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I think it's sort of like.

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Good morning. So it's my very pleasant. My great pleasure to explain the basic physics of why stars and as very dangerous objects.

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And my colleague Phillip will explain more fully how that rolls out, how the how the danger and how the how the damage unfolds.

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And then see Bissaka. We'll talk about possible how these objects are used and possibly misused in in contemporary cosmology.

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OK, so my outlines, I'm going to bed about how physics, right, how stars age,

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and then I'm that will that involves a return to something you probably studied under the title of solid state physics as an undergraduate.

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Now being relabelled condensed metaphysics, which is the physics of degenerate gases.

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How does this apply to stars and then talk about the two types of chemical which nature has four stars?

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They can be either buried or cremated.

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So the main point about a star, obviously, is that it radiates and self gravitating objects like stars and galaxies,

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as we covered back in in the January 20 18 Saturday morning in a different context in the Galaxy Dynamics context,

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we explained why self gravitating objects have negative specific heats.

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So as they as you draw heat out of them, they heat up, the temperature goes up when you call them.

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So a star responds to the loss of of energy by radiation from its surface, by contracting and heating.

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The heating, of course, happens because the gas gets compressed as the thing contracts.

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And that's the thing contracts, the gravity that binds it gets stronger.

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So this is a vicious circle. Every contraction sets up, sets it up for further contraction.

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So the temperature rises through the life in the middle of a star, the temperature light rises through the through the life of the star.

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But most of the time in the temperature is fairly stable because a small increase in temperature greatly speeds the nuclear reactions,

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the fusion reactions that provide the heat that is being radiated from the surface.

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So we have a.

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So you don't need a big contraction in order to boost the heat that's being produced, which would slightly expand the system in principle and so on.

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But as as the star progresses through the synthetic chain from hydrogen to helium, from helium to carbon and oxygen from carbon and oxygen,

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silicon and so on, the nuclei are developing bigger and bigger charges, which means there's a bigger and bigger cooling barrier to overcome.

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So as the star, in order to get fusion so as the star ages and move through this succession of fuels hydrogen, helium, carbon,

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oxygen, et cetera, the temperature has to go up in order to to make them to to open up the next store of nuclear energy.

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And the reason, of course,

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that the the nuclear reactions are very sensitive to temperature is that they the fusion events happen from very rare encounters of nuclei,

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which are on the right.

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The extreme tail of the Maxwell value and distribution in a small increase in the temperature can greatly increase the number of of nuclei.

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If you're very far out in the tail. So the key thing then about the summary of stellar evolution this potted way is that through the life of the star,

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the central density rises a lot and the temperature rises somewhat less.

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But although it does rise a fair amount.

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And what that if you if you're raising the temperature, raising the density without comparably raising the temperature,

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you're pushing the gas towards a degenerate configuration,

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a configuration in which quantum mechanics becomes a non-classical gas that is a gas in which you.

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The physics is very strongly influenced by basic quantum mechanics.

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So let's just talk about degenerate gases because we get the star is going to end with a core which is degenerate.

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So the pressure inside a star is like the sun is provided.

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All reasonable normal stars that you can see is provided by the electrons.

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And in a neutron stars is provided by the neutrons,

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whatever it's it's it's overwhelmingly provided by fermions particles with half half of each bar of spin.

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And these things are subject to the penalty exclusion principle, which says that you can't have more than one particle in each single particle state.

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So in order to figure out which states are occupied and what you need to know in order to work,

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work out what the pressure is going to be at a given density, you want to count states.

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So in one dimension, we do it very straightforwardly.

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We say we put the we imagine we imagine our gas is inside some box of side length L and the walls of the box have an enormous potential energy.

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So in order to hold the particle in, that means the wave function has to vanish on the walls, as you probably remember.

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And the consequence of that is that the states come like this.

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This is this is a fundamental state which vanishes at the two ends and is a cosine in between.

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Then the next state up in energy is this which vanishes both at the walls and in the middle.

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So it's a sort of sine function. And then you come down here and you have three half wavelengths of the wave function inside the box.

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So the wavelengths of the fundamental is twice the size of the box because the box is just half a wavelength in size.

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And the third state is has, the wavelength is two thirds of the length of the box.

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So the wave numbers K two, which are two pi over lambda integer multiples of pi over lambda.

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So when we go to three dimensions, we have, uh, we have to fit it.

