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The Sun s Source of Energy E= m c2 AND STARS! Announcements q Homework # 5 starts on Thursday, Nov 3th. It is due on Tue, Nov 15th q Exam # 2 will take place on Tuesday, November 8th: q Please remember to bring your ID. No ID = No Exam q Please remember to bring a pencil # 2 q More infos (including lectures and units which it is based on) on www.astro.umass.edu/ ~calzetti/astro100 Assigned Reading q Unit 50, 52.1-2-3, 54.1-2-3, 55 Goals for Today q Investigate how our Sun produces its energy q To understand how the Sun does not implode under its own weight. q To begin a study of stars – what they’re made of, what kinds are out there, how similar or dissimilar they are from the Sun, how they are born, and how they die The Sun s Energy Source is in its Core The Core is where all the action is. n n n n The core is the only place in the Sun where the temperature and density are high enough to support nuclear fusion. Every second, about 600 million tons of Hydrogen are fused into 596 million tons of helium. The remaining mass (4 million tons) is converted to energy in line with Einstein’s formula E = mc2 The Sun is about 5 billions years old, and has used up about 1/2 of its `fuel’. Survey Question The energy emitted by the Sun is produced 1) in a small region at the very center of the Sun. 2) uniformly throughout the entire Sun. 3) throughout the entire Sun but more in the center than at the surface. 4) from radioactive elements created in the Big Bang. Nuclear Fusion in the Sun n Hydrogen is constantly being transformed into helium in the Sun’s core. Energy is produced because 1 nucleus of He weights less than 4 protons. One slide on Neutrinos - Neutrinos are generated in the P-P chain in the core of the Sun - Neutrinos - are thought to only have a tiny mass - travel at the speed of light - only weakly interact with matter - Neutrinos are the only thing that comes directly out of the core of the Sun without running into other things along the way. There are trillions of neutrinos passing through you right this instant! The first two people to measure solar neutrinos won the 2002 Nobel Prize in physics (Ray Davis, Masatoshi Koshiba) An aside about nuclear fusion as a viable energy source A few key points about the P-P Chain: • It is a “clean” form of energy production. n Put 4 protons (Hydrogen) in and get one Helium and some energy back out. • Given fuel (in the form of Hydrogen) it is a self-sustaining reaction. • However, it requires *very* high temperatures (107 K), and large masses of Hydrogen Fusion is highly improbable! n n n n Gravity increases the temperature in the Sun, which enables protons to overcome the Coulomb repulsion and have the strong force take hold While two protons collide, one must be transformed into a neutron, which requires the weak force For each proton, this happens once every billion of years. Without the `weak force bottleneck’, stars would burn too fast or too slow, and maybe prevent life on planets. Nuclear Fusion vs. Fission Survey Question The chemical composition of the Sun 3 billion years ago was different from what it is now in that it had 1) 2) 3) 4) more hydrogen and more helium less helium and less hydrogen more helium and less hydrogen more hydrogen and less helium Nuclear Fusion and the Sun n n n n Nuclear fusion produces energy The energy heats the gas in the Sun `Heating of the gas’ means that the gas particles (electrons and protons) are accelerated and have more kinetic energy (called thermal pressure) The kinetic energy of the gas particles compensates for the Sun’s self-gravity Hydrostatic Equilibrium in the Sun Thermal Pressure Gravitational Contraction What is Hydrostatic Equilibrium? n n A star is a ball of gas held in hydrostatic equilibrium, which is a perfect balancing between its own self-gravity and the thermal pressure of the hot gas, cooling from center to the surface The energy to produce the thermal pressure comes from nuclear fusion reactions at the center of the Sun What is Thermal Pressure? n n n Pressure in a gas arises from collisions of atoms and molecules. The higher the temperature, the faster the atoms/molecules in the object are (T ~ v2), thus more energetic collisions More energetic collisions result in higher pressure Think of a hot-air balloon. To keep it inflated (high pressure) you need to keep the air inside it heated. How does a star hold itself?! This balance between weight and pressure is called hydrostatic equilibrium. The pressure is provided by the motions of the very hot gas that makes the Sun. To keep the gas hot, the Sun has to produce energy in its core, and it needs to be hotter in the center. The Sun's core, for example, has a