Sept 23 After taking a week off to learn about atomic spectra and to work with atomic spectra, we're now back learning about the structure and energy sources of stars. I. Structure We reminded ourselves that stars are hot at their centers because a self-gravitating gas in equilibrium must have a high pressure and temperature at the center. If it doesn't, it can't hold itself up against gravity, and will not be in equilibrium. We reminded ourselves that heat flows from a hotter place to a cooler place, so photons are constantly leaking out of a star. This loss of energy causes the star to change its structure. [We'll later say that nuclear fusion in the core essentially replaces this energy, so the structure of the star stays relatively constant until there's no more hydrogen in the center of the star.] We reminded ourselves that the center of the Sun is a perfect place for nuclear fusion: 1) It's hot there. In fact it's hot enough for nuclear fusion! 2) The dominant particle at the center of the Sun is the lightest element, hydrogen, which is the easiest to fuse. 3) Most of the mass of the star is available to be used as a container for the fusion factory at the center. On Earth, one of the problems with making a power plant out of a fusion reactor is that there is no container capable of withstanding temperatures of 10 million degrees! The Sun has a natural such container. Let's say it again one more time... THE SUN IS HOT IN ITS CENTER BECAUSE IT HAS NO CHOICE. That's how self-gravitating gases hold themselves up against gravity. THE SUN IS EVOLVING BECAUSE IT'S LEAKING PHOTONS OUT OF ITS EXTERIOR. FUSION SLOWS THIS EVOLUTION FOR A WHILE. EVEN IF FUSION WERE NOT THE DOMINANT SOURCE OF ENERGY IN THE SUN, FUSION MUST BE GOING ON BECAUSE IT'S HOT IN THE CENTER< DENSE IN THE CENTER, AND FULL OF HYDROGEN IN THE CENTER. II. How do we make energy? We reminded ourselves that breaking chemical bonds, as in burning kerosene or trees, does not create enough energy to power the Sun for more than about 100,000 years. So if the Sun is older than 100,000 years... We talked about POTENTIAL ENERGY and KINETIC ENERGY, and gave examples of water at the top and bottom of a waterfall. We also mentioned conservation laws (which are described in your book), and pointed out that for this waterfall example, the sum of potential and kinetic energy, BOTH AT THE TOP AND BOTTOM OF THE WATERFALL, is constant. We then talked about the concept named KELVIN-HELMHOLTZ CONTRACTION. If you allowed the Sun to shrink a little bit, the potential energy stored up in the original configuration is converted to heat and light. So by shrinking the Sun, I can make light. Over the 3000 or so years of written history, this effect would be immeasurable. So Kelvin-Helmholtz contraction is a way to make energy, and in fact stars make energy this way at some times in their evolution, but they don't do that on the main sequence. If they did, all 10 billion year old 1 solar mass stars would be substantially smaller than all 1 billion year old 1 solar mass stars, and they aren't! Luckily for humans' understanding of stars, Albert Einstein provided the clues that astronomers and physicists used to realize that fusion goes on in the cores of stars. Let's examine the simplest fusion reaction, called the proton-proton chain. 1 1 2 + H + H ==> H + e + nu 1 1 1 Superscripts count the number of protons PLUS neutrons in the nucleus. Subscripts count the number of protons. The number of protons determines the name of the element. e-plus is a positively charged electron, or positron. It's the antiparticle of an electron. If you put an electron and an antielectron close together, they annihilate each other, turning into pure energy. nu is the Greek letter "nu", the neutrino. More about neutrinos later. 2 H is "heavy hydrogen" or deuterium. It's an isotope of hydrogen, pretty much, but not identical, chemical properties So, in words, Hydrogen plus Hydrogen makes deuterium plus a positron plus a neutrino. Ok, step 2 2 1 3 H + H ==> He + gamma 1 1 2 Deuterium plus Hydrogen makes light helium ("helium-3") plus a gamma ray. A gamma ray is an energetic form of light! Then, step 3 3 3 4 1 1 He + He ==> He + H + H 2 2 2 1 1 He-3 plus He-3 makes regular He plus two regular Hydrogens. Adding it all up, 4 Hydrogens fuse together to make 1 Helium, plus light, plus a couple of particles. The light is important, because that's what we need. The positron runs into an electron almost instantly and makes even more light. The neutrino escapes the star, and we'll talk about it more, later. If you look at these equations