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We the waves go like, is the X where K is is a vector k dot x k top position vector and K the the wave vector has three components K,

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K, Y and Z, and they all have to satisfy a condition of this type.

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Each one of them has to be an integer multiple of Pi over L.

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So the number of so each of these,

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each of these allowed wave vectors is going to be we can think of it is the position vector of a point on a three dimensional cubic lattice.

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Big, which has and the points in this cubic lattice are separated by Delta K, which is PI over L.

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So if we want to know how many of these points there are inside a sphere of radius k f,

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then we just have to work out the volume of that sphere for PI times,

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the radius cubed and divide by the volume associated with just one of these cells, which is Delta K cubed.

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So that gives us this relationship here. That is the number of points inside a reasonably large sphere of Radius K if we're talking about fermions.

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In other words,

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spin half particles which have two quantum states for each spatial way function because the spin could be up and the spin could be down.

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So the number of of quantum states associated with wave vectors of lengths smaller than CF is twice this.

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In other words, eight pi, whatever. Also, we know that momentum.

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Sorry, we know that the momentum is H. Bach from basic quantum mechanics.

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So the number of states which have momentum less than this %f the Fermi momentum is going to be there.

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So the the four is become an eight by the by the spin thing and K has been replaced by PAF upon par.

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So the conclusion is, if we have any particles in the box,

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the minimum momentum of the fastest particle is going to be this Fermi momentum because you can't pack them in more densely than that,

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you can pack them in less density than that if you've got a good supply, if you've got a means of heating the gas.

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So you may remember pictures a bit like this that if the temperature is reasonably high,

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then the the states, the low lying states will they're always occupied.

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This is the expectation of the number of of particles in a state.

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So it it's one more or less one until you until you get within Katie of the energy here associated with PAF.

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And then it begins to fall. And if the temperature is high, you you have a you know, it starts to fall significantly before it gets to this wall.

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But if the temperature is low and it is typically at the end of a life of a star like the Sun, then you have a very sharp drop off.

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And that's essentially we're going to. You can do the calculation when you don't assume a sharp drop off,

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but life is extremely much easier if you assume a sharp drop off and it'll be an adequate approximation in this approximation.

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I'm going to be making that the states glow the the with momentum less than %f are completely occupied.

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That's taken and the states above are completely empty.

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Sudden, sudden change. So we're talking about the minimum kinetic energy that you can have the kinetic energy at effectively negligible temperature.

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So where are we we we have that if we have a political density and overall cubed,

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then the so the political densities and overall cubed, then the the the Fermi momentum is related to it like this.

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What's happened is we've lost the V from here. We've stuck it well.

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We've lost the old cube to stuck it there. So what we conclude is so we have a three here.

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So if we if we take the cube root of both sides of this equation,

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that leaves the conclusion that the Fermi momentum is goes like the volume per particle to the minus the power.

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And this number here is effectively it's essentially HPR.

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This number here is is virtually one. So we have we have we have that relationship that all right.

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And I think I've I've already said this, that we're that instead, of course,

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Katie's going to be a lot less than the energy associated with this firm in momentum, so it will be in this in this rapid death phase.

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So relativity says that up and you will see it's highly relevant that the E,

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the energy of a particle and the momentum of a particle or related to each other by the difference in squares being m squared, c squared.

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So if we differentiate this, if we apply this relation with that turn to the energy associated with this Fermi momentum,

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the most energetic particles that we need at low temperature.

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And this turned into the Fermi momentum. We find that EDI ifdef d e f is equal to PV DPF, but we know how PAF depends on on V.

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So differentiating that relationship, we discover how f DF depends on on the specific volume v,

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uh, we have here APF, which we know goes like features of one third.

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So getting rid of that, this v becomes the V to the minus five sets.

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So this tells us how if the F depends on the V and if we remind ourselves about thermodynamics,

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some dynamics says that the internal let the change in the internal energy is equal to the temperature times,

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the change in the entropy minus the pressure times, the change in the volume.

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So this is going to apply to the whole box and therefore the volume should be in times the volume per particle,

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which is what little v is the volume per particle. So this is the whole volume.

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So this is just the second law of thermodynamics.

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The relationship of you to the energy associated with the Fermi energy is not completely straightforward.

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Obviously, its end times, the energy in the box is obviously in time.

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Some energy because this is an energy particle and in front, here is a number on the order of one which actually lies in these bounds here.

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My point is that most of the particles most of the states are quite close to the edge of that sphere in space.

