AST 301Introduction to AstronomyJohn LacyRLM [email protected] LiRLM [email protected] JeonRLM [email protected] site: www.as.utexas.eduGo to Department of Astronomy courses,AST 301 (Lacy), course websiteTopics for this weekDescribe the reactions in the proton-proton chain.How does Einstein’s equation, E = m c2, help explain hownuclear reactions generate energy?Describe how neutrinos allow us to observe the interior ofthe Sun, and say what was found.Describe the ideas of thermal and hydrostatic equilibriumfor a star.How are flux (or apparent brightness), luminosity, anddistance of a star related?How do we measure flux and distance of a star?How do we measure temperatures and masses of stars?How do we use the Hertzsprung-Russell diagram to makesense of the temperatures and luminosities of stars?Energy from the SunThe Sun radiates tremendous amount of energy from itssurface. Where does this energy come from?Nuclear fusion inside the Sun generates energy whilefusing hydrogen nuclei to make helium nuclei.The reaction chain is referred to as the proton-proton chainbecause the first reaction is the fusion of two protons.The best way to explain how nuclear reactions generateenergy is to note that a helium atom has less mass thanthe 4 hydrogen atoms that were fused to make it.Einstein’s famous equation, E = m c2, says that mass canbe converted into energy (or energy into mass) and tocalculate the energy generated by destroying a mass myou multiply m by the square of the speed of light.Four forcesTo understand nuclear fusion, we need to know about theinteractions between the particles in an atomic nucleus.We already know something about gravity and electricalforces. There are two more forces that matter.The strong, or nuclear, force is an attraction between theparticles in a nucleus (protons and neutrons).It is stronger than the electrical force, but only acts atshort distances.The weak interaction allows one type of particle to becomeanother.A neutron can decay into a proton, an electron and aneutrino. Energy is released by this reaction.Or with some energy put in, a proton can become aneutron and a positron.Conservation lawsThe four forces cannot change several quantities, whichmust be the same before and after a reaction.We say these quantities are conserved.(Is energy conserved in nuclear reactions?)electrical charge lepton numberproton +1 0neutron 0 0electron -1 +1positron +1 -1photon 0 0neutrino 0 +1anti-neutrino 0 -1Masses and Energieselectron e-9x10-31 kg 511 keVproton p+1836 e-938.3 MeVneutron n 1839 