So the sun has joined the main sequence. Let's remind ourselves of what that means, that means we have a core in which hydrogen is fusing generating helium. This is supporting the rest of the envelope by thermal radiation pressure. And there's a theorem that the luminosity surface temperature, profile, etcetera is all determined essentially by the mass of the cloud the, the, the ball of hydrogen you're forming. But there are also dependencies on the composition. What composition, it's hydrogen and helium. Yes, but there are those trace amounts of carbon, nitrogen, oxygen. They adjust delicately both the dynamics of nuclear reactions and of heat transfer, so metallicity makes a difference. In addition, the rate at which a star rotates can make a difference, the existence of a close binary partner, some affects of the atmosphere of the star and when we're observing it also unaccounted for affects in the interstellar medium can alter a star's appearance. This, these causes are why the main sequence is not an infinitesimally thin line, but rather a strip because we have to account for differences in rate of rotation, composition, etc. And so the, but other than that the star settles down and sits there in equilibrium and if its a star with the mass of the sun it will sit there for about ten billion years. During which time we saw it, things are not exactly static, there is some evolution going on. What is going on is that the core is contracting. And the main reason the core is contracting, you remember, is because of our old equation p is (n/v)*(kboltzmann)*t. When we take four protons and form an alpha particle out of them. And in the process eject two positrons that take two electrons out of the mix. We have gone from a total of eight particles, four protons and four electrons, to a total of three particles, one alpha nucleus and two electrons. And, the net result of this is that the number of particles is decreasing. If the core does not contract then the pressure will decrease, pressure can't decrease because it's holding up the external envelope. There's no real intuitive reason way I can think of to explain this, but the net result is that the compression and the resulting heating of the core more than compensate for the decrease in the concentration of hydrogen. The rate at which fusion is occurring increases and then the core is now producing more luminosity, more energy, the need to puff, push more energy through the envelope puffs the envelope out and so the radius of the star slowly increases and its luminosity slowly increases and since the rise in temperature of the outer envelope does not track the main sequence. the star is starting to turn away from the main sequence if the temperature not changing it's moving vertically up the HR diagram. And this is where we pick up our story and where things start to be interesting. So, we meet our Sun at the ripe old age of about, almost eleven billion years. It has grown somewhat, as we discussed. It's got a radius of about 1.6 solar radii, it's got a luminosity that's almost double what it started with. by now it has been accumulating helium in the core to the extent that the inner 3%, not by volume but by radius. So, the first point 03 of the solar radius is essentially a chunk of helium that's, or ball of helium and the helium just sits there it's inert, it's not producing energy. Therefore, there's no temperature gradient, there's no flow of energy out of the helium. So there's no temperature gradient, it's all at the same temperature, which is the temperature of the hydrogen immediately adjacent to it and outside this helium core, of course, is a shell of hydrogen in which fusion is occurring, and that's what's powering the star. and the rate of fusion in the shell exceeds the rate that was previously going on in the core. Which is why the star is more luminous than it was and over these eleven billion years or so, the envelope has slowly been expanding. And the core has slowly been growing as helium, hydrogen fuses in the shell, more and more helium is being deposited into this inert core, which begins to grow. And this is a picture of the solar system at this point in time, where we are in terms of the sun's main sequence and evolutionary tract, is that for the first ten and a half billion years of its existence the sun sat very happily at this point. And it is now rising away from the main sequence, its luminosity is increasing, and its temperature is starting to decrease slightly. As the, envelope puffs out, so the evolutionary track is turning somewhat to the right. What's the next thing that happens? Well there is an issue here and the issue is well maybe have an optional clip or I'll do a calculation associated to this but. The core being isothermal means again PV is NKT, you need a higher pressure in the center of the core than at the outside of the core because the center is supporting the mass, the weight of the outside against gravity. This means the center of the core has to be more dense than the outside of the core. Not too complicated a calculation from this shows you that if the core is too large a fraction of the star, it cannot support the weight of the outer layers no matter what density you give it and what this tells you. Is that as the correlate fact-, the calculation, if you do it in detail, shows you that a core whose mass is more than 8% of the mass of the star cannot support. The atmosphere outside it. When the mass of the inert helium core in the center of the sun exceeds eight% of the solar mass, and it will, remember that's about the mass of Jupiter. When it exceeds eight% of the solar mass, it can no longer sustain the weight of the atmosphere and the core starts to collapse. Collapse rapidly. What is rapidly? Rapidly means on the gravitational scales, tens of millions of years. Does, that was this Kelvin-Helmholtz Scale we talked about. So the core starts to collapse rapidly. This releases, of course, a great deal of Kelvin-Helmholtz gravitational potential energy. It also compresses the hydrogen burning shell immediately outside the core, because that falls in as the core collapses. This in turn, increases the luminosity that, that hydrogen shell is putting out. That puffs out the star's atmosphere and cools it down and the result. Is that the envelope has puffed up. It's radius is larger, the external temperature