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So that's why this number is close to but less than one.

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But on the other hand. So this is just the average energy, the average radius inside this sphere.

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OK, so we have a simple relationship between DCF from here.

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This gives us the relationship between DCF and %DV.

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So we considering changes adiabatic changes in which there's no heat put in or taken out, so there's no entropy change.

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So we have the pressure from this relationship. Here is simply x.

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This number, which is essentially one times the derivative of the Fermi energy with respect to the specific volume.

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And we've um yeah, we we know what the f by the volume is from the last slide.

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So we end up with this feature of the minus five thirds of a AVF and a we know what this is.

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This is essentially C square. This is a squared C squared right edge.

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Bussey squared effectively with some stupid numbers, numerical factors on the order of one.

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So we've got these key relationships that the Fermi momentum goes like the minus the power of the specific volume.

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And we have that. The pressure goes like the minus five first power over e f.

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And we also have, of course, this relationship here.

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If we're in the non relativistic regime, then the Fermi energy is then in the non relativistic regime.

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Uh, this is completely dominated by the rest mass energy MC squared.

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In other words, this momentum, this is unimportant in the non relativistic regime so we can replace this f by M.C.

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squared in the highly relativistic regime ultra relativistic regime the opposite one.

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This becomes unimportant and basically e becomes c p.

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So we should consider these two limiting cases that the Fermi energies is less than the rest mass energy of whatever fermions are doing the work,

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or it's much greater than if it's much less than then we simply have the pressure goes like V to the minus five minus five thirds,

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which means that PV to the five thirds is a constant.

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So and you probably remember from some dynamics that for ideal gas is PV to the gamma was a constant where gamma was one number.

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In fact, five thirds if it was a monotonic gas and its other numbers of the events that xDai atomic gas.

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So that's just recovering the monotonic gas thing.

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If we're in the ultra relativistic regime, on the other hand, we should replace this if it's by C.P.

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And that means we've got another power of P on the bottom, but P goes like V to the minus one third.

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So this five 3rds then becomes four 3rds and we find that P V to the four thirds

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is a constant in the if the Fermi energy is well above the rest mass energy.

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So now let's for the first time, allow gravity on the on stage and imagine we have a ball of gas radius.

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Big, bigger. And let us push that radius in a bit.

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Then the change in the volume per particle is going to be this right.

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It's the change in the volume of the ball. This is four pi all squared.

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D. R. And we have to divide by end because we want the volume per particle, not the volume of the whole ball.

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Then we have that we know do is minus %DV.

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So again, this is the volume of the whole bowl. And we know that there is some kind of constant times vs the minus camera TV,

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so all we have to do now is put in for TV and put in for vehicles like our vehicles, like our cubes, of course.

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So we have from this V to the minus gamma becomes the knowledge of the minus three gamma and then.

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We haven't all squared D.R. all squared deal.

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So we have the you in the relativistic regime and the relativistic regime, where gamma is four thirds, this becomes a minus four plus two.

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We have an arch, the minus two dear. And if in the non relativistic regime we come as five thirds,

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we have a large the minus three d R. So this is the this is the increase in the energy when I when I squash the ball in by air.

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OK, now when we squash the ball in, since it's self gravitating, it's gravitational energy changes.

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And this is a worthwhile.

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So the expression for the gravitational energy of the ball is of this form, where y is a number on the order of on the order of one, right?

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So GM squared over R is basically what it is, which is sort of go over all the potential associated with a mass of a mass of times,

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the amount of mass that you've got in this potential. So why is a number on the order of one but a little bit less than one?

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And let's not bother about it. It wouldn't be important. So the change in the gravitational energy when we change R is going to be this amount.

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If we decrease R, this is and this is going to be negative.

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Gravity is going to be the these gravitational energy of the ball is going to go down.

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The ball is going to the gravity is going to do work on whom is it going to do work?

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It's going to do work on the thermal energy. All right.

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So the key thing is this this change in gravitational energy is scaling is one overall squared.

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And up here in the non relativistic regime, it's scaling is one.

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Overall, the balancing item in the box is scaling is one overall cubed or one overall squared and the ultra realistic case.

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So in the non relativistic case, if you contract it, the the thermal energy rises faster.

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Well, the rate at which it rises increases as all shrinks faster than the then gravity is supplying is able to do work.

