will look like in the artist's point of view.
00:32:55And then, as I said, this kind of also the semantic thing that it will absorb all the hydrogen in the core and it will start to burn hydrogen in the shell and it will be created a helium core.
00:33:09And then hydrogen shell will kind of expand here.
00:33:13And then at some point, the helium starts to fuse in the center.
00:33:18For this, the star needs to contract to have a higher density and temperature in the center.
00:33:24But then again, it will be exhausted.
00:33:26And then the helium will start to fuse in the shell.
00:33:29Yeah, in the shell.
00:33:30And then at some point, the envelope of the star will be ejected.
00:33:34And what we will see is a cold planetary nebula.
00:33:38This is clearly misnamed because when astronomers first saw it in the telescope, we saw it.
00:33:46They pointed out it was like very dull nebula, but perfectly outlined as large as Jupiter and looks like a failing planet.
00:33:56That's why it's cold like this.
00:33:57But this is just the depth of the star.
00:34:00You can see the star and then there is an envelope all around going here.
00:34:05And this is the star depth.
00:34:07So the star traveled, for example, the sun starting from here.
00:34:11It went to the giant phase and then been back and then up and then going there.
00:34:17And then arriving at this point, this is the stars.
00:34:20And we finally start our lecture about white dwarves.
00:34:24Here's our first lecture.
00:34:29about white dwarves.
00:34:32So, in 1844, German Strömer, Friedrich Besser, who was also in the Green Edition, maybe we heard about him.
00:34:41So, he was following the movement of series A star, which is not that far from us.
00:34:48And what he saw in the proper motion, that it doesn't follow this kind of straight line, but it has some kind of biggles.
00:34:55I just won't into it here, but for the more precise, you can say some biggles.
00:35:01And this tells us that it has some pain companions, which distorts the motion of the star.
00:35:08And here are the orbits of the stars.
00:35:12And from this orbital movement, he deduced that the mass of this star is around 0.8 solar masses.
00:35:22And he was quite surprised why he could not see it.
00:35:27Because it's a quite massive star and should be visible.
00:35:31Then it was observed later by American telescope major Adam Quark.
00:35:37And only in 1915, Volcker Adams measured the spectra, as we showed before.
00:35:42And from the spectra, you could obtain the temperature of the star.
00:35:47And here obtain is like 8,000 Kelvin.
00:35:50So, huge temperature.
00:35:52But a huge temperature, and we cannot see it.
00:35:57And knowing the luminosity of the star, and the temperature from the spectra, and using Stefan-Wolzmann's law,
00:36:12we can obtain the radius of the star.
00:36:15And then what they obtain is like 20,000 kilometers only.
00:36:18It's like close to Earth.
00:36:20And actually, current estimation shows that this star is about the size of the Earth.
00:36:25So, the size of the Earth, but contains about one solar masses,
00:36:29that gives enormous density, like 50,000 grams per cubic centimeter.
00:36:34So, this is huge and was a big surprise.
00:36:39And this is, you can see actually this C-spin series on the sky.
00:36:44You will see series A in the Winter Triangle.
00:36:48And actually, 97% of the stars in the Milky Way will become white dwarves.
00:36:54And just to compare the density with the 50,000 grams per cubic centimeter.
00:37:01You know, we have around 13.
00:37:03Water is one.
00:37:05Very nice.
00:37:06And the most kind of densest metal on the surface, of course, is like 23 grams per cubic centimeter.
00:37:12And here is the density of planets.
00:37:14The curves with the densest.
00:37:16So, it's like huge density.
00:37:19How this star can resist the pressure of gravity?
00:37:25How it can survive?
00:37:26Because there are no nuclear reactions going in the center of the stars.
00:37:30And it was, again, predicted with quantum mechanics that Fowler said that the generate gas can stop the collapse.
00:37:41So, what is degenerate gas?
00:37:43Wolfgang Pauli postulated that if you have, for example, two electrons, they are called fermions because they have half integer spin.
00:37:52Namely, one half.
00:37:56And he postulated that they cannot occupy the same quantum state.
00:38:01So, in the school, we've all been taught chemistry.
