Classes of Sept 25 and 29 We'll not put the notes in the identical order as we discussed the material in class. Again, remember that the notes are intended as a supplement, not as a replacement for the classes or text or other readings. I. Energy flow from the center of the Sun outwards (The three forms of energy flow) There are some very good links to this in the Lectures area of the website, so I think I'll only outline the material. There are three ways to transport energy... radiation/convection/conduction. In a star like the Sun, almost all energy is transported by radiation, except very near the surface where convection takes over. Nature always chooses the most efficient way of transporting energy. For instance, in a red giant, convection is the most important transport mechanism throughout a large fraction of the star. Whe you're transporting energy by radiation, the energy can only travel until the photon gets absorbed. Near the center of the Sun, this distance is tiny, so the photons are absorbed and reemitted countless times. When the photons are reemitted, they may not be travelling in the same direction as before. Furthermore, the laws of quantum mechanics say that there is a chance two photons (or more) will be emitted, which is fine as long as energy is conserved. So, the gamma rays created at the center of the Sun take a long time, around a million years, to reach the surface of the Sun. This is simply because of the countless absorptions and reemissions. These gamma rays are also changed into many optical photons. II. Solar neutrino experiment Check out the link to Dr Rick Pogge's notes from Ohio State. It can be found in this same area of the website, the Lectures area, look below. It's "even more notes [from Rick Pogge] http://www.astronomy.ohio-state.edu/%7Epogge/Ast162/Unit2/sunshine.html III. Stellar evolution- the war between gravity and pressure- gravity wins As your book so eloquently states, gases behave differently from bricks. When a brick loses energy it simply cools off. When a self-gravitating gas loses energy, it can't hold itself up, changes its structure, and heats up! So a brick losing energy cools off, a star losing energy heats up! This seemingly weird property of self-gravitating gases is what allows stars to defeat gravity for a while. All of stellar evolution can be thought of as the war/balance between gravity and some outward pressure. There are times in the evolution of a star, like when the gas cloud is collapsing to become a star, when there is no way to resist gravity and the star is forced to rapidly change its structure. There are times, like on the main sequence, when nuclear fusion replaces the energy leaking out of the star, so that the structure of the star changes very very slowly. There is no way to turn gravity off! a) pre-main-sequence evolution A gas cloud starts to collapse (enough material gets assembled in one place, an exploding star gives a gas cloud a kick, that sort of thing). It's giving off light! As it collapses it gets hotter and hotter, eventually growing hot enough in the core to begin nuclear fusion. But while it's collapsing, it's big and cool, and enshrouded in gas and dust. So it's SORTOF LIKE a red giant, and it's certainly red and cool and luminous. Since it's surrounded by dust, it's best seen in the infrared (that's why we just launched the SIRTF spacecraft, remember the homework problem?) or in the radio part of the spectrum. Remember my discussion of sunsets and dirty windshields? So yes, the star shines, and can be very bright, even without nuclear fusion. It just can't last a long time making energy by converting gravitational potential energy into heat and light. (Remember Kelvin-Helmholtz?) You likely will find it useful to look at "several pages on stellar evolution" in the Sept 30 FIGURES area. And of course, this huge collapsing gas cloud starts to spin faster and faster from conservation of angular momentum. Remember the demonstration of us as Olympic figure skaters? b) main-sequence evolution Once fusion starts, it provides the energy source to replace the energy leaking out of the star. So the structure of the star doesn't have to change to make up this energy loss (or at least it changes very slowly!). So the dominant thing to remember about the main-sequence portion of stellar evolution is that the star is pretty darn stable. And yet it is slowly changing. The fusion reaction 4H --> 1 He + energy is turning 4 gas particles into one. Well, the perfect gas law can be written P is proptional to nT/V. But now there's less n! So there's less pressure. So the core has to readjust its strcture (shrink a bit). So in fact, over the main sequence lifetime of the Sun, its luminosity will approximately double. But that's a small effect over 10 billion years. The sun will get hundreds of times brighter when it becomes a red giant. So, relative stability reigns until there's not enough hydrogen down in the core where it's hot enough to fuse hydrogen. There's no way to get hydrogen from the cool part of the star down into the hot part. So fusion ends, and the star has no way to fight gravity so its structure starts to change rapidly. c) On the way to becoming a red giant. At this point it's easiest to think of the star as a 2-component object, the core and the envelope. We've already seen what's happening to the core after hydrogen "burning" ends. The core starts to shrink and heat up. As the core shrinks and heats up, it's depositing more photons into the envelope. Well, the envelope was in equilibrium already, so this addition of photons pushes it out of equilbrium, so it has to readjust its structure. Plus, photons carry along a "push". When a photons is absorbed, the electron of the atom in question jumps one or more energy levels. But the atom is also given a kick. So photons can also provide a pressure. More about that later. So, again seemingly paradoxically, the core contracts and the envelope expands. The expanding envelope cools off. But it's gotten bigger. So we end up with a large, cool, luminous envelope, a red giant. d) red giant At around this same time, as the star is rapidly on the way to becoming a red giant, a shell source of hydrogen can ignite. Because of the hot core, it's now possible to heat up some of the unburned