I think it's sort of like.
Good morning. So it's my very pleasant. My great pleasure to explain the basic physics of why stars and as very dangerous objects.
And my colleague Phillip will explain more fully how that rolls out, how the how the danger and how the how the damage unfolds.
And then see Bissaka. We'll talk about possible how these objects are used and possibly misused in in contemporary cosmology.
OK, so my outlines, I'm going to bed about how physics, right, how stars age,
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.
Now being relabelled condensed metaphysics, which is the physics of degenerate gases.
How does this apply to stars and then talk about the two types of chemical which nature has four stars?
They can be either buried or cremated.
So the main point about a star, obviously, is that it radiates and self gravitating objects like stars and galaxies,
as we covered back in in the January 20 18 Saturday morning in a different context in the Galaxy Dynamics context,
we explained why self gravitating objects have negative specific heats.
So as they as you draw heat out of them, they heat up, the temperature goes up when you call them.
So a star responds to the loss of of energy by radiation from its surface, by contracting and heating.
The heating, of course, happens because the gas gets compressed as the thing contracts.
And that's the thing contracts, the gravity that binds it gets stronger.
So this is a vicious circle. Every contraction sets up, sets it up for further contraction.
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.
But most of the time in the temperature is fairly stable because a small increase in temperature greatly speeds the nuclear reactions,
the fusion reactions that provide the heat that is being radiated from the surface.
So we have a.
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.
But as as the star progresses through the synthetic chain from hydrogen to helium, from helium to carbon and oxygen from carbon and oxygen,
silicon and so on, the nuclei are developing bigger and bigger charges, which means there's a bigger and bigger cooling barrier to overcome.
So as the star, in order to get fusion so as the star ages and move through this succession of fuels hydrogen, helium, carbon,
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.
And the reason, of course,
that the the nuclear reactions are very sensitive to temperature is that they the fusion events happen from very rare encounters of nuclei,
which are on the right.
The extreme tail of the Maxwell value and distribution in a small increase in the temperature can greatly increase the number of of nuclei.
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,
the central density rises a lot and the temperature rises somewhat less.
But although it does rise a fair amount.
And what that if you if you're raising the temperature, raising the density without comparably raising the temperature,
you're pushing the gas towards a degenerate configuration,
a configuration in which quantum mechanics becomes a non-classical gas that is a gas in which you.
The physics is very strongly influenced by basic quantum mechanics.
So let's just talk about degenerate gases because we get the star is going to end with a core which is degenerate.
So the pressure inside a star is like the sun is provided.
All reasonable normal stars that you can see is provided by the electrons.
And in a neutron stars is provided by the neutrons,
whatever it's it's it's overwhelmingly provided by fermions particles with half half of each bar of spin.
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.
So in order to figure out which states are occupied and what you need to know in order to work,
work out what the pressure is going to be at a given density, you want to count states.
So in one dimension, we do it very straightforwardly.
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.
So in order to hold the particle in, that means the wave function has to vanish on the walls, as you probably remember.
And the consequence of that is that the states come like this.
This is this is a fundamental state which vanishes at the two ends and is a cosine in between.
Then the next state up in energy is this which vanishes both at the walls and in the middle.
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.
So the wavelengths of the fundamental is twice the size of the box because the box is just half a wavelength in size.
And the third state is has, the wavelength is two thirds of the length of the box.
So the wave numbers K two, which are two pi over lambda integer multiples of pi over lambda.
So when we go to three dimensions, we have, uh, we have to fit it.
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,
K, Y and Z, and they all have to satisfy a condition of this type.
Each one of them has to be an integer multiple of Pi over L.
So the number of so each of these,
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.
Big, which has and the points in this cubic lattice are separated by Delta K, which is PI over L.
So if we want to know how many of these points there are inside a sphere of radius k f,
then we just have to work out the volume of that sphere for PI times,
the radius cubed and divide by the volume associated with just one of these cells, which is Delta K cubed.
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.
In other words,
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.
So the number of of quantum states associated with wave vectors of lengths smaller than CF is twice this.
