The late stages of a star's life produce exciting astrophysics. Every star starts by burning the most abundant nuclear fuel, hydrogen, and turning it into helium. This defines a main sequence star of which the sun is one example. We've seen that the lifetimes of massive main sequence stars are far shorter than the lowest mass main sequence stars. The formal relationship is that the lifetime on the main sequence, goes as the mass of the star to the minus 2.5 power, a very rapid dependence. What happens when the hydrogen is exhausted? Although there is convection in a star mixing the material, the end of a stars life does not denote the end of the hydrogen. There's always some hydrogen leftover unfused. But in general, the star will form two distinct parts. The loss of energy support in the center, as hydrogen fusion stops, leads to the inner part of the star collapsing. Meanwhile, energy is generated from the collapsing core that drives off and diffuse envelope into space. This diffuse envelope after the sun leaves the main sequence, will read to the red giant stage. Seen from afar, we did not see into the core, always see is the photosphere, and this photosphere of the sun will then cool, and become a large object, a red giant. While the diffused envelope expands and cools to temperatures of a few thousand kelvin, the core collapses and reaches a new significantly higher temperature close to a 100 million kelvin. At this point, helium nuclei can fuse to form carbon. Meanwhile, there is still some burning in a shell of hydrogen into helium. So both processes occur in parallel, and indeed in very massive stars, a whole series of different fusion processes occur in parallel at different temperatures, increasing moving towards the center of the star. The star reaching this new equilibrium state is once again stable forming carbon from helium. But this fuel will not last as long as the temperature is hotter, the burning rate is higher, and the lifetime is shorter as a red giant. When the energy sources removed by the end of the helium turning into carbon, once again the star must find a new configuration. When the red giant exhausts its fuel, the carbon rich core must collapse. In low and intermediate mass stars up to about twice the suns mass, the temperature never gets hot enough 600 million kelvin for carbon to fuse into new elements, and so it's the end of the process. Meanwhile, the helium and hydrogen-burning shells outward from the core overcome gravity, and gently blow off parts of the outermost star into space. Perhaps a third of the stars total mass is lost in this way, this is what's called a planetary nebulae. This ejected gas is heated by the ejection itself and glows luminously. Astronomers can see the glowing gas and the chemical elements it's made of, and some of those most beautiful hubble space telescope pictures are a planetary nebulae. The name itself is a misnomer, because when early astronomers were taking images, they thought, they detected planets or resolved dots of light in the sky. Planetary nebulae have nothing to do with planets. Astronomers follow the late stages of stellar evolution, not by watching an individual star, we don't live long enough, and humans won't live long enough to see this happen. As always, we look at statistical populations of stars, and catch different stars at different stages of their evolution, piecing together the story that way. The diagram for doing this is the HR diagram. In the HR diagram, a stars properties changed dramatically, once it leaves the main sequence. So they move very rapidly in terms of their luminosity and surface temperature. To understand what happens to the carbon rich core in an evolved star, we have to consider a different state of matter than normal matter, it's called degenerate matter. It builds on an idea in physics called the Pauli Exclusion Principle, which says that no two particles should can share exactly the same quantum properties. In collapsed and dense states of matter, this exclusion principle, no two particles sharing the same properties amounts to an equivalent of a pressure that supports the matter in a very dense state. The particles can literally not be on top of each other. When the material is very dense as it is in the collapsed core of a star, the electrons are not allowed to be in their ground states, and they become relativistic moving at nearly the speed of light. Degenerate matter is difficult to create in the lab, but we understand its properties based on quantum theory. It's definitely a strange state of matter. In this situation, the pressure holding up the star is no longer dependent on temperature. So it's a completely different situation from the hydrostatic equilibrium that keeps normal stars in their normal stage. For degenerate matter, the laws of physics are different, governed by the quantum theory. The more massive star has the smaller it becomes, the stars that are left behind at the end of a massive star evolution are white dwarfs. Typical mass of a white dwarf is about one or a half a solar mass, and the sun will end its life this way, as a white dwarf of about 0.7 times the mass that it currently has. So the gravity that crushes them and the carbon core is stopped by this electron degeneracy pressure, and the final object is stable, a white dwarf. It's a strange state of matter, semi-crystalline. So the people who metaphorically refer to these evolved stars as giant diamonds in the sky are not entirely wrong. What happens next takes place essentially forever. The star in its collapsed carbon rich degenerate state typically has a high temperature. That's why the stars are seen as white on the sky. Tens of thousands of kelvin. With no new energy principle possible in the core, all it can do is cool off slowly, radiating as a black body, and radiating its energy into deep space. So the fate of white dwarfs is to cool and slowly redden until they turn into dark embers billions or 100 billions or even trillions of years from now. There's no end to the process in principle. Since most stars are low mass stars, white dwarf is the fate of most stars in the universe. And so we can visualize the universe, and the very far distant future as a set of slowly, cooling, and darkening embers. White dwarf is not the only form of degenerate stars, we'll talk about other forms. A white dwarf is supported by electron degeneracy pressure. But if the mass is higher, the star remnant can collapse to an even denser state, and be supported by the degeneracy pressure of pure neutrons, this is a neutron star. If the mass is higher still, there is no force of nature, no quantum force, no degeneracy pressure that can stop the continued collapse. This is how we end up in principle with a black hole. A white dwarf is an extraordinary state of matter. If we imagine a star, a little more massive than the sun at the end of its life. It will collapse to a star about the mass of the sun but about the size of the earth. This means, it's 200,000 times denser than the earth. One cubic inch of this material brought to the earth would weight 10,000 tons. The men who worked out the theory of white dwarfs was Subrahmanyan Chandrasekhar. One of the giants of astrophysics of the 20th century. He won a nobel prize for this and related work. He predicted the gravity will overcome the electron degeneracy pressure at a particular mass. If the white dwarf has a mass more than 1.4 times the mass of the sun, this is referred to as the Chandrasekhar limit. As we consider the end states of stars in the final phases of their evolution, a cosmic cycle comes into view. Stars are born out of cosmic gas and dust, which itself has been enriched by the ejecta of previous generations of stars. Since the stars never collapse completely, but always eject some of their material, and in the case of a supernova maybe most of it, material is recycled into space. So even as time passes and stellar remnants form that are collapsed objects, some significant fraction of the material is sent back into space with new heavy elements mixed in to become part of a new generation of stars. This process is continued for billions of years. We can see schematically, what the fate of stars is by considering time on one axis and the mass of all the possible stars on the other axis. The lowest mass stars which is the vast majority of them, will live on the main sequence for a long time, go through a giant phase, eject a planetary nebulae envelope, and then leave the collapsed carbon rich remnant of a white dwarf. The most massive stars have more exotic and unstable short-lived phases such as a shoop supergiant phase. Then they can die as a supernova leaving behind, either a neutron star or a black hole. In the late stages of evolution of most stars, two different things are happening, energy released in the core is driving out a large envelope and ejecting material into interstellar space. Most stars lose 30 percent or more of their mass this way, and this material is recycled, enriched with heavy elements to become part of new generations of stars. Meanwhile, the core continues to contract, to try and find a new equilibrium state supported by a new type of fusion process. In low mass stars this is not possible, the core becomes carbon rich and is supported by the degeneracy pressure of electrons in an incredibly dense state. For higher mass stars, other fusion is possible and the core is massive enough to collapse beyond the white dwarf state to even denser forms of matter.