00:38:06And this is how we usually plot it, for example, for hydrogen, helium, and lithium, how electrons occupy the orbitals.
00:38:14So, we start with just one electron.
00:38:17It can be with different spin, up and down.
00:38:19There are just two quantum states.
00:38:21But then, you cannot have two electrons on the same orbit with the same spin.
00:38:26Here.
00:38:27So, it goes here in helium because it has two electrons.
00:38:30And then in lithium, we need to put it on another orbit.
00:38:33And here's kind of orbits of hydrogen.
00:38:37We have a first orbit and then another one.
00:38:40So, if you start to put electrons on these shells, you always need to fill it, like one up, one down, and then other ones.
00:38:51So, electrons cannot be kind of in the same, in other words, phase space.
00:38:57So, when doing the broil, we also discovered that the particles can have some properties of the wave.
00:39:04So, we can imagine, like, when the broil wave of two particles start to overlap, they fill each other, and they start to repose.
00:39:13So, if you have, like, normal electrons with the temperature moving around, and then you squeeze them, you kind of put them in order.
00:39:21But if you try to put them in the same position with the same momentum, you cannot do it.
00:39:26It was one of the principle of quantum mechanics by Werner Heisenberg, that we cannot, for example, measure the position of electrons and its inputs together.
00:39:39There is also some inequality with the plant constant.
00:39:43And then, from this, you can actually estimate that, for example, in the star, we have a lot of electrons.
00:39:49And then, the distance between them is proportional, is very proportional to density.
00:39:54Then, from Heisenberg principle, we can calculate that momentum will be proportional to density to the power of one-third.
00:40:03And if your relativistic Fermi energy is kind of energy of these gas will be proportional to n to the power of one-third.
00:40:12And then, the associated pressure will depend only on the density of the gas, but not on the temperatures.
00:40:19So, it's only dependent on the density here.
00:40:22And then, this is exactly this pressure that stops the collapse in whitewash.
00:40:27So, is it understandable or I lost you already?
00:40:32You can ask some questions, maybe.
00:40:36Because, this is not an easy concept, I understand.
00:40:41But, I try to, here, to explain somehow.
00:40:44This is, yeah, what does resist the whitewash.
00:40:49So, typical whitewash has star, has size of the Earth.
00:40:55And, it's around open six solar masses.
00:40:58And, it's composed usually of carbon and oxygen.
00:41:01Here, kind of like, different atmospheres of whitewash.
00:41:06The interesting consequences of this degeneracy, for example, if you have a normal star, and you put some mass on top of the star.
00:41:16To resist new gravity, it will, kind of, rise the temperature and will, kind of, expand a bit.
00:41:26But then, here, for the whitewash, if you put some mass on the whitewash, the only thing to resist the increasing gravity is actually to contract.
00:41:36So, the more massive is whitewash, here's the observational point.
00:41:42The more massive is whitewash, the smaller.
00:41:45This is, I'd be counter-intuitive, but this is what it is.
00:41:50And, here's the mass radio curve of whitewash.
00:41:54And, here's the kind of current state of the art, in this view, that there is a Gaia mission that scans all the sky and discovers, like, 500,000 whitewash.
00:42:07But, before, we only knew, like, 30,000 whitewash.
00:42:12And, here's the mass distribution.
00:42:15And, this could be from whitewash merger, or merger of two stars together.
00:42:23Before becoming whitewash.
00:42:25And, here's what they see.
00:42:27That, there is some hydrogen-dominated atmosphere for whitewash in the helium.
00:42:32So, there are two branches here.
00:42:35Maybe there is some branch here.
00:42:37It's a lot of new data, and now people analyze and debate about this, the evolution of whitewash.
00:42:44But, the basic thing is that whitewash just, kind of, cools down and crystallizes.
00:42:51You can see here the points for the crystallization.
00:42:54Actually, I don't know.
00:42:56I started, like, at 30 minutes.
00:42:59What is the time that I should stop?
00:43:02Like, would it be okay, like, 15 minutes more for you?
00:43:10I don't know.
00:43:11Maybe you're tired.
00:43:12No?
00:43:13Okay.
00:43:14Yeah, and then it crystallizes.