carefully, you can see that the amount of positive charge is conserved. So here's another conservation law, discussed in your book, that can help physics students predict what nature's going to do. Energy is also conserved. BUT WAIT, I just said energy is conserved, and that we made a lot of energy in the form of gamma rays. What's the deal? Well, 4 Hydrogens weigh 0.7% more than one Helium. Einstein taught us that 2 E = mc (E equals m c-squared) m is mass, E is energy, c is the speed of light. Since c-squared is a really big number, a little bit of mass can be converted into a lot of energy. This is one of the secrets (at least till the 1930s) of atom bombs, and is one of the secrets of stars. So how much Hydrogen do we have to fuse to make 1 Solar Luminosity? [There are a few pages on the website about this!] Every second, 600 million tons of H gets turned into He. 0.7 percent of that 600 million tons vanishes, or 4 million tons per second gets converted into energy. These seem like, and are, really big numbers. But the Sun has 10**27 tons of fuel, or enough fuel to last 10**27/10**6 seconds, or 10**21 seconds or 10**13 years. Let me note that I was really sloppy with numbers here, dropping huge factors (like turning 4x10**6 into 10**6). But the point is that fusion provides enough energy to allow the Sun to be as old as we know it is. So we can sleep well tonight. If you do the numbers right, you get that the Sun can survive as a main-sequence star for more than 10**10 (10 billion) years. III. So can we understand the main sequence now? What have we learned today? 1) The equilibrium between gravity and gas pressure provides a hot central core for a star. It's not too much of a leap, even without doing the math, to realize that a more massive star is going to have a hotter core, because there's more material to hold up. So, more massive main sequence stars have hotter cores. More heat needs to leak out, the more massive star will be more luminous. 2) It turns out that fusion is incredibly temperature sensitive. Something like T**8, temperature to the 8th power. So a small change in central temperature makes a big change in emitted light. 3) So all main sequence stars do indeed have something in common. They have fusion going on in their cores. The huge range in luminosities from the most massive main sequence stars to the least massive now makes sense. It all has to do with the changes in the central temperature. 4) So as long as we can supply this huge amount of energy to the star, the star's structure doesn't have to change. If we can't supply this energy, the star's structure will change rapidly. IV. Finally, atomic energy We've already talked about fusion. In general, when you fuse two light elements to make a heavier element, you release energy. "Just as gases give up gravitational potential energy when they come together to form a star, so particles release energy in uniting to form an atomic nucleus." This process works up to Iron, which is the most tightly bound atom. So stars can create energy from fusion until they try to make something heavier than iron, then they're in deep yogurt. Elements more massive than iron (more protons in nucleus) actually are less bound then iron. You can get a handle on it by imagining how hard it must be for the strong force to keep all of those protons together when they really want to fly apart because of electrical repulsion. So, breaking apart a heavy atom, called FISSION, releases energy, too. Fission is the process that releases energy in an "atom bomb", the kind of bomb that was dropped on Hiroshima and Nagasaki at the end of WW II. A fusion bomb is called a "hydrogen bomb". To show you how much more energy is stored in the nucleus of an atom than in a chemical bond, we measure the output of a hydrogen bomb in units of "megatons of TNT." TNT (something liKe dynamite) makes energy from a chemical reaction. A hydrogen bomb, pretty much the size of a desk or two, makes enough energy that you'd need megatons, millions of tons, of dynamite, to have the equivalent. You've seen what a few hundred pounds of explosives does, say in Iraq truck bombings, or in the Oklahoma City bombing. The energy transferred from the jet plane to the World Trade Center building was about one kiloton, or 1000 tons of TNT. A typical hydrogen bomb in our arsenal is around 1 megaton, and we have around 12000 such bombs. So a typical hydrogen bomb contains 1000 times more energy than a jumbo jet filled with fuel crashing into a building at full speed. This amount of energy is why the Sun is capable of shining for 10 billion years!