layers of hydrogen to the fusion temperature. So here's a new source of energy, at least for a while. This shell source often burns unstably as the star continues to readjust its structure. Finally, the core is hot and dense enough that Helium can fuse. The reaction tuns out to be 3 heliums make one carbon plus energy. So at this point, the star is again rather like a main sequence star. There's fusion in the core, which allows the star to resist gravity. But this time it's helium fusion at a vastly higher temperature. So this fusion ends quite quickly because the rate of fusion is an incredibly large power of the temperature (for hydrogen it was T**8, for helium it's T**20 or so, if I'm remembering right). e) Low mass stars versus high mass stars We can describe the evolution of all stars in the same generic way. Gravity versus fusion. High mass stars can undergo more fusion reactions than will low mass stars, because we can make the center of the star hotter and still have the gas behave fairly normally. So low mass stars, like the Sun, will only undergo H-->He and He-->C, and that's all, no more fusion is possible. High mass stars can continue to fuse elements, with the highest mass stars able to fuse elements all the way up to Iron. Remember that iron is the most tightly bound atomic nucleus, so to fuse things heavier than iron sucks up energy rather than creating energy. So iron is the endpoint of massive star normal evolution. f) Low mass stars Well, we told you that the rule was: if there's no source of energy the gas must shrink and heat up. So what happens when a low mass star is done with being a helium burner? The core starts to shrink and heat up. But before the core can get hot enough to burn Carbon, something else happens to stabilize the star FOREVER. This really hot but really dense gas in the core of a low mass star has its electrons so tightly packed together that the electrons resist getting any closer. This state of matter is called DEGENERATE MATTER. Degenerate matter is something like a solid, but it is still a gas. the atomic nuclei are still behaving like a gas, but the electrons are behaving something like a solid. In any case, if you squeeze on a degenerate gas, it will not get any smaller (that's a bit of a lie, but not a big one). So this degenerate core resists gravity. This core is now more like a brick than a gas, and as it loses energy it will stay the same size but will cool off. This core is quite tiny, and for a one solar mass main sequence star contains about 0.6 solar masses of material. So we have an 8000 mile degenerate gas, with densities a million times or more the density of water. We have roughly one solar mass packed into something the size of the earth! This is a white dwarf star. So all "low mass' stars make white dwarfs. We'll talk on Thursday about what happens to white dwarfs and what happens to low mass stars, but we'll examine you on what happens to white dwarfs on exam 2. So up to and including the creation of white dwarfs is legal for exam 1. Exam 2 material includes the stuff at the very end of Sept 30's class, namely, that white dwarfs of different masses have different sizes, and that there's an upper mass limit to white dwarfs. g) Mass loss A normal main sequence star like the Sun actually loses a minute amount of mass all the time. It's called THE SOLAR WIND and is a wind of (mostly) hydrogen particles. We have collected solar wind particles from spacecraft orbiting earth! Sometimes the solar wind gets stronger when there's a "surface storm", a flare, on the Sun [we didn't talk about this]. During one of these storms, the solar wind can get so strong that it endangers astronauts, and it can get so strong that it compresses the Earth's magnetic field, disturbing communications, shutting down satellites, that sort of thing. The more luminous a main sequence star is, the more strong is this normal mass loss. Part of the reason for this mass loss is the radiation pressure we've already talked about. Well, if you try to make a really massive star, the radiation pressure can get so large that the star refuses to form, or tears itself apart. In the red giant phases, mass loss is more extreme for a couple of reasons. First, the typical atom in the star is very far from its center. So gravity isn't holding onto it as tightly as it did when the star was a main sequence star. So pushing it away is easier. Second, there are these [relatively minor] pulses of fusion from the shell burning. These "burps" give a good kick to the outer layers of the star, and the outer layers drift away. Eventually these outer layers drift so far away that they don't really belong to the star anymore, and join the "interstellar medium." But there's a beautiful intermediate step... h) Planetary nebulae There's a stage when the core of the star is a very hot white dwarf, and the envelope is far away "but not too far away". The photons from the white dwarf are absorbed by this envelope of [mostly] hydrogen, and are then reemitted. This setup is exactly the same one that you had in the spectroscopy lab! You have a tube of gas that got lots of energy from electricity and was not reemitting it as light. You saw that it could be very bright. In the case of a planetary nebula (an unfortunate name kept for historical reasons... these objects have nothing to do with planets), the energy input is the photons from the white dwarf, and the hydrogen cloud glows just like our discharge tubes! I showed you pictures of planetary nebulae yesterday, there's a link in the Figures section of the website, check it out. i) Massive stars There are a couple of qualitative differences between massive star evolution and low mass evolution, even though the basic rules are identical. First, massive stars don't develop degenerate cores till much farther along in their evolution, if at all (we didn't really explain why this is the case, though I think your book does, but it's a subtle point that isn't too important for Astro 203). Second, they have many more cycles of fusing ever heavier elements than do the low mass stars. We'll be talking a lot about massive stars in this course because most of the topics in the book, supernovae and the like, have to do with massive stars. So, much more about massive stars later.