00:43:18The interesting thing, very fundamental, is whitewash has a mass limit on top of it.
00:43:24So, as we discussed before, we can calculate the Fermi energy of whitewash.
00:43:29This will be kind of kinetic energy, which depends on the density of whitewash.
00:43:34Or you can say that depends on the number of particles in total in whitewash divided by the radius of whitewash.
00:43:43We can also calculate the gravitational energy, which depends on the mass of the whitewash and the mass of the baryon, also divided by r.
00:43:52And you can see that both are proportional to r.
00:43:55And usually in equilibrium, this is the real theory, kinetic and gravitational energy in the globe.
00:44:01And then, from these two energies, we can obtain that there exists a maximum number of particles, which is 10 to the power of 57.
00:44:11And then we can calculate the maximum mass of whitewash.
00:44:14That was first derived by Chandrasekhar.
00:44:17Then he was traveling from India to England on a boat to start his PhD actually.
00:44:23He already discovered this and later he obtained Nobel Prize and so on.
00:44:28So, the interesting thing, that this doesn't depend on the nature of the particles.
00:44:33It could be electrons that stop the collapse or could be neutrons.
00:44:39Also, it will be kind of the same maximum mass.
00:44:43And the radius only of the star will be different.
00:44:47For whitewars, it will be like 5,000 kilometers, as we discovered before.
00:44:52And for the star, it goes on neutrons, which we will discover later.
00:44:55Neutron star, it is 3 kilometers only.
00:45:00And then, as I said, whitewars crystallizes.
00:45:03And it kind of represents a huge diamond of 10 to the 34 carats.
00:45:10In comparison with the largest diamond found on Earth in the South African mine.
00:45:15And then cotton gifted to the British royal family.
00:45:18And here's Queen Mary, wearing a lot of the angelaries with this diamond.
00:45:25The final fate of the whitewars is that it just cools down and becomes black.
00:45:34And that's basically it.
00:45:36But this is kind of a hypothetical object.
00:45:40Because the time for the creation is larger than the time of the universe.
00:45:45So, quite boring unless the whitewars is in the relationship or he's in the binary system.
00:45:51So, as I discussed before, a lot of stars are in the binary system.
00:45:56Then, the interesting situation can be created.
00:46:00We have some complex star, whitewars, and main sequence star.
00:46:05Suppose, for example, they have the same month.
00:46:08But this star is much, much bigger here.
00:46:11So, at some point, when it feels it's a so-called Roche log.
00:46:15So, at some point, when it feels this sphere.
00:46:19Here, the gravitational attraction to this point, and to this point, are the same, actually.
00:46:26So, the particles, the particle kind of belong to this star.
00:46:31But it also starts to belong to this star.
00:46:33And it starts to leak from this Lagrange point.
00:46:37And falls, in the end, forming accretion disk.
00:46:41And falls on the whitewars.
00:46:43And this is called Roche log overflow.
00:46:46So, star here creates this huge accretion disk.
00:46:51And in the end, matter radiates all its angular momentum.
00:46:54And falls on the whitewars.
00:46:56So, what happens if matter is accumulated on top of the whitewars?
00:47:03Explosion.
00:47:04Because you have a lot of hydrogen compressed on top of the whitewars.
00:47:11And it starts to fastly burn and explode.
00:47:14And you can see here the kind of explosion on the whitewars.
00:47:18And this is called classical nova.
00:47:20And the first was discovered by Tico Bragi.
00:47:24Also, he has actually observed supernova.
00:47:27But anyway, he wrote his book, the nova stella.
00:47:30And this is why historical eudaimical nova.
00:47:34There are some recurrents nova.
00:47:36Which works like every end years.
00:47:40And there is Ticharona varialis.
00:47:42That was observed in 1966.
00:47:45Sorry, 1866.
00:47:47Then in 1946.
00:47:49And then there is 80 years difference.
00:47:52And maybe to observe in 2066.
00:47:56And it will be visible by the naked eye.
00:47:59So, maybe we will be lucky to see this on our sky.
00:48:04And here is another example of nova occurring in the sky.
00:48:09The other thing is that if whitewars accretes a lot of matter.
00:48:16Yeah.
