We saw last lecture that the mass of a main sequence star determines its temperature and luminosity. High mass means high gravity so for the star to be stable (hydrostatic equilibrium) requires that the thermal pressure pushing outwards which balances gravity has to go up as well, so the temperature (and density) goes up. And the nuclear reaction rate is INCREDIBLY sensitive to temperature - a little bit more temperature means that the particle velocity is a little bit higher, so MANY more protons get within the range of the strong nuclear force which can overcome the electrical repulsion. Massive stars are MUCH MUCH more luminous. But their lifetime on the main sequence is determined by how much hydrogen fuel they have available (mass), and the rate at which they spend it (luminosity). Massive stars with lots of fuel resources squander them in a short lived blaze of glory, while very low mass stars eke out the small amount of fuel they have to glow dimly over a main sequence lifetime much longer than that of the Sun. Hence we can estimate the age of a cluster of stars as that of the most massive stars still on the main sequence - this is called the main sequence turnoff.
But whether its a long or short lifetime, all stars eventually come to the end of it. Our own Sun is about halfway through its main sequence lifetime of 10 billion years - so its got another 5 billion years of shining steadily on the main sequence. But then, when all of the hydrogen in the core has been fused to helium there is no more energy available to the core. This marks the end of the main sequence lifetime, and from here on in the star is in its last gasps, trying but failing to find a stable energy source to combat gravity. Most of a star's life is spent on the main sequence, but this last 10 per cent of its life as a star can be spectacular!
The weight of the layers above still push down on the core, only now there are no fusion reactions to heat the core to hold it up against gravity. So gravity takes over and the core shrinks. The layers outside the core collapse too, the ones closer to the center collapse quicker than the ones near the surface. As the layers collapse, the gas compresses and heats up as there is gravitational energy released. This holds up the core for a little while, but to get more gravitational energy it has to contract still further ...
But can the core contract indefinitely ? How close can we squash material together before it protests ? With classical ideas of electrons and protons/nuclei as being almost point-like particles, then plainly we can squash them together until they 'almost touch' before odd things start to happen. But as we've said before, electrons are not like this - they can behave a bit more like a wave. And a wave doesn't have a well defined position, it's spread out. So it might object at much larger spacings than we'd expect from point particles. And now we hit another odd property of matter - suppose you have two water or sound (or light!) waves of the same wavelength in the same place. They would add up together to make you a wave thats twice as big. But the electron waves ARE NOT LIKE THIS. They have a Greta Garbo sense of 'I want to be alone'. You CAN'T get two electrons with the same energy in the same space. This is NOT due to them being of the same charge (we'll see later on that neutrons do this too!!). The size of the space for each electron is determined by the electron wavelength, but by analogy with light waves, as the space becomes smaller so then the electron wavelength has to becomes smaller i.e. its energy has to get bigger. But earlier when we looked at pressure we saw that normal thermal pressure is caused by the motion of nuclei and electrons - the faster they move (i.e. the more energy they have) then the more pressure they exert. But here we are saying that the electrons have energy even if they are NOT HOT - they have energy just because they are confined to a small space. The more energy they have the faster the move so the bigger the pressure - this is called electron degeneracy presssure. (Its more usual to talk about it in terms of energy levels, but I think its harder to visualise - the two explanations sound different but are ultimately identical!) Electron degeneracy is a purely quantum mechanical effect - ultimate core collapse of a star can be held off by this odd property that electrons want to be alone! This is what stabilises a white dwarf against gravity (page 3 of this is specifically about electron degeneracy pressure.
For very low mass stars, masses less than 0.5x that of the Sun, then this is what happens. These stars transport energy by convection so they are all mixed inside so the hydrogen runs out in the whole star. The core shrinks, and shrinks, and shrinks, becoming degenerate before the core temperature rises high enough to do anything more entertaining! So it can't contract any more, so can't get any more gravitational energy. This is a white dwarf made up of helium. It fades and cools becoming a black dwarf.
Stars from 0.5-6 solar masses are much more complex. These carry the energy in the interior mostly by radiation so the core is made up of helium but the outer layers are still mostly hydrogen and they are not mixed together during the main sequence life of the star. So when the core starts contracting, and heating up because of gravity then eventually the layer just outside the core gets hot and dense enough for fusion to start. So there are 2 sources of energy - the gravitational shrinking and H fusion in a shell around the core, and this core and shell are much more luminous than the original main sequence core! So the outer layers of the star (which hadn't contracted by very much so still feel much the same gravity) suddenly have MUCH more luminosity going through them. So the thermal pressure is much bigger than the gravity, so the outer layers expand tremendously (our sun will be bigger than the orbit or mercury and Venus, and possibly also of Earth), and so cool down.... This is a red giant. Plotting this on an HR diagram we'd see the star go from the main sequence to much higher luminosity and much lower temperatures - ie it moves up and to the right on an HR diagram.
But the core keeps on contracting, and its temperature goes up, and the shell burning around the core keeps on going, adding more helium ash to the core. And eventually the temperature goes high enough (over 100 million K) that it can start to fuse helium to carbon. You'd have thought that the core would fuse 2 helium nuclei to make Beryllium, but the isotope of Be which you'd make from 2 helium nuclei would have 4 protons and 4 neutrons and happens to be highly unstable and falls apart very very fast! So you have to stick another helium on before it does so, and go to an extremely stable isotope of carbon (carbon 12 with 6 protons and 6 neutrons). See this nice little animation . So then we have Hydrogen fusing to helium in a shell and He fusing to Carbon in the core. This releases lots of energy and heats the core, so it expands, pushing the He and H fusing layers outward. The total luminosity drops, so the the outer layers don't have as much thermal pressure as before to balance gravity, so they contract and heat up a bit (so the star moves down and to the left in an HR diagram).
But the core is soon all converted to Carbon (very very quickly for stars less than about 3x the mass of the Sun - its called the helium flash and happens because the helium core goes degenerate before it starts to fuse. But even though there is a huge increase in luminosity for a very short time this doesn't result in any flash of light from the surface as the luminosity has to struggle out). So then it has a carbon core contracting by gravity, and helium fusing to carbon in a shell and hydrogen fusing to helium in an outer shell. So it goes up to being a red giant again, only now it has a helium fusing shell as well as a hydrogen fusing shell. So the total luminosity is higher than before, so the outer layers expand again to even further out than they were before (Earth definitely gets it this time!). So the outer layers are a long long way from the core, so the gravity holding them onto the star is quite weak. And the shell burning isn't really very stable - if there is a bit more luminosity than normal then the outer layers get pushed out and become detached from the star. So we have material illuminated by the hot core - this is a planetary nebulae (nothing to do with planets - some of them looked a bit like a disk with early, small telescopes!) - and a really pretty collection of HST pictures of planetary nebulae. The exposed core can't keep on contracting as it hits the limit where degeneracy pressure won't let it go any smaller. So the core starts off as a hot carbon white dwarf, and then cools down to a black dwarf.
There is a nice java animation of stellar evolution on an HR diagram. And some good general sites on the death of low mass stars , stellar evolution and star life and death
see Kuhn p426-441