In other words, eight pi, whatever. Also, we know that momentum.
Sorry, we know that the momentum is H. Bach from basic quantum mechanics.
So the number of states which have momentum less than this %f the Fermi momentum is going to be there.
So the the four is become an eight by the by the spin thing and K has been replaced by PAF upon par.
So the conclusion is, if we have any particles in the box,
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,
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.
So you may remember pictures a bit like this that if the temperature is reasonably high,
then the the states, the low lying states will they're always occupied.
This is the expectation of the number of of particles in a state.
So it it's one more or less one until you until you get within Katie of the energy here associated with PAF.
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.
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.
And that's essentially we're going to. You can do the calculation when you don't assume a sharp drop off,
but life is extremely much easier if you assume a sharp drop off and it'll be an adequate approximation in this approximation.
I'm going to be making that the states glow the the with momentum less than %f are completely occupied.
That's taken and the states above are completely empty.
Sudden, sudden change. So we're talking about the minimum kinetic energy that you can have the kinetic energy at effectively negligible temperature.
So where are we we we have that if we have a political density and overall cubed,
then the so the political densities and overall cubed, then the the the Fermi momentum is related to it like this.
What's happened is we've lost the V from here. We've stuck it well.
We've lost the old cube to stuck it there. So what we conclude is so we have a three here.
So if we if we take the cube root of both sides of this equation,
that leaves the conclusion that the Fermi momentum is goes like the volume per particle to the minus the power.
And this number here is effectively it's essentially HPR.
This number here is is virtually one. So we have we have we have that relationship that all right.
And I think I've I've already said this, that we're that instead, of course,
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.
So relativity says that up and you will see it's highly relevant that the E,
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.
So if we differentiate this, if we apply this relation with that turn to the energy associated with this Fermi momentum,
the most energetic particles that we need at low temperature.
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.
So differentiating that relationship, we discover how f DF depends on on the specific volume v,
uh, we have here APF, which we know goes like features of one third.
So getting rid of that, this v becomes the V to the minus five sets.
So this tells us how if the F depends on the V and if we remind ourselves about thermodynamics,
some dynamics says that the internal let the change in the internal energy is equal to the temperature times,
the change in the entropy minus the pressure times, the change in the volume.
So this is going to apply to the whole box and therefore the volume should be in times the volume per particle,
which is what little v is the volume per particle. So this is the whole volume.
So this is just the second law of thermodynamics.
The relationship of you to the energy associated with the Fermi energy is not completely straightforward.
Obviously, its end times, the energy in the box is obviously in time.
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.
My point is that most of the particles most of the states are quite close to the edge of that sphere in space.
So that's why this number is close to but less than one.
But on the other hand. So this is just the average energy, the average radius inside this sphere.
OK, so we have a simple relationship between DCF from here.
This gives us the relationship between DCF and %DV.
So we considering changes adiabatic changes in which there's no heat put in or taken out, so there's no entropy change.
So we have the pressure from this relationship. Here is simply x.
This number, which is essentially one times the derivative of the Fermi energy with respect to the specific volume.
And we've um yeah, we we know what the f by the volume is from the last slide.
So we end up with this feature of the minus five thirds of a AVF and a we know what this is.
This is essentially C square. This is a squared C squared right edge.
Bussey squared effectively with some stupid numbers, numerical factors on the order of one.
So we've got these key relationships that the Fermi momentum goes like the minus the power of the specific volume.
And we have that. The pressure goes like the minus five first power over e f.
And we also have, of course, this relationship here.
If we're in the non relativistic regime, then the Fermi energy is then in the non relativistic regime.
Uh, this is completely dominated by the rest mass energy MC squared.
In other words, this momentum, this is unimportant in the non relativistic regime so we can replace this f by M.C.
squared in the highly relativistic regime ultra relativistic regime the opposite one.
This becomes unimportant and basically e becomes c p.
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,
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,
which means that PV to the five thirds is a constant.
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.