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And that means that the oscillations are stable, that the system will oscillate in and out, stably converting thermal energy,

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increasing its thermal energy when it goes in and decreasing its, well, increasing its negative gravitational energy, if you like.

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But if in the ultra relativistic case, these two scaled together.

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And that means that way, if you push it in, it was in equilibrium.

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You push it in. It's still in equilibrium. You push it in some more. It's still in equilibrium.

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The thing that's become very infinitely squishy is cable. Just to cruise down to no to no volume.

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Just because of this change in the way that the thermal energy scales,

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the change in the thermal energy scales with with radius having changed, that has profound consequences.

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So that's the sort of intuitive back of envelope stuff.

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If you write down the proper differential equations and integrate them, you find this sort of behaviour.

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So what we're plotting here is the logarithm of the central density in the star model made out of this ideal to generate gas.

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And it's normalised to the density of water because water has a significant density,

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it's the density basically of close packed oxygen atoms or whatever.

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And if you have something which which is made of as like a white dwarf of sort of oxygen atoms and carbon atoms, they're pretty much the same, right?

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And you have it at a density higher than that of water.

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It means that the electrons are not going to be tied to individual atoms anymore.

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They're going to be swimming around. There isn't space in there to have atoms any longer.

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All right. So in the density you see is like 10 million times in these two models, one model has a mass of them of the Sun.

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That's the top. That's the dashed model. And the other model has a mass of point eight of the Sun.

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So the key key to key observations? Well, one one thing is obvious that is you increase the mass of the model, the central density goes up.

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What's not at all obvious is that the the radius of this thing, which is very well-defined,

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the density declines fairly slowly and then really drops like [INAUDIBLE].

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When you reach the outside, this is logarithmic scale. So this is this is a serious drop.

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The radius decreases as the mass increases. So if you have a white dwarf and you put some extra material on it, it doesn't grow.

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It shrinks. The other thing that's very notable here is this this is the Fermi energy,

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which is the minimum energy of the faster electrons that provide the pressure right?

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If the thing has any finite temperature, the this the the actual energy will be of the fastest.

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Electrons will be above the Fermi energy. The minimum energy is divided by M.C. squared, the the rest mass energy of an electron.

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So even in this lighter white dwarf, the central Fermi energy is above the rest mass energy of an electron.

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And for the Sun, for something of the mass of the Sun, it's more than three times the mass of an electron.

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If you make a series of models, which you do by integrating the equations from an ever higher central density and look

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at the the mass of the model that you end up with versus the radius of its edge,

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you get a plot like this. So each of these dots is obtained by integrating the equations.

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And for low masses, you have large radii.

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For high masses, you have smaller ready. I've made that point, but look at the shape of this curve, it goes up and it's very clearly stops going up,

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and it's headed to a point with mass one point forty four solar masses.

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And this is the result for which Chandrasekhar and Fowler shared the, I think, nineteen seventy eight or something, no Nobel prise.

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Meanwhile, if you if you plot for the same series of computations mass versus central fermions, you divide it by M.C. squared.

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It starts off going up and by and then it really it really shoots through the roof.

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So this this is all, of course, a little bit naive, but it's a clear signal.

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This is saying that that the minimum energy of the fast is electrons is a thousand M.C. squared.

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It is a seriously moving particle.

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We really are into the ultra relativistic regime when we're once we're close to this one point forty four solar masses.

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If you solve the same equations for a star, which is held up not by electrons, but held up by just neutrons.

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The picture is is almost indistinguishable. Right here is here.

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The dotted one is not mass star, which has a mass of one point two solar masses.

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The full one is one that has a massive point seventy five solar masses.

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The difference is in the scale, right? The previous one was in the scale was in thousands of kilometres, and this is in a scale of kilometres.

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So this the radial scale is shrunk by a factor of many hundreds.

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And the density scale has also changed. We were going up to densities like here 10 to the seven tens of the seven times the density of water.

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And now we're going up to densities of 10 to the 14 times the density of water.

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But the basic principle is the same that what's happening here is this as we approach the Chandrasekhar mass,

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this mass of one point forty four solar masses, the particles the Fermi energy is becoming a relativistic and that's destabilising the whole set up.

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So the connexion to stellar evolution now just just some empirical facts really?

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Well, I mean. Results of complicated calculations during the sixties and seventies stars,

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which have a mass in this range here between half a solar mass and eight times the mass of the sun,

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generates enough heat in their centres that they they can ignites.