00:48:17It can, as I said, like there is a nova explosion.
00:48:22But then there is another thing that whitewars can detonate.
00:48:27Yeah.
00:48:28So, in contrast to the normal star.
00:48:32Where, as I said, like we cannot explode it.
00:48:34Because if you put some energy.
00:48:36Or put some mass.
00:48:38The sun will just expand a bit.
00:48:40And then it will adjust always.
00:48:42To any perturbation.
00:48:44Like all this.
00:48:45So, sun is kind of like normal wood burden.
00:48:48And then if you put some pressure on the whitewars.
00:48:52Or if you start to some reactions.
00:48:55It's pressure only proportional to density.
00:48:58So, it doesn't feel the temperature rise.
00:49:01So, all the matter can start to detonate.
00:49:04Independent of the temperature.
00:49:07And then if whitewars merge with each other.
00:49:12Or there is some accretion on whitewars.
00:49:14They can detonate.
00:49:16And actually here is kind of simulation.
00:49:19Oh, sorry.
00:49:20Yeah.
00:49:21Simulation of wave propagation in the tubes.
00:49:24Of chemical reactions.
00:49:26And here is flame propagation in whitewars.
00:49:29So, at some point.
00:49:31There starts some explosion.
00:49:33So, the matter starts to burn.
00:49:35And then because the thermal heat is not radiated away.
00:49:44There is created a shock wave.
00:49:46That actually compresses the matter again.
00:49:49And it starts to explode.
00:49:51And then it flowers this shock wave.
00:49:54And this is called the Burge mechanism.
00:49:56Which also can be seen here.
00:49:58So, here you start some reactions.
00:50:00And there is a shock wave that compresses the matter.
00:50:02And compression leads to the nuclear reaction.
00:50:05Here, for example.
00:50:06And then it powers the shock wave.
00:50:08And again.
00:50:09And again.
00:50:10It's kind of like self-sustained process here.
00:50:12And then, in the end, whitewars can explode.
00:50:16Here is another simulation of whitewars explosion.
00:50:21On the different scales.
00:50:24You can see here.
00:50:25And this is what is called.
00:50:27Supernova 1A.
00:50:29And these are actually detected historical supernovas.
00:50:34For example.
00:50:35Here are some Chinese scripts.
00:50:38In the second year of the apple.
00:50:40In the 10th month.
00:50:42In the 10th month.
00:50:43And so on.
00:50:44And so on.
00:50:45They saw a new star.
00:50:47On the sky.
00:50:48And the size was half a bamboo mat.
00:50:51It displayed various colors.
00:50:54Both placing and otherwise.
00:50:56It gradually lessened.
00:50:57And in the 6 months of the succeeding year.
00:51:00It disappeared.
00:51:01So this was the first observed supernova.
00:51:04And actually.
00:51:05Later.
00:51:06Like nowadays.
00:51:07Already.
00:51:08With a modern telescope.
00:51:09We really see.
00:51:10This shell.
00:51:11Exploding.
00:51:12Like.
00:51:13And moving outwards.
00:51:14And we can.
00:51:16And by just.
00:51:17Kinematic movements.
00:51:18We can estimate the age.
00:51:20Of the supernova.
00:51:21And by.
00:51:22Descripts.
00:51:23The location.
00:51:24And actually.
00:51:25They coincide.
00:51:26And.
00:51:27We can confirm.
00:51:28That this was the first.
00:51:29Supernova.
00:51:30That was.
00:51:31Detected.
00:51:32By humans.
00:51:33And the.
00:51:34Brightest supernova.
00:51:35Was observed.
00:51:37In the.
00:51:382006 year.
00:51:39And it was visible.
00:51:40Even during.
00:51:41Dead time.
00:51:42And.
00:51:43Recording.
00:51:44All over the world.
00:51:45He's kind of like.
00:51:46Artists impression.
00:51:47How it could look like.
00:51:48On the night sky.
00:51:49A thousand years ago.
00:51:51So isn't.
00:51:52The sky now.
00:51:53Is.
00:51:54A bit boring.
00:51:55And.
00:51:56Here.
00:51:57Is.
00:51:58His historical supernova.
00:51:59That he observed.
