 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to continue talking about the Sun, specifically the solar interior. We've looked at how the energy is generated, but now we want to see how we understand it and look at the theory and observation of what we have seen and understand for the solar interior. So how do we model the interior of the Sun? Well, done properly we use the equations of stellar structure, what you're shown here. No, you don't need to know these from my class, but we want to know the concepts of what we're doing with this. So yes, this is a set of differential equations and we can solve these to determine what the things like the pressure, mass, luminosity and temperature are at every point inside the Sun. So how can we do this? Well, it's a computer model. You put in your estimates for what things are like at the center of the Sun, and then you calculate, you integrate outward to the surface. And then you find out, because we can observe the properties at the surface, we know what the mass of the Sun is, we know what the luminosity and the surface temperature of the Sun are. So if our initial assumptions are incorrect, then we will end up with numbers at the surface that are not matching the Sun and then we make modifications as we do in the scientific method. So what else has happened? And then we repeat the process. So we'll make some adjustments. Maybe it's a little warmer or a little denser at the core. And we can make those adjustments and run the models again until we find models that work and match the exterior visible features of the Sun that we know, we know those properties. So what do we know about the Sun? Well, we also know the Sun is made of a plasma, which means that the atoms are ionized and have electrons removed. By the time you get down to the center, everything is ionized. There are no electrons attached to any atoms, regardless of what atom they are. And it behaves like a hot gas. It has no solid, no liquid. It is completely a hot gas because of the incredibly high temperatures that exist. We also know that the Sun has been stable for billions of years. How do we know this? Well, we're still here. If the Sun were changing much in terms of temperature, life on Earth would not be able to survive. If you recall the Stefan Boltzmann Law, the energy output of a star depends on the fourth power of the temperature. So a slight change in temperature, either up or down, will have a significant effect on the energy output and would make Earth too hot or too cold. So we know that the Sun has been in a very stable range for billions of years because life still exists here. This is done by what we call hydrostatic equilibrium. And that is where pressure and gravity are balanced that keep the Sun in this equilibrium. So for any point in the Sun, gravity is trying to pull objects down to the center. There's a pressure from the interior, from the energy generation that pushes outward, and these two balance exactly. If they were not, the Sun would either expand or contract. We will see what happens when it gets out of hydrostatic equilibrium when we look at the evolution of stars later on. So we know that the Sun has been stable. So the surface temperature, as I said, the surface temperature of the Sun remains essentially constant. Any major change would mean life, no life on Earth. We know from previously we discussed how energy is transferred. We transfer energy by convection in the outer portion of the Sun and radiation in the interior portion of the Sun. So we transport energy in two ways, convection and radiation. Now, what we can do is take all of this information and try to put it together to get a model of the Sun. And what we know is that the energy is generated only at the core. So only in this very central region are the temperatures and pressures significant enough for energy generation for nuclear fusion by the proton-proton chain to occur. The energy moves outward first by radiation, then by convection until it reaches the photosphere and then, of course, travels through the universe by radiative radiation. So any model of the interior needs to match what we see on the photosphere of the Sun. So if we cannot match that, then something is wrong with our models. So what kind of observations can we make that will help us with this? Well, we can see pulsations in the Sun. We call this helioseismology. Seismology on the Earth is the study of earthquakes, but the Sun does pulse. It moves in and out. And we can see the red and blue here are red shifts and blue shifts. Now, how this varies depends on the interior structure of the Sun. So we can use this to adjust models. We can see what the models predict in terms of pulsations. And if they're not predicting what is observed, then we know we need to make modifications of those models. And we work back again to find out more about the Sun. So we put together the observations that we make along with our understanding of the physics to be able to model our Sun. Now, the other thing we look at are the neutrinos. If you recall, we talked about those when we talked about the proton-proton chain. They are formed in the first step of the proton-proton chain. Now, first of all, what are