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ASTR 209
Ian Lovatt

Page 1 of 8 Astr 209 Lecture 3d October 2 2010 The Solar Model, solar wind, sunspots, the corona The Solar Model This is a mathematical model (not a plastic scale-model to put on your desk). You start with the idea that the Sun is a big ball of hydrogen and helium atoms (i.e. you know what the Sun is composed of). You know its mass (using a combination of Kepler’s Third Law, and Newton’s Law of Gravity). The gas is in equilibrium: I will say more about equilibrium later, but for now this means that the core is hot enough to keep the pressure high enough to prevent the Sun from shrinking under its own weight. Mass and composition are the details you put into the model. The Sun is hot enough (except at the surface) for the H and He atoms to move fast enough, and collide violently enough to knock the electrons of f the H and He atoms. Almost all of the Sun is a PLASMA, a soup of positively-charged nuclei, and negatively charged electrons. Note: this use of the word “plasma” has nothing to do with blood, although the word in both cases refers to a particular type of fluid. Plasma in our context is a “state of matter”. For instance, ice is the solid state of water. If you heat ice, it changes to liquid water. If you heat liquid water, it boils, changing to steam, the vapor-phase of water. If you heat steam, eventually the atomic collisions are violent enough to IONIZE the atoms, producing a plasma of positively charged nuclei, and negatively charged electrons. If you slam nuclei together at speeds close enough to light-speed (in a particle accelerator), you find the constituents of the nuclei behave like a fluid, for a very short time interval (something like 10 -24seconds) and over a very short distance (approximately the size of a nucleus – about 10 -15m). The second part of the model involves calculations. It turns out that the Sun’s radius in this state is controlled by the number of electrons in the Sun. (This involves “Heisenberg’s Uncertainty Principle, which I will discuss when we get to white dwarfs and neutron stars. For now, I will claim that you can calculate the Sun’s radius, knowing its mass and its composition!) Page 2 of 8 If you know the radius, you can calculate the pressure at various levels inside the Sun, due to the gas above that particular level. You can use the ideal-gas law to calculate the temperature at the Sun’s core. If you know the temperature, and some nuclear physics, you can calculate the rate at which H nuclei should fuse to become He. This means you can also calculate the rate at which the Sun radiates neutrinos. Combine the fusion rate with a knowledge of how energy is transported through a plasma, and you can calculate the surface temperature, and the rate at which the Sun radiates energy (luminosity). The third part of the model involves comparing predictions to measurements. So far, everything that we can confidently calculate (radius, surface temperature, neutrino rate, etc) turns out to have the values we predict. Conclusion? As far as energy production and radiation go, we think we understand the Sun. Here are some predictions of the solar model that we have not yet been able to verify. Since the predictions we CAN check have been verified, we have confidence in these predictions. • By studying the vibrations of the Sun’s surface, we can calculate the temperature and density at various depths below the surface. In a similar way, we can learn about the Earth’s interior by studying earthquakes. • Previously, we looked at a crude prediction of the Sun’s lifespan. • The Sun is in a finely-tuned GRAVITATIONAL EQUILIBRIUM (or hydrostatic equilibrium. Imagine that the temperature in the core increases by a small amount. The fusion rate is very sensitive to temperature, so the fusion rate increases. This increases the core’s temperature even more; the nuclei are flying around faster than before, and the collisions with the layer just outside the core are more violent. This is another way of saying that the core’s pressure increases. The core expands, pushing the outer layers even further out. But this act of pushing outer layers requires energy, which comes from the kinetic energy of the gas nuclei. So as the core expands, it cools. The fusion rate decreases, and the core’s pressure decreases. Now the outer layer squeezes and shrinks the core. But as the core’s pressure increases, its temperature increases, and we are back to starting point. It turns out that the Sun does NOT oscillate noticeably [the solar constant varies by ± 0.1% ], although the luminosity a typical Sun-like [G-type] star varies by about ± 4% . It also turns out the when stars more massive than the Sun run out of hydrogen to fuse in the core, they DO oscillate in size and luminosity. These are called variable stars; we will discuss them later. Page 3 of 8 • We predict the Sun has gradually becoming more luminous (brighter) over its lifespan. In particular, we thank that the Sun now is about 30% brighter now than when it first became a star and began fusing hydrogen. Every time four hydrogen nuclei fuse, to become one helium nucleus, the number of nuclei decreases. The pressure in the core shrinks ever so slightly. (Similarly, a bicycle tire’s pressure decreases if you remove some of the air [oxygen and nitrogen molecules]). The outer layers squeeze and shrink the core, and the core’s temperature rises. The fusion rate then increases slightly. Energy is released more rapidly in the core, and the Sun’s luminosity increases. This has consequences for life in the Solar System. The Earth is now a little too far from the Sun for liquid water to form, in an atmosphere with no carbon dioxide. (The Moon’s temperatures are below 273 kelvins.). With a little bit of carbon dioxide [a greenhouse gas], we are in the Sun’s so-called habitable zone. But this zone gradually moves outward from the Sun as it gets warmer. Will the habitable zone one day in the DISTANT future encompass Mars? Might life develop on Mars? Maybe Mars’s atmosphere long ago was thick enough, and had enough carbon dioxide, for liquid water, and perhaps life, to form The solar model has three parts: input (mass and composition), calculations, and testable, falsifiable predictions. the Sun’s corona Observations 1. solar eclipse of Aug 7, 1869, Harkness and Young discovered a feeble emission line in the green part of the spectrum. Nobody could match this line with an emission line produced in a lab. By the 1890s, the line was being linked to a hypothetical substance not then discovered on Earth, which was given the name co
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