8 March 2005AST 2010: Chapter 151 The Sun: A Nuclear Powerhouse

8 March 2005AST 2010: Chapter 152 Happy Sun

8 March 2005AST 2010: Chapter 153 Why Does the Sun Shine? The Sun gives off energy The energy must come from somewhere — there’s no free lunch Conservation of energy is a fundamental tenet of physics Where does the energy come from? Until the 20th century only 2 possibilities were known: Chemical reactions Gravity

8 March 2005AST 2010: Chapter 154 The Sun’s Energy Output How bright is the Sun? The Sun produces 4x10 26 watts The watt is the unit for the rate of energy use, commonly seen on light bulbs and appliances. Our largest power plants produce around 5 x 10 9 watts of power (5,000 megawatts) Sun’s power = 8 x of these power plants (10,000 trillion) Anyway you look at it, the Sun gives off a lot of energy

8 March 2005AST 2010: Chapter 155 Chemical Reactions What are chemical reactions? An example: Rearrange the atoms in molecules, as in 2H 2 + O 2  2H 2 O This reaction combines hydrogen and oxygen (gases) to produce water plus energy Reverse the process: 2H 2 O  2H 2 + O 2 By adding energy, we can dissociate water into hydrogen and oxygen The energy factor is often left out of chemical-reaction formulas, for convenience

8 March 2005AST 2010: Chapter 156 Is the Sun Powered by Chemical Reactions? If the Sun is powered by burning coal or oil, how long could its fuel last? Only a few thousand years! A process that uses fuel more efficiently is needed — something that gets more energy out of every kilogram of material

8 March 2005AST 2010: Chapter 157 Gravity Squeeze? Gravitational contraction: falling layers of the Sun's material compresses the Sun  heat energy Drop a book  noise! Gravitational potential energy turns into sound energy A contraction of 40 m per day would account for the Sun’s energy output Efficiency ~ 1/10,000 % Gravity could power the Sun for about 100 million years but the Sun is thought to be at least 4 billion years old! So gravity can't be the Sun's main energy source but it did help ignite the Sun when it formed

8 March 2005AST 2010: Chapter 158 Mass, Energy, and the Theory of Relativity To understand the way the Sun produces its energy, we need to learn a little about nuclear physics and the special theory of relativity Nuclear physics deals with the structure of the nuclei of atoms The special theory of relativity deals with the behavior of things moving at close to the speed of light

8 March 2005AST 2010: Chapter 159 Converting Mass to Energy E = mc 2 Out of the special theory of relativity comes the most famous equation in science: E = mc 2 This equation tells us that mass (m) is just another form of energy (E)! The c 2 is the square of the speed of light 1 gram of matter is equivalent to the energy obtained by burning 15,000 barrels of oil

8 March 2005AST 2010: Chapter 1510 …but there are rules We can’t simply convert atoms into energy We rearrange the protons and neutrons in nuclei to get a lower-mass configuration The difference between initial mass and final mass is converted to energy Chemical energy comes from rearranging atoms to configurations of lower energy (mass) Nuclear energy comes from rearranging nuclei to configurations of lower mass (energy) In each case, we get out the energy difference

8 March 2005AST 2010: Chapter 1511 Elementary Particles 5 particles play a fundamental role in the Sun Protons and neutrons make atomic nuclei Electrons orbit nuclei of atoms Photons are emitted by the Sun Neutrinos are also emitted Particle name Mass (MeV/c 2 ) Charge (e) Proton Neutron Electron0.511 Neutrino< Photon00

8 March 2005AST 2010: Chapter 1512 The Atomic Nucleus Two ways to rearrange nuclei and get energy: Fission It produces energy by breaking up massive nuclei like uranium into less massive nuclei like barium and krypton A-bombs, nuclear reactors Fission needs uranium-235 and plutonium-238 Problem: no uranium or plutonium in the Sun Fusion It produces energy by fusing light nuclei like hydrogen to make more massive nuclei like helium H-bomb The Sun has lots of Hydrogen!!