decreases, so the star starts moving to the right along the HR diagram. This is what the solar system will look like with a larger, cooler sun. notice the time, 700 million years have elapsed. And the sun is now a sub giant star, it is moving, it'll spend these 700 million years moving to the left and slightly heating up. Moving to the right, sorry. So, cooling down and slightly increasing in luminosity. As the envelope puffs up. What's a subgiant star? Well, an example of a subgiant star is Procyon in Canis Minor. you can look up its data, that's a good example of a subgiant star. Notice, the Sun will only last about 700 million years as a subgiant whereas, it lasted ten billion as a main sequence star. Subgiants are more rare, but because they are luminous, notice they are, the Sun will be more luminous at the end of its subgiant phase we can see some of them. So we've left our core collapsing. What does that do? Well, once the core starts to collapse, then compression heats the shell, luminosity of the hydrogen fusion shell increases dramatically, this puffs up the envelope. As it puffs up it cools out cools down it cools down to a temperature of a few 1,000 degrees where Negative hydrogen ion opacity again controls the opacity of the external atmosphere. So it's approaching that Hiachi temperature that we talked about, because the external atmosphere is opaque. That means that instead of radiation transfer at the outer atmosphere, we have sort of deep convection cells over here. These dredge up to the surface the products of early fusion in the core. And we see a change in the spectrum of the star. What comes up, well. Trace amounts of carbon, nitrogen, and oxygen, whose isotopic abundances have been slightly shifted by the the CNO processes that have been going on I'll be at, at a smaller rate in the interior of the star in a bigger star. We'd see the sea in no abundances that are adjusted by the action of the CNO cycle. Now whenever a star puffs up this large, note the sun is acquiring a radius of 160 solar radii, it's doing it rather quickly within about 600 million years. This quick puffing up is always accompanied by enhanced stellar wind and mass loss. Notice that the outer layers are now much farther from the center that they were. Much less strongly gravitationally bound. So the sun at this point might loose as much as 28% of it's mass in it's red giant phase. The way this would look in the solar system, is that poor Mercury will have completely been subsumed in the sun. Venus and Earth still exist I'll be it temperatures there would be very hot what's an example of a red giant that we know well the star that we call al debaron and probably should call a dubron is a red giant with 1.7 solar masses so its a slightly more massive than the sun red giant with a luminosity about 500 times that of the sun in fact at the peak of its red giant phase and we'll talk about that the sun with have a luminosity over 2,000 times the correct solar luminosity and so the sun is puffing up cooling down. And this goes on, and the core is collapsing. Now, neither the puffing up and cooling down can go on forever, nor for that matter can the core collapsing. So. Something's going to stop the core collapse. And remember that thermodynamic pressure is not able to do this because of this Schoenberg-Chandrasekhar limit Before we go there let's remind ourselves where we are on the HR diagram. We have finished the sub giant phase and we are now climbing the red giant phase. And this phase is the phase that will last for the next 600 million years or so. and the sun becomes more and more bright, more and more luminous at a pretty constant temperature determined as I said by H minus ionization. And then what. Well first of all the court cannot continue to collapse its. Collapses stopped by a quantum effect called electron degeneracy pressure will meet this effect again and while we haven't done much quantum mechanics we can explain some of it. electron degeneracy is the result of the poly exclusion principle. Which remember tells you that only one electron or two if you account for a spin states, can occupy a given state. And there is a finite number of electron states up to a given energy in any volume of space. This electron degeneracy, if you want, is the reason why when I clap my hands they don't go through each other. Although low lying states in this region of space are occupied. All of these electrons would have to be excited to higher energy states. The neat thing about this is it has nothing to do with temperature. Even if you have zero temperature, electrons are all at the lowest possible state. If you try to squeeze too many of them into too small a volume, some of them have to. Reach excited states even at zero temperature. So what this does is it produces a temperature independent contribution to the pressure. When you try to squeeze system with electrons in it too tight one of the things you're doing. It's, you're squeezing some electrons into higher energy states. In normal systems, this is not, in normal gases this is an irrelevant contribution, even at the center of the sun. You can make a calculation that it's less than a fraction of a percent of the total pressure at the center of the sun. But when this degenerate helium core, when this helium core collapses, its density becomes so high that in fact. Electron degeneracy pressure is what ends up supporting the sun's atmosphere. And what is going on is that, The degeneracy pressure, as I said, is temperature independent. But it's very strongly dependent on density. It increases as the density^(5/3). The constant, ke, is slightly dependent on the details of the model. And for the parameters relevant to the sun I gave it here. You plug it in, as I said, you'd find that the sun is highly non-degenerate today. But that the helium core will become degenerate, and this is what will cease its collapse. The important thing about degenerate matter is that. Its pressure is independent of temperature. If you heat a gas, it will expand because when T goes up P goes up. When you heat a degenerate gas it will not expand because P is completely independent of T, until thermal pressure grows enough to overtake degeneracy pressure. So this will stop the course collapse it will stop when it reached degeneracy. What does that do to the outside of the sun, we'll see in the next clip.