In fact, five thirds if it was a monotonic gas and its other numbers of the events that xDai atomic gas.
So that's just recovering the monotonic gas thing.
If we're in the ultra relativistic regime, on the other hand, we should replace this if it's by C.P.
And that means we've got another power of P on the bottom, but P goes like V to the minus one third.
So this five 3rds then becomes four 3rds and we find that P V to the four thirds
is a constant in the if the Fermi energy is well above the rest mass energy.
So now let's for the first time, allow gravity on the on stage and imagine we have a ball of gas radius.
Big, bigger. And let us push that radius in a bit.
Then the change in the volume per particle is going to be this right.
It's the change in the volume of the ball. This is four pi all squared.
D. R. And we have to divide by end because we want the volume per particle, not the volume of the whole ball.
Then we have that we know do is minus %DV.
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,
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.
So we have from this V to the minus gamma becomes the knowledge of the minus three gamma and then.
We haven't all squared D.R. all squared deal.
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.
We have an arch, the minus two dear. And if in the non relativistic regime we come as five thirds,
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.
OK, now when we squash the ball in, since it's self gravitating, it's gravitational energy changes.
And this is a worthwhile.
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?
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,
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?
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.
If we decrease R, this is and this is going to be negative.
Gravity is going to be the these gravitational energy of the ball is going to go down.
The ball is going to the gravity is going to do work on whom is it going to do work?
It's going to do work on the thermal energy. All right.
So the key thing is this this change in gravitational energy is scaling is one overall squared.
And up here in the non relativistic regime, it's scaling is one.
Overall, the balancing item in the box is scaling is one overall cubed or one overall squared and the ultra realistic case.
So in the non relativistic case, if you contract it, the the thermal energy rises faster.
Well, the rate at which it rises increases as all shrinks faster than the then gravity is supplying is able to do work.
And that means that the oscillations are stable, that the system will oscillate in and out, stably converting thermal energy,
increasing its thermal energy when it goes in and decreasing its, well, increasing its negative gravitational energy, if you like.
But if in the ultra relativistic case, these two scaled together.
And that means that way, if you push it in, it was in equilibrium.
You push it in. It's still in equilibrium. You push it in some more. It's still in equilibrium.
The thing that's become very infinitely squishy is cable. Just to cruise down to no to no volume.
Just because of this change in the way that the thermal energy scales,
the change in the thermal energy scales with with radius having changed, that has profound consequences.
So that's the sort of intuitive back of envelope stuff.
If you write down the proper differential equations and integrate them, you find this sort of behaviour.
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.
And it's normalised to the density of water because water has a significant density,
it's the density basically of close packed oxygen atoms or whatever.
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?
And you have it at a density higher than that of water.
It means that the electrons are not going to be tied to individual atoms anymore.
They're going to be swimming around. There isn't space in there to have atoms any longer.
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.
That's the top. That's the dashed model. And the other model has a mass of point eight of the Sun.
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.
What's not at all obvious is that the the radius of this thing, which is very well-defined,
the density declines fairly slowly and then really drops like [INAUDIBLE].
When you reach the outside, this is logarithmic scale. So this is this is a serious drop.
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.
It shrinks. The other thing that's very notable here is this this is the Fermi energy,
which is the minimum energy of the faster electrons that provide the pressure right?
If the thing has any finite temperature, the this the the actual energy will be of the fastest.
Electrons will be above the Fermi energy. The minimum energy is divided by M.C. squared, the the rest mass energy of an electron.
So even in this lighter white dwarf, the central Fermi energy is above the rest mass energy of an electron.
And for the Sun, for something of the mass of the Sun, it's more than three times the mass of an electron.
If you make a series of models, which you do by integrating the equations from an ever higher central density and look
at the the mass of the model that you end up with versus the radius of its edge,
you get a plot like this. So each of these dots is obtained by integrating the equations.
And for low masses, you have large radii.
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,
and it's headed to a point with mass one point forty four solar masses.
And this is the result for which Chandrasekhar and Fowler shared the, I think, nineteen seventy eight or something, no Nobel prise.