neutrinos? Well, they are weakly interacting particles. Weakly interacting means they don't interact through gravity or the electromagnetic force as ordinary matter does. They don't have any charge and they don't interact through gravity. They're not affected by that. They can travel through the entire Sun without interacting. Here we see, for example, a photon trying to get out and it constantly is absorbed and re-emitted and sometimes it goes one direction and then the other and it slowly makes its way out. That may take thousands or tens of thousands of years. Whereas the neutrino zips right out through the Sun, traveling it close to the speed of light reaching the Earth if it's heading in that direction in about eight minutes. So the key is we don't see the photons for thousands of years. The neutrinos come out immediately. If we can detect these neutrinos, it can give us some insight into what is going on at the center of the Sun right now. So what is this problem? Well, the solar neutrino problem that we had was that we weren't detecting the right number of neutrinos. How can we detect things that don't interact? Well, say one in a billion billion neutrinos will interact with the chlorine atom. So they do interact through the weak force and it happens very rarely, but it can happen. So most of those will pass right through you. They're passing right through us right now as I speak. And what it does when it does interact, it converts to a radioactive argon nucleus. That decays giving off light. Well, light can be detected. So that gives us a direct look into the interior of the Sun. Now, while I say one in a billion billion, it's actually a probability. Each one has some very tiny probability of interacting with that chlorine atom. We can use our understanding of quantum mechanics and probabilities to then determine how many neutrinos the Sun would be giving off and what fraction of those we should be detecting. So we built neutrino detectors such as the one shown here, which are large tanks of cleaning fluid, which contain chlorine. And they're put in mines well below the Earth's surface. Note how it's very well shielded here so that cosmic rays do not give us false detections because a cosmic ray could also interact with that chlorine atom but cosmic rays are easily shielded from when you have to go through lots of Earth. So they're shielded that way and therefore we should be detecting only the neutrinos which can go right through the Earth without any problem. And the problem that we had was that we were only detecting one-third of the number of neutrinos that the models of the solar interior were predicting. So if we predicted, say, 100 to be detected, we were detecting around 30, about one-third of the amount. Now that's a pretty significant amount, a pretty significant difference in what we're doing. So that tells us something is wrong. So what could be wrong? Well, what could be wrong? Well, is the solar model wrong? Well, that's very possible because if the temperatures were cooler than we predict, that would mean fewer neutrinos which would fit with the observations. But how do we reconcile this? How do we make this fit with the models because they seem to work for everything else? The other thing is, do we not understand the neutrino? Could we not understand the neutrino? We didn't know at the time whether the neutrino had mass or not. So if the neutrino had a tiny amount of mass, it may oscillate between what are called the different flavors. There are three flavors of neutrinos. Only the one, what we call the electron neutrino, is what could be detected. That was the one that might interact with chlorine. These other flavors would not be detected. So we would need different methods to be able to detect them. If the neutrino oscillates between three flavors by the time it gets from the Sun to Earth, it's now split between these three different types. One third are the original type, one third are the second type, and one third are the third type. So that would again help us with our explanation. So what was found? Well, in 1998 we got the first evidence of neutrino oscillation that was seen and then clear evidence a couple years later. So in 2001, and we find that neutrinos can indeed oscillate between these three flavors. And that during the trip from the Sun to Earth, two-thirds of those produced have changed into another type. So we should only be detecting one-third of the amount, which is correct. We are now detecting the right amount that we expect to be able to detect. We're detecting the correct number, confirming our models of the solar interior. So let's go ahead and finish up with our summary. And what we looked at is that we used the models to understand the interior of the Sun, and we used the observations, different types of observations to refine these models and make them better. And we looked at one example, which was the solar neutrino problem, which the resolution of confirmed our solar model and changed our understanding of the neutrino. So that concludes this lecture on the solar interior theory and observation. We'll be back again next time for another topic in astronomy. So until then, have a great day, everyone, and I will see you in class.