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They can cause hydrogen to fuse into helium. And then in the second stage of life, they they are able to fuse helium into carbon and oxygen.

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But they don't then get hot enough to fuse the carbon and oxygen into this,

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into the nuclei further up the periodic table because they when they're sort of about halfway through doing this,

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turning their helium into carbon and oxygen, they they blow the envelopes away into interstellar space.

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And that's the birth of a planetary nebula. And here is a planetary nebula,

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a ball of gas which is being ionised by hard radiation coming off this extremely hot carbon and

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oxygen degenerate object in the middle here and glowing as it recedes rather in rather a gentle way.

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This isn't an exploding star. This is just a. This is just blowing off steam, right?

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But in the more massive stars,

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what gets blown because what's going to stick around here is going to have a mass of less than the Chandrasekhar mass and the more

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massive stars was blown off here is going to be is going to be a lot of it is going to be most of the mass in less massive star,

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it will be less than most of the mass.

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OK, so that leaves this white dwarf, which has, as we've seen, a radius of a few thousand kilometres like the Earth.

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But it has a mass which is comparable to the mass of the Sun,

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and it's supported by the Fermi energy if it's to generate electrons which are mildly or strongly relativistic.

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And and we are surrounded by these things all over the place, right?

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The many zillions and zillions and zillions of stars in the galaxy have been through this phase and have left these these white dwarfs,

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which cool they take. They they continue to cool even if they were formed.

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These stars were formed fairly early in the life of the galaxy. And if you look for faint, rather bluish stars that move rather fast across the sky,

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it's some fact that it moves rather fast across the sky is telling you that it's relatively close to you.

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It will be a white dwarf, and there are gazillions of these.

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Stars which have more than eight solar masses generate enough heat in their cores that they can ignite carbon and oxygen and turn it into silicon,

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and most of them can turn the silicon, et cetera.

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Further up the periodic table until you get to iron, so that these stars eventually produce a core of iron,

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which has a mass comparable to the mass of the sun,

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which is supported by the by the degeneracy pressure is supported by the Fermi energy of mildly mildly or strongly relativistic electrons.

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So essentially, in the middle of such a massive star late in its life, you have a white dwarf made out of iron.

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And other Asian group elements. And either of these two end points is a dangerous situation.

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The easiest to understand is the fate of the more massive stars.

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So Aaron is the most tightly bound nucleus. There's no way you can get any more nuclear energy.

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You've had it. So the scheme the star has had for resisting gravity for possibly billions of years,

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possibly tens of millions of years, depending on its mass, is now defunct.

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The only way it can replace the energy that it radiates from its surface is by contracting.

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And that is not a safe game. So as we said, most of the pressure in this cause contributed by these two generate electrons,

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although pressure from photons can be can can make a significant contribution because it'll be very it'll be very hot in this call.

265
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So as the Fermi energy rises well above the the rest mass energy we get, we go, we go relativistic.

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The scope of this core becomes squashy. So that's just to remind you of this argument that the that for the relativistic in the relativistic case,

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the way that the gravitational and thermal energy scales with all is the same.

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So there's nothing to there's nothing to pick out. A particular radius is preferred and the temperature rises.

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So, so the thing begins to contract. There's nothing to stop it contracting.

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And if and if he contracts the radiation field, the middle gets hotter.

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The radiation field becomes contains harder and harder photons, higher and higher energy photons.

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And some photons then have sufficient energy to simply blast an iron nucleus into into fragments.

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And the electrons all have a choice. They can live free or they can marry a proton and form a neutron.

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But the cost of living free, which is the Fermi energy,

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is constantly going up because the density is going down because the star has to replace the energy,

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which it's radiating on its surface and has got no other thing to do that to contract.

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So, of course, more and more of them decide they'd rather be married than free.

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But that is a serious issue because they are contributing the pressure and every electron that decides

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to give up the ghost and marry reduces the pressure and increases what the others have to do.

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It's obviously an unstable cycle. It's obviously a vicious cycle, right?

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They they that pushes up the firm that causes contraction, that pushes up the Fermi energy and more give up the ghost.

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So you obviously have the core quickly goes into freefall.

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This on the order of one solar mass. One of the solar masses of iron is just losing precious support on a very short timescale.

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And curiously, in the as it goes into freefall,

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the nuclear synthesis which the star has laboriously done for hundreds of thousands of years is all undone.

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Because the rules of the game have now changed. It was advantageous to build bigger nuclei.