00:52:00In his catalog.
00:52:01Here.
00:52:02He showed.
00:52:03And.
00:52:04He wrote down.
00:52:05In his book.
00:52:06And there.
00:52:07Just.
00:52:08Here's.
00:52:09A comparison.
00:52:10You can see.
00:52:11That the supernova.
00:52:12Can be as bright.
00:52:13As a whole galaxy.
00:52:14And.
00:52:15This is.
00:52:16Massive.
00:52:17Massive.
00:52:18Burst.
00:52:19With a lot of energy.
00:52:20Yeah.
00:52:21Here it is.
00:52:22And this.
00:52:23That's to show you.
00:52:24How.
00:52:25The sky.
00:52:26Will look like.
00:52:27In.
00:52:28Billions of years.
00:52:29Actually.
00:52:30The hundred meter galaxy.
00:52:31Is approaching us.
00:52:32In.
00:52:33In.
00:52:34Two billion years.
00:52:35What we will still.
00:52:36We will see it.
00:52:37On the sky.
00:52:38Without our naked eye.
00:52:39We will look like this.
00:52:41And this is.
00:52:42In.
00:52:43Very nice.
00:52:44I think.
00:52:49Yep.
00:52:50I think at some point.
00:52:51Yeah.
00:52:52We can stop.
00:52:53Because you need also.
00:52:54To go to.
00:52:55Observe.
00:52:56These crystals.
00:52:57And we can continue.
00:52:59This exploration.
00:53:01Next time.
00:53:02So.
00:53:03Excuse me.
00:53:04Why does.
00:53:05Like.
00:53:06Why does the path in the sky.
00:53:08Change.
00:53:09Like.
00:53:10Brutally.
00:53:11From.
00:53:12Like.
00:53:13Um.
00:53:14Three.
00:53:15Eighteen.
00:53:16Four.
00:53:17Million.
00:53:18Three.
00:53:19Years.
00:53:20Like.
00:53:21The.
00:53:22The.
00:53:23The.
00:53:24The.
00:53:25The.
00:53:26The.
00:53:27The.
00:53:28The.
00:53:29The.
00:53:30The.
00:53:31The.
00:53:32The.
00:53:33The.
00:53:34The.
00:53:35The.
00:53:36The.
00:53:37The.
00:53:38The.
00:53:39The.
00:53:40The.
00:53:41The.
00:53:42The.
00:53:43The.
00:53:44The.
00:53:45volt.
00:53:46Light.
00:53:47So.
00:53:48Yeah.
00:53:49Je vais vous demander à plus de questions pour cette lecture.
00:53:56Juste une question.
00:53:59Pourquoi auparavant la cible nôtre nôtre nôtre nôtre nôtre?
00:54:10Parce que c'était rare que σon państwo est visibleevery et puis, et par des précédentes.
00:54:23Non c'était supernovation. C'était comme lôtre .
00:54:38a explosion on the surface of the white dwarf,
00:54:41but the white dwarf kind of doesn't care.
00:54:44I mean, there is something exploded all around,
00:54:46and white dwarf stays there,
00:54:48and it waits at some point,
00:54:50and there is some accumulation of matter on its dark face,
00:54:54and then at some point there is explosion again.
00:54:57Yeah, so it's pretty stable then.
00:54:59Yeah, it's kind of like predictable,
00:55:02because we have two points,
00:55:04and then we hope that there is the third one.
00:55:07We hope it will be there, but...
00:55:09I mean, no one knows. We still didn't see it.
00:55:12Thank you.
00:55:14Yes, please.
00:55:16Yeah, thank you.
00:55:18So, we're talking about crystallization,
00:55:21and then compared with diamonds.
00:55:25So, does it mean that there is carbon in the white star?
00:55:32Yes, exactly.
00:55:36The typical white dwarf is composed of carbon,
00:55:41maybe hydrogen, and so on.
00:55:43It's kind of like typical composition,
00:55:45because as I showed before,
00:55:47when you have like helium burning,
00:55:50I discussed it at some point.
00:55:53Yeah, this is what creates carbon.
00:55:56It's helium burning.