Meanwhile, if you if you plot for the same series of computations mass versus central fermions, you divide it by M.C. squared.
It starts off going up and by and then it really it really shoots through the roof.
So this this is all, of course, a little bit naive, but it's a clear signal.
This is saying that that the minimum energy of the fast is electrons is a thousand M.C. squared.
It is a seriously moving particle.
We really are into the ultra relativistic regime when we're once we're close to this one point forty four solar masses.
If you solve the same equations for a star, which is held up not by electrons, but held up by just neutrons.
The picture is is almost indistinguishable. Right here is here.
The dotted one is not mass star, which has a mass of one point two solar masses.
The full one is one that has a massive point seventy five solar masses.
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.
So this the radial scale is shrunk by a factor of many hundreds.
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.
And now we're going up to densities of 10 to the 14 times the density of water.
But the basic principle is the same that what's happening here is this as we approach the Chandrasekhar mass,
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.
So the connexion to stellar evolution now just just some empirical facts really?
Well, I mean. Results of complicated calculations during the sixties and seventies stars,
which have a mass in this range here between half a solar mass and eight times the mass of the sun,
generates enough heat in their centres that they they can ignites.
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.
But they don't then get hot enough to fuse the carbon and oxygen into this,
into the nuclei further up the periodic table because they when they're sort of about halfway through doing this,
turning their helium into carbon and oxygen, they they blow the envelopes away into interstellar space.
And that's the birth of a planetary nebula. And here is a planetary nebula,
a ball of gas which is being ionised by hard radiation coming off this extremely hot carbon and
oxygen degenerate object in the middle here and glowing as it recedes rather in rather a gentle way.
This isn't an exploding star. This is just a. This is just blowing off steam, right?
But in the more massive stars,
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
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,
it will be less than most of the mass.
OK, so that leaves this white dwarf, which has, as we've seen, a radius of a few thousand kilometres like the Earth.
But it has a mass which is comparable to the mass of the Sun,
and it's supported by the Fermi energy if it's to generate electrons which are mildly or strongly relativistic.
And and we are surrounded by these things all over the place, right?
The many zillions and zillions and zillions of stars in the galaxy have been through this phase and have left these these white dwarfs,
which cool they take. They they continue to cool even if they were formed.
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,
it's some fact that it moves rather fast across the sky is telling you that it's relatively close to you.
It will be a white dwarf, and there are gazillions of these.
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,
and most of them can turn the silicon, et cetera.
Further up the periodic table until you get to iron, so that these stars eventually produce a core of iron,
which has a mass comparable to the mass of the sun,
which is supported by the by the degeneracy pressure is supported by the Fermi energy of mildly mildly or strongly relativistic electrons.
So essentially, in the middle of such a massive star late in its life, you have a white dwarf made out of iron.
And other Asian group elements. And either of these two end points is a dangerous situation.
The easiest to understand is the fate of the more massive stars.
So Aaron is the most tightly bound nucleus. There's no way you can get any more nuclear energy.
You've had it. So the scheme the star has had for resisting gravity for possibly billions of years,
possibly tens of millions of years, depending on its mass, is now defunct.
The only way it can replace the energy that it radiates from its surface is by contracting.
And that is not a safe game. So as we said, most of the pressure in this cause contributed by these two generate electrons,
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.
So as the Fermi energy rises well above the the rest mass energy we get, we go, we go relativistic.
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,
the way that the gravitational and thermal energy scales with all is the same.
So there's nothing to there's nothing to pick out. A particular radius is preferred and the temperature rises.
So, so the thing begins to contract. There's nothing to stop it contracting.
And if and if he contracts the radiation field, the middle gets hotter.
The radiation field becomes contains harder and harder photons, higher and higher energy photons.
And some photons then have sufficient energy to simply blast an iron nucleus into into fragments.
And the electrons all have a choice. They can live free or they can marry a proton and form a neutron.