8 March 2005AST 2010: Chapter 1513 How Does Fusion Work? Nuclear fusion: a process by which two light nuclei combine to form a single larger nucleus However, nuclei are positively charged Like charges repel Two nuclei naturally repel each other and thus cannot fuse spontaneously For fusion, electrical repulsion must be “overcome” When two nuclei are very close, the strong nuclear force takes over and holds them together How do two nuclei get close enough?

8 March 2005AST 2010: Chapter 1514 Fusion needs fast moving nuclei Fast moving nuclei can overcome the repulsion They get a running start Lots of fast moving nuclei means high temperature The core of the Sun has a temperature of 15 million degrees kelvin Low speed High speed

8 March 2005AST 2010: Chapter 1515 Fusion Powers the Sun Temperatures in the cores of stars are estimated to be above the 8 million K needed to fuse hydrogen nuclei together Calculations have shown that the observed power output of the Sun is consistent with the power produced by the fusion of hydrogen nuclei The observed neutrinos from the Sun produced are expected as one of the byproducts of fusion reactions Hypothesize: all stars produce energy by nuclear fusion

8 March 2005AST 2010: Chapter 1516 Proton-Proton Chain Fuse two hydrogen ( H= 1 proton) to make deuterium ( 2 H= 1 proton+1 neutron), neutrino, and positron Fuse one deuterium and one hydrogen to make helium-3 ( 3 He= 1 proton+2 neutrons) and a gamma ray (energetic photon) Fuse two helium-3 to make helium-4 ( 4 He ) and two hydrogen

8 March 2005AST 2010: Chapter 1517 Why a Complicated Chain? Fusion would be simpler if four protons would collide simultaneously to make one helium nucleus That is simpler, but less likely rare for four objects to collide simultaneously with high enough energy chance of this happening are very, very small rate too slow to power the Sun The proton-proton chain: each step involves collision of two particles chance of two particles colliding and fusing is much higher so nature slowly builds up the helium nucleus

8 March 2005AST 2010: Chapter 1518 Fusion and Solar Structure Fusion occurs only in Sun's core This is the only place that is hot enough Heat from fusion determines the Sun's structure

8 March 2005AST 2010: Chapter 1519 Heat from Core Determines Sun's Size Force equilibrium Hydrostatic equilibrium: balance between thermal pressure from the hot core pushing outwards gravity squeezes the star collapse to the very center Nuclear-fusion rate is very sensitive to temperature A slight increase/decrease in temperature causes fusion rate to increase/decrease by a large amount

8 March 2005AST 2010: Chapter 1520 Gravity and Pressure Force equilibrium Newton's second law: F = ma Static equilibrium: no acceleration if forces on object balance Gravity tries to pull 1/4 pounder to center of the Earth Pressure from table opposes gravity Hydrostatic equilibrium in the Sun “Cloud of gas" (like 1/4 pounder) Gravity pulls cloud to the center Pressure from gas below opposes gravity Heat from fusion in the hot core increases pressure Energy output controls size of sun! pressure from table weight from gravity cloud pressure from hot gas weight from gravity

8 March 2005AST 2010: Chapter 1521 Temperature and Pressure Temperature corresponds to the random motion of atoms in a gas Pressure is the amount of force per unit area on piston from gas Generally pressure increases with increasing temperature

8 March 2005AST 2010: Chapter 1522 Balancing Fusion, Gravity, and Pressure If the fusion rate increases, then thermal pressure increases causing the star to expand star expands to a new point where gravity would balance the thermal pressure the expansion would reduce compression of the core the temperature in the core would drop the nuclear fusion rate would subsequently slow down the thermal pressure would then drop the star would shrink the temperature would rise again and the nuclear fusion rate would increase stability would be re-established between the nuclear reaction rates and the gravity compression

8 March 2005AST 2010: Chapter 1523 Hydrostatic Equilibrium The balance between pressure, heat from fusion, and gravity determines the Sun's size Big stars have cooler cores Small stars have hotter cores and, thus, are more compressed