00:55:58And then our sun and these stars are not massive enough
00:56:02to start fusion of carbon,
00:56:04because it has more protons,
00:56:06so it has more repulsion in the cooling barrier,
00:56:09so we cannot easily fuse it.
00:56:11And so even the lattice is the same?
00:56:15This is just kind of a bit of speculation, for sure.
00:56:23I mean, there's going to be some other things in the star,
00:56:27but I think the lattice is quite similar.
00:56:29I don't know.
00:56:30Do you know what is the lattice in diamond?
00:56:32Here, it should be value center cubic.
00:56:39So, probably it's just the most energetically favorable lattice,
00:56:42here and there.
00:56:44Could be, but of course it's simplifying,
00:56:48and just kind of a nice picture.
00:56:51Yes, please.
00:56:53So, what's the difference between a classical Nova and a supernova,
00:56:56or is it the same thing?
00:56:58Ah, okay.
00:56:59This was poorly explained by me, sorry.
00:57:02In the...
00:57:06So, classical Nova is when white worlds accretes matter on its surface,
00:57:12and then it doesn't evolve itself,
00:57:14only the surface kind of like explodes and explodes.
00:57:17It's kind of like less luminous.
00:57:20It's just Nova.
00:57:21But then, smart people said, like, let's call it supernova,
00:57:25because it's more luminous and so on.
00:57:27And it actually correspond to the complete disruption of the white dwarf.
00:57:32And it happens only once in the life of white dwarf,
00:57:36when it dies.
00:57:38So, it's like super, and it creates actually a lot of iron.
00:57:42So, most of the mass of the nuclear synthesis of the elements of this explosion
00:57:47will go to create iron.
00:57:50And so, this is super bright.
00:57:53Yeah.
00:57:54And it was observed, like, typically observed, like, once a hundred years in our galaxy.
00:58:02But, yeah, we're still waiting for the next one.
00:58:06So, yes.
00:58:07For Nova, it needs to be part of a binary system.
00:58:11Yes.
00:58:12Here, it also needs to be part of binary system.
00:58:16Because if you have just white dwarf, it will cool down and nothing will happen.
00:58:21So, it depends on the accretion rate, or there are now kind of, like, more consensus,
00:58:27that most of the supernova 1A comes from the merger of two white dwarves.
00:58:33So, two stars, then they evolve to form white dwarves.
00:58:40And then they rotate around each other, and they start to move closer and closer,
00:58:45because they mean gravitation away, but it's another topic.
00:58:48And then, at some point, they just collide, and then they exceed kind of, like, a limit on
00:58:53the mass, or actually a limit to start carbon fusion.
00:58:59And then, this flame propagation and the white dwarf stars, and everything is disrupted.
00:59:07Yes.
00:59:08Can I ask for a question?
00:59:11Yes.
00:59:12Yes, sure.
00:59:13It's very, very, very fitting when the gas and the tide
00:59:18So, at some point, there's a situation.
00:59:23Mm-hmm.
00:59:24So, there's a huge gas of, like, at some point, it's just that, randomly,
00:59:29there'll just be some kind of region of that cloud which exceeds the mass,
00:59:34and the whole process starts.
00:59:37Yes, great question.
00:59:39So, actually, in this, for example, in this cloud,
00:59:46it's also called, like, a wave of star formation.
00:59:57There could be some perturbation, for example, supernova.
01:00:01For example, if there is a supernova somewhere nearby,
01:00:05you can start to move with a shortwave here, and it starts to kind of compress the gas.
01:00:10And actually, one of the hypotheses for solar system form was optionally that it was supernova somewhere nearby,
01:00:17that led to compression of our cloud and the solar system form.
01:00:22So, there is kind of some perturbation here.
01:00:25There's also magnetic field.
01:00:27Well, it's very complex, but just naively, it could be any perturbation around, and so on.
01:00:36And then, yeah, kind of, like, cloud starts to collapse, and so on.
01:00:40There, here and there, start forming region, fragmentation, and so on.
01:00:46Yes.
01:00:47No questions?
01:00:48No?
01:00:49Ah, you have questions?
01:00:50No?
01:00:51No?
01:00:52No?
01:00:53No?
01:00:54Okay, then, thank you very much for listening.
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