But the cost of living free, which is the Fermi energy,
is constantly going up because the density is going down because the star has to replace the energy,
which it's radiating on its surface and has got no other thing to do that to contract.
So, of course, more and more of them decide they'd rather be married than free.
But that is a serious issue because they are contributing the pressure and every electron that decides
to give up the ghost and marry reduces the pressure and increases what the others have to do.
It's obviously an unstable cycle. It's obviously a vicious cycle, right?
They they that pushes up the firm that causes contraction, that pushes up the Fermi energy and more give up the ghost.
So you obviously have the core quickly goes into freefall.
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.
And curiously, in the as it goes into freefall,
the nuclear synthesis which the star has laboriously done for hundreds of thousands of years is all undone.
Because the rules of the game have now changed. It was advantageous to build bigger nuclei.
But now with all these, with all these hard photons blasting you apart and all these very high energy electrons deciding to.
To be absorbed by the nuclei, it's advantageous actually to split the nuclei up.
Of course, splitting them up, it consumes a huge amount of energy, all the energy that was released through the life of the star.
It now just on a collapsed line, which is which is only seconds is required to split them apart again.
But gravity is a very generous donor and it provides the energy and they all split up.
OK, so. We've we've we're going to have very many free neutrons.
The neutrons, which are unstable in the laboratory, the stable in this strange place because the B,
because in order to decay by beta decay, a neutron has to emit an electron.
Where's it going to meet the electron? Well, it has to be emitted.
The only the only spare spaces is above the Fermi energy, so you can only decay if you're a neutron inside the star.
If you can somehow get hold of the energy to put your ejected electron above the Fermi energy, well, they can't do that.
So they. So then they're now essentially stable and they build up in numbers.
And eventually the neutrons are packed together during this collapse, packed together so tightly that they become degenerate to.
So even though the temperature is enormous,
it's not enormous enough to keep the at this incredible density to keep these neutrons with thermal energy above the Fermi energy.
The collisions between between nuclei,
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.
And that these these collisions are now sufficiently energetic, that they're emitting neutrinos pretty much as freely as they emit photons,
so at very high energies, weak interactions and not the very high energies, weak interactions become sort of not rare.
The cross-sections for them go up sort of lecture unification and all that.
So enormous numbers of neutrinos are produced.
And the density in the kid in this in the core of the star is so high that even neutrinos are somewhat trapped.
They're not long term trapped, but they're trapped enough that they have to diffuse out and in diffusing out,
they impart momentum to the material which is trapping them, which of which they're scattering.
So they impart momentum to the envelope of the star, which is falling in onto the collapsing core as they brushed by.
And uh, so. So you have now a collection of of neutrons coming together to form to form a ball colliding with each other,
being very rapidly cooled or losing energy by this by radiating all these neutrinos, which which rush out very quickly.
And you may get a neutron star formed, but but the mass of this core originally was essentially the Chandrasekhar mass.
So the mass of the neutron star that's going to form is going to be very close to the neutron star mass anyway.
And if and if it creates some extra material, it can go over over the edge and disappear into a black hole.
OK, now let's talk about the other kind of of of of event, the other kind of degenerate object,
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,
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.
Energy will be released in enormous amounts, and this energy will be enough to unbind this object even.
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.
But if you if you heat it to a certain temperature, it's the the energy locked up inside, it will suddenly become available.
That's exactly what a white dwarf is, and we're surrounded by them.
So in the Sun, nuclear burning is stable because if if the temperature rises somewhere,
the rate of nuclear reactions rises that produce, that makes that place a little bit hotter, which then expands.
The density goes down, the temperature goes down. Both of those reduce the rate of nuclear reactions, so everything returns to normal.
But in a white dwarf, the the rate at which nuclear reactions occurs depends on the temperature because the nuclei are not degenerate.
But the pressure which is contributed by the electrons doesn't effectively is independent of the temperature.
So if the temperature goes up somewhere, the rate of nuclear reactions goes up.
But the but the system doesn't respond by expanding because the pressure providing electrons say So what?
Your temperature is still pathetic. Your energy level is still pathetic.