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But now with all these, with all these hard photons blasting you apart and all these very high energy electrons deciding to.

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To be absorbed by the nuclei, it's advantageous actually to split the nuclei up.

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Of course, splitting them up, it consumes a huge amount of energy, all the energy that was released through the life of the star.

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It now just on a collapsed line, which is which is only seconds is required to split them apart again.

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But gravity is a very generous donor and it provides the energy and they all split up.

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OK, so. We've we've we're going to have very many free neutrons.

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The neutrons, which are unstable in the laboratory, the stable in this strange place because the B,

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because in order to decay by beta decay, a neutron has to emit an electron.

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Where's it going to meet the electron? Well, it has to be emitted.

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The only the only spare spaces is above the Fermi energy, so you can only decay if you're a neutron inside the star.

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If you can somehow get hold of the energy to put your ejected electron above the Fermi energy, well, they can't do that.

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So they. So then they're now essentially stable and they build up in numbers.

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And eventually the neutrons are packed together during this collapse, packed together so tightly that they become degenerate to.

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So even though the temperature is enormous,

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it's not enormous enough to keep the at this incredible density to keep these neutrons with thermal energy above the Fermi energy.

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The collisions between between nuclei,

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what's left of them and between neutrons are becoming more and more energetic because the temperature is going up because everyone's being compressed.

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And that these these collisions are now sufficiently energetic, that they're emitting neutrinos pretty much as freely as they emit photons,

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so at very high energies, weak interactions and not the very high energies, weak interactions become sort of not rare.

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The cross-sections for them go up sort of lecture unification and all that.

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So enormous numbers of neutrinos are produced.

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And the density in the kid in this in the core of the star is so high that even neutrinos are somewhat trapped.

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They're not long term trapped, but they're trapped enough that they have to diffuse out and in diffusing out,

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they impart momentum to the material which is trapping them, which of which they're scattering.

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So they impart momentum to the envelope of the star, which is falling in onto the collapsing core as they brushed by.

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And uh, so. So you have now a collection of of neutrons coming together to form to form a ball colliding with each other,

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being very rapidly cooled or losing energy by this by radiating all these neutrinos, which which rush out very quickly.

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And you may get a neutron star formed, but but the mass of this core originally was essentially the Chandrasekhar mass.

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So the mass of the neutron star that's going to form is going to be very close to the neutron star mass anyway.

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And if and if it creates some extra material, it can go over over the edge and disappear into a black hole.

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OK, now let's talk about the other kind of of of of event, the other kind of degenerate object,

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the carbon and oxygen white dwarf such as the Sun will make. So this thing is a powder keg in the following sense that if you can heat this,

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any part of this to tend to the 10 K the energy the temperature required to cause to enable carbon and oxygen nuclei to fuse into silicon, et cetera.

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Energy will be released in enormous amounts, and this energy will be enough to unbind this object even.

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Right. So it is just like having TNT or something, a chemically unstable substance, which you can, you know, throw around and everything, it's OK.

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But if you if you heat it to a certain temperature, it's the the energy locked up inside, it will suddenly become available.

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That's exactly what a white dwarf is, and we're surrounded by them.

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So in the Sun, nuclear burning is stable because if if the temperature rises somewhere,

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the rate of nuclear reactions rises that produce, that makes that place a little bit hotter, which then expands.

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The density goes down, the temperature goes down. Both of those reduce the rate of nuclear reactions, so everything returns to normal.

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But in a white dwarf, the the rate at which nuclear reactions occurs depends on the temperature because the nuclei are not degenerate.

328
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But the pressure which is contributed by the electrons doesn't effectively is independent of the temperature.

329
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So if the temperature goes up somewhere, the rate of nuclear reactions goes up.

330
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But the but the system doesn't respond by expanding because the pressure providing electrons say So what?

331
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Your temperature is still pathetic. Your energy level is still pathetic.

332
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So if the temperature rises, the reaction rate rises, which causes the temperature to rise to more, which it's another of these runaways.

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So this thing is clearly a high explosive.

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And if the if it's detonated, it will in seconds turn solar mass or so of carbon and oxygen to iron group elements.

335
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So what's the detonator? We don't really know. That's the sad part, right?

336
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So one possibility is that two white dwarfs spiral together from two to white dwarfs in a binary spiral together and shock each other.