temperature of about 15 million K. My House’s Thermostat Air temperature inside drops below the set point of the thermostat Electrical signal triggers ignition of furnace Furnace shuts off Furnace burns oil/gas and generates heat Air warms thermostat until electrical signal is shut off Radiators transfer energy from water to air Heat is absorbed by water running near furnace causing water temperature to rise Hot water is circulated throughout house The Solar Thermostat Outward thermal pressure of core is larger than inward gravitational pressure Core expands Nuclear fusion rate rises dramatically Expanding core cools Contracting core heats up Core contracts Nuclear fusion rate drops dramatically Outward thermal pressure of core drops (and becomes smaller than inward grav. pressure) A Balancing Act n n If the Sun contracts, the temperature goes up, the rate of fusion increases, the thermal pressure increases, and the Sun re-expands. If the Sun expands too much, the temperature drops, the rate of fusion drops, the pressure drops, and the Sun contracts. Sunshine: Good or Bad? The Sun’s need to compensate for the contraction of self-gravity by producing thermal pressure means: q It needs to maintain the thermal pressure, by keeping its gas hot q However, the energy lost via radiation (sunshine) needs to be replaced (bad for the sun, good for us) q The replacement happens in the center of the Sun, via nuclear fusion q As energy flows from hot to cold, the center of the Sun needs to be hotter than its `surface’ (the gaseous photosphere). q Some evidence…. The Sun is hotter towards the center: the limb is slightly darker Survey Question Suppose you could magically inject, all at once, a large amount of energy into the core of the Sun. What would happen? 1) The Sun would contract as the core heated up. 2) The Sun would contract as the energy became gravitational potential energy and find new equilibrium with the grav. pressure. The Sun would end up being smaller in size. 3) The injected energy would heat the core, causing the Sun to expand. The energy would eventually be radiated off into space and the Sun would return to normal size. 4) The injected energy would heat the core, causing the Sun to expand. The Sun would find a new equilibrium with the gravitational pressure and end up being larger in size. This ends our trip through the Sun However, the Sun is a star like many…. Let’s expand our horizons: Stars n All stars (including our Sun) are made up of the same elements, in roughly the same proportions: other – Hydrogen (~70%) – Helium (~28%) – other elements (~2%) n All helium hydrogen stars have nuclear fusion going on in their cores – just like our Sun. n There are four principal characteristics of a star: – Luminosity – Surface Temperature – Size – Mass Three of them (luminosity, size, and mass) require knowledge of the distance of the star from us. How do we measure the distance to a star? We need it to get: luminosities, radii, masses Parallax (a.k.a. triangulation) For getting distances Using triangulation requires: 1. A baseline (distance over which observer moves). 2. Measurement of angles to the object from each end of the baseline. 3. Mathematical relationships between angles and lengths of sides of triangle. This is called trigonometry. Stellar Parallax The measurements are taken six months apart. The baseline is the diameter of the Earth’s orbit. What is seen What is seen The ½ of the angle between the current location and the 6-month location is called the stellar parallax = P. Parallax Distance 1 (AU) D (in Parsecs) = P (in arcseconds) P, the parallax angle, is measured in arcseconds 60 arcseconds = 1 arcminute 60 arcminutes = 1 degree There are 3600 arcseconds in a degree The larger P, the smaller D The smaller P, the larger D 1 parsec = 3.26 light years = 3.086x1016 meter Parallax would be easier to measure if 1) the stars were further away. 2) Earth's orbit were larger. 3) Earth moved backwards along its orbit. 4) none of these. Parallax would be easier to measure if 1) the stars were further away. 2) Earth's orbit were larger. 3) Earth moved backwards along its orbit. 4) none of these. Star A has a parallax angle that is twice that of Star B. What is the relationship between their distances? n Star A is closer than Star B n Star B is closer than Star A n The stars are at the same distance n Not enough information is given Another Method to Measure Distances n If you can `identify’ a star, i.e., determine its luminosity (for instance we observe another star in the distance which has the same color and spectrum of our Sun, we may infer it has to have the same luminosity as the Sun), we can derive a distance from the Inverse Square Law: d= √L / 4 π B L /(4 "B) !