So if the temperature rises, the reaction rate rises, which causes the temperature to rise to more, which it's another of these runaways.
So this thing is clearly a high explosive.
And if the if it's detonated, it will in seconds turn solar mass or so of carbon and oxygen to iron group elements.
So what's the detonator? We don't really know. That's the sad part, right?
So one possibility is that two white dwarfs spiral together from two to white dwarfs in a binary spiral together and shock each other.
I mean, you can set off high explosives right by hitting it with a hammer. Send the shockwaves through it, the shock wave hits,
it gets a dip of the relevant temperature once you once you've started to get about the relevant temperature all the way.
Another possibility, which is probably more or more favoured by the pundits,
is that the white dwarf secretes material hydrogen or helium for some ordinary companion star,
which pushes the mass of the whole star above the Chandrasekhar mass.
And it disappears and then it starts to contract.
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.
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.
So we've said the stars, we said the cells squishy. We've said that the you've seen this diagram already,
that the Fermi energy just disappears off to infinity as the mass of the system approaches the Chandrasekhar mass.
So that at some point the the the star is capable to oscillate with large amplitude in radius because it's become very squishy.
Every time its density goes up by compression, the temperature goes up the.
It's relatively easy to get the nuclei to fuse because they're embedded in an incredibly dense,
sparse of negatively charged particles so they can come quite close to each other
on account of shielding before they even see each other and start to repel. And so you,
you have something that's a little bit like you find that the numerical calculations show that
significant level of fusion occurs when the temperature is only something like 10 to nine degrees K,
a factor ten lower than the benchmark temperature, which so you get a sort of low level of a low level of burning.
The core becomes convective. But the core is actually very efficiently heated by what's called the Irkut process,
which is the absorption of an electron when when the material sorry the absorption of electron by a nucleus.
And then in this convection, the nucleus will be carried to someplace where the density is lower than the Fermi.
Energy is lower and it will be to decay and then it'll be carried back down again.
So it'll be repeatedly absorbing an electron and emitting an electron.
And each time it does either of these two, a neutrino is emitted.
And these neutrinos escape. So the thing starts to radiate significantly in neutrinos.
So the core has a new mode of cooling, which is those calculations suggest make this.
This era of slow fusion lasts for about a thousand years, but then somehow it gets out of hand.
The temperature rises somewhere.
To the fusion temperature and a wave sweeps through the white dwarf,
which may be a definite creation wave, that's one that travels slower than the sound speed,
or it may be a detonation wave, which ones that travels fast, or maybe one that starts as denigration finishes a detonation.
But the damn thing blows up,
and the energy released in that turning of the carbon and oxygen into iron group elements simply blows the whole star completely apart,
and we think nothing is left. So quick word about energetics.
The escape energy from a white dwarf with the mass of the Chandrasekhar mass is about 12000 kilometres a second.
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.
And it turns out that the energy of supernova remnants the what the energy of what you see of the disturbed gas
and the radiation and so on that comes out of the thing is always about 10 to the one tenth of the 44 joules.
That's an empirical fact. The energy,
the binding energy here of a neutron star is is more than 200 times larger than
this because we don't then have twenty two thousand kilometres in the bottom.
We have 10 or 20 kilometres in the bottom, so it during the during a core collapse supernova,
hundreds of times more energy is released than is in the supernova than we see in the supernova remnant.
These two events have very different energy budgets. But but the but the debris have comparable budgets,
and the reason is that most of the energy from a core collapse supernova is carried off by these neutrinos.
Neutrinos, which were only once observed they were observed when there was a supernova in 1987 in the Large Magellanic Cloud,
which is very close to us. But but this surely is the main event of a core collapse supernova.
OK, well, here are my conclusions that there are these two fundamentally different processes, though.
So incineration the thermonuclear one and burial which can end the life of a star.
And basically, it's all about the Chandrasekhar mass,
the limitations on the existence that come from quantum mechanics and relativity working together of degenerate of cold self gravitating balls of gas.
Thanks.