337
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I mean, you can set off high explosives right by hitting it with a hammer. Send the shockwaves through it, the shock wave hits,

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it gets a dip of the relevant temperature once you once you've started to get about the relevant temperature all the way.

339
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Another possibility, which is probably more or more favoured by the pundits,

340
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is that the white dwarf secretes material hydrogen or helium for some ordinary companion star,

341
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which pushes the mass of the whole star above the Chandrasekhar mass.

342
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And it disappears and then it starts to contract.

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And we're not sure what the what the answer is, but I'll just briefly summarise what's work on on the Chandrasekhar mass model.

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So that's where you push it. You just pile stuff on to the white dwarf to get its mass over the critical mass and it goes down the tubes.

345
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So we've said the stars, we said the cells squishy. We've said that the you've seen this diagram already,

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that the Fermi energy just disappears off to infinity as the mass of the system approaches the Chandrasekhar mass.

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So that at some point the the the star is capable to oscillate with large amplitude in radius because it's become very squishy.

348
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Every time its density goes up by compression, the temperature goes up the.

349
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It's relatively easy to get the nuclei to fuse because they're embedded in an incredibly dense,

350
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sparse of negatively charged particles so they can come quite close to each other

351
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on account of shielding before they even see each other and start to repel. And so you,

352
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you have something that's a little bit like you find that the numerical calculations show that

353
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significant level of fusion occurs when the temperature is only something like 10 to nine degrees K,

354
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a factor ten lower than the benchmark temperature, which so you get a sort of low level of a low level of burning.

355
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The core becomes convective. But the core is actually very efficiently heated by what's called the Irkut process,

356
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which is the absorption of an electron when when the material sorry the absorption of electron by a nucleus.

357
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And then in this convection, the nucleus will be carried to someplace where the density is lower than the Fermi.

358
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Energy is lower and it will be to decay and then it'll be carried back down again.

359
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So it'll be repeatedly absorbing an electron and emitting an electron.

360
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And each time it does either of these two, a neutrino is emitted.

361
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And these neutrinos escape. So the thing starts to radiate significantly in neutrinos.

362
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So the core has a new mode of cooling, which is those calculations suggest make this.

363
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This era of slow fusion lasts for about a thousand years, but then somehow it gets out of hand.

364
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The temperature rises somewhere.

365
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To the fusion temperature and a wave sweeps through the white dwarf,

366
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which may be a definite creation wave, that's one that travels slower than the sound speed,

367
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or it may be a detonation wave, which ones that travels fast, or maybe one that starts as denigration finishes a detonation.

368
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But the damn thing blows up,

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and the energy released in that turning of the carbon and oxygen into iron group elements simply blows the whole star completely apart,

370
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and we think nothing is left. So quick word about energetics.

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The escape energy from a white dwarf with the mass of the Chandrasekhar mass is about 12000 kilometres a second.

372
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The energy the binding energy of such an object is about 10 to the 44 joules or change of the 51 ERGs in old money.

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And it turns out that the energy of supernova remnants the what the energy of what you see of the disturbed gas

374
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and the radiation and so on that comes out of the thing is always about 10 to the one tenth of the 44 joules.

375
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That's an empirical fact. The energy,

376
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the binding energy here of a neutron star is is more than 200 times larger than

377
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this because we don't then have twenty two thousand kilometres in the bottom.

378
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We have 10 or 20 kilometres in the bottom, so it during the during a core collapse supernova,

379
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hundreds of times more energy is released than is in the supernova than we see in the supernova remnant.

380
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These two events have very different energy budgets. But but the but the debris have comparable budgets,

381
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and the reason is that most of the energy from a core collapse supernova is carried off by these neutrinos.

382
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Neutrinos, which were only once observed they were observed when there was a supernova in 1987 in the Large Magellanic Cloud,

383
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which is very close to us. But but this surely is the main event of a core collapse supernova.

384
00:46:06,390 --> 00:46:12,690
OK, well, here are my conclusions that there are these two fundamentally different processes, though.

385
00:46:12,690 --> 00:46:23,550
So incineration the thermonuclear one and burial which can end the life of a star.

386
00:46:23,550 --> 00:46:27,120
And basically, it's all about the Chandrasekhar mass,

387
00:46:27,120 --> 00:46:40,320
the limitations on the existence that come from quantum mechanics and relativity working together of degenerate of cold self gravitating balls of gas.

388
00:46:40,320 --> 00:46:51,286
Thanks.