8 March 2005AST 2010: Chapter 1524 Other Particles Helium is not the only product in the fusion of hydrogen Two other particles are produced Positrons Neutrinos

8 March 2005AST 2010: Chapter 1525 Gamma-Ray Propagation in the Sun The positrons quickly annihilate the electrons Photons produced in core of the Sun take about a million years to move to the surface This migration is slow because they scatter off the dense gas particles The photons move about only a centimeter between collisions In each collision, they transfer some of their energy to the gas particles As they reach the photosphere, gamma rays have become visible photons Because the photons have lost some energy in their journey through the Sun

8 March 2005AST 2010: Chapter 1526 Neutrinos These particles have no charge and are nearly massless They rarely interact with ordinary matter Neutrinos travel extremely fast at almost the speed of light if their mass is tiny Neutrinos pass from the core of the Sun to its surface in only two seconds They take less than 8.5 minutes to travel the distance from the Sun to the Earth

8 March 2005AST 2010: Chapter 1527 Neutrino Counting In principle We can use neutrino count at Earth as indicator of the Sun’s energy output The problem: Neutrinos have a very low probability of interacting with matter They could pass through a light year of lead and not be stopped by any of the lead atoms!

8 March 2005AST 2010: Chapter 1528 Neutrino Abundance The Sun produces a lot of neutrinos In one second several million billion neutrinos pass through your body Do you feel them? Not to worry! The neutrinos do not damage anything The great majority of neutrinos pass right through the entire Earth as if it weren’t there

8 March 2005AST 2010: Chapter 1529 Detecting Neutrinos Increase the odds of detecting neutrinos by using a LARGE amount of a material that reacts with neutrinos in a measurable way A chlorine isotope changes to a radioactive isotope of argon when hit by a neutrino A gallium isotope changes to a radioactive isotope of germanium Neutrinos can interact with protons and neutrons and produce an electron The electron can be detected

8 March 2005AST 2010: Chapter 1530 Neutrino Detectors Neutrino detectors use hundreds of thousands of liters of these materials in a container buried under many tens of meters of rock to shield the detectors from other energetic particles from space called cosmic rays Even the largest detectors can detect only a few neutrinos per day

8 March 2005AST 2010: Chapter 1531 Solar Neutrino Production (1) Number of neutrinos produced in the Sun is directly proportional to the number of nuclear reactions taking place in the Sun's core Same principle with neutrinos produced via the Carbon- Nitrogen-Oxygen chain The more reactions there are, the more neutrinos are produced and the more that should be detected here on the Earth Physicists find that the number of neutrinos coming from the Sun is smaller than expected Early experiments detected only 1/3 of the expected number of neutrinos These experiments used hundreds of thousands of liters of cleaning fluid (composed of chlorine compounds) or very pure water

8 March 2005AST 2010: Chapter 1532 Solar Neutrino Production (2) Later experiments using many tons of gallium were able to detect the more abundant low-energy neutrinos However, those experiments also found the same problem Too few neutrinos (the gallium experiments found about 2/3 the expected number) The puzzling lack of neutrinos from the Sun is called the solar neutrino problem

8 March 2005AST 2010: Chapter 1533 The Solar Neutrino Problem Physicists evaluated a number of possible reasons for the problem Nuclear fusion is not the Sun's power source? Not supported by observations, not likely to be the correct reason The experiments were not calibrated correctly? Unlikely that all carefully-tuned experiments were tuned in the same wrong way. Experiments independently verified by many other scientists; astronomers think that the results are correct. The nuclear reaction rate in the Sun is lower than what our calculations say? Possible, but many people have checked and re-checked the physics of the reaction rates Strong constraints in how much one can lower the temperature in the core of the Sun to slow down the reactions

8 March 2005AST 2010: Chapter 1534 Solar Neutrino Solution Three types of neutrinos exist The Sun produces only one type, called electron neutrinos The experiments detect only the electron type On their way from the Sun, neutrinos can transform from one type to another This can explain why we only detect 1/3 of the mix at Earth This also implies that neutrinos have mass, which is very small, but not zero