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The life of a star

The fate of stars is described by Pierre Binétruy to show that some of the more massive ones end up as black holes.
Let me start with a question. How do you define a star?
Well a star is defined as a celestial body that produces and emits energy. Now where does the energy of a star come from? Well one believes that energy is of a nuclear origin. So let me explain, how one thinks that a star, which is a star like the Sun, which is in equilibrium, is functioning.
So there are two competing effects. The first one is due to the nuclear reactions inside the star. Those produce energy, which has a dilatational effect on the size of the star.
And so that tends to increase the size of the star. The second effect is gravitational attraction. The different parts of the star are attracting each other through gravitation, and so that tends to contract the size of the star. And so the star, in its normal evolution, is under equilibrium, under these two contradictory effects, dilatation and contraction. And so this is why, for example, the Sun has a fixed size. Now at the end of the evolution of the star, the nuclear fuel is exhausted. The nuclear reactions stop at the core of the star. And so that dilatation effect, which is due to the heat produced by the nuclear reaction, stops.
And so one is left with only this effect of contraction, and the star starts contracting. Now that contraction is stopped, at some point, by the reaction of the matter of the particles that are the constituents of the matter of the star. And so this is this reaction of matter that we’re going to describe now. I have first to explain a very fundamental property of elementary particles. I have here, a torch and our traditional packet of sugar. And it is the physicist, the quantum physicist, Wolfgang Pauli, who told us the difference between the particles which compose a sugar cube, and the particles which make the light ray.
In the case of a sugar cube, or any form of matter like this table, the particles, which are protons, neutrons, and electrons, are what we call fermions. According to Pauli, and this is what is called the Pauli Principle, fermions cannot be in the same microscopic state. So that means that, in the same way as I pile up these sugar cubes, at the microscopic level, I have to pile up, the different microscopic states, because none of the particles which compose the sugar lumps are in the same microscopic state. So I have to add the microscopic state, and that’s precisely connected with the, sort of, additive character of matter.
On the other hand, in the case of the light ray, like this torch, the photons, which compose the light rays, can be in the same microscopic state. They are what we call bosons. And an example is a laser beam. A laser beam is the addition of many photons, which are in the same microscopic state. So this is why a laser beam is very, very coherent. It’s precisely because of this reason. So you see that there is a fundamental difference between the fermions of matter, which give matter its sort of additive character, and the light rays or photons, which you cannot seize between your hands, because this is the, sort of, immaterial nature of light.
Let us return to our star, which has exhausted all its nuclear fuel. The core of the star is then undergoing some contraction due to the gravitational attraction.
Now at some point, this process will be stopped by electrons. Electrons are fermions, and they cannot be squeezed into the same microscopic state. And so at some point, the contraction would force them to precisely be in the same microscopic state, and so they will exert a reaction. They will exert pressure outward, and resist this contraction. And so one gets through this reaction, a very compact object, which is known as a white dwarf. Now the process of contraction has released some energy, some gravitational energy is released in the form of heat, and so that heat is going to be directed towards the outer layers.
So the outer layers will be heated up by this energy released because of the contraction, and so again, they will start to grow. And so the outer layers are going to turn into a very large star, which is known as a red giant.
That’s precisely what one expects about the final history of the Sun. The Sun, at some point, will have exhausted all its nuclear fuel. The core of the Sun is going to contract into a very compact object, a white dwarf, and the outer layers of the Sun are going to turn into a red giant, which will swallow the first planets, so one imagines that they will be big enough to even swallow the Earth. So you see the size of this red giant, and so, the future of our Sun is a white dwarf at the centre and a red giant.
So you have an example here of a red giant called Mira, which gives you an idea of the future of our own Sun.
Now let me return to what we call supernova explosions of type Ia. It turns out that, in a certain number of cases, the white dwarfs are in binary systems. You’ve seen binary systems are rather frequent in the Universe. So sometimes, white dwarfs, which are very compact and massive objects, have a star, which is a companion, like in this artist’s view. And because of the gravitational attraction of the star, of the white dwarf, it will start sucking matter, and start being bigger and bigger. At some point, it becomes too big and starts exploding. This is precisely what is called a supernova explosion of type Ia.
When the star is more massive, the gravitational collapse is not stopped by the pressure of the electrons. What happens is that the energy developed by the collapse, is used in order to turn electrons and protons in the star into neutrons. And so soon enough, one gets a star, which is only made of neutrons, and it is then the pressure of the neutrons, the impossibility for neutrons to mix, which stops the process. One obtains what one calls a neutron star.
If the star is even more massive, then even the pressure exerted by the neutrons is insufficient to stop the collapse process. And so all the matter in the core of the star, all the neutrons, will collapse toward the centre of the star, thus producing, what we call, a black hole. Now this process is producing lots of gravitational energy, which is transmitted to the outer layers of the star, wich then explode. And so this is why the production, the birth of black holes, and for that matter also neutron stars, is often connected with explosions, cosmic explosions, very violent phenomena, such as supernova explosions or gamma-ray bursts.
To summarise, we have seen that stars, like our own Sun, are in equilibrium under two opposite effects. The first one is a contraction, which is due to the gravitational attraction. The other one is a dilatation, which is due to the energy released by nuclear reactions inside the star. When stars have exhausted all their nuclear fuel, their core contracts under the effect of gravity. And depending on the mass of the star, this core could evolve into a white dwarf, a neutron star, or for the more massive ones, into a black hole. The formation of these very compact stars is generally associated with violent explosions of the external layers of the star.
And we have also seen that the intuitive difference between matter and radiation is explained, at microscopic level by the fundamental difference between the particles, which are the constituents. Matter is formed of fermions, whereas radiation is formed with bosons. And fermions cannot be in the same microscopic state. This confers to matter its additive character.
Why is it important to follow the life cycle of a star? Because they end up as compact stars such as white dwarfs, neutron stars or… black holes. Meanwhile, we will discover a fundamental property of matter, that distinguishes it from light and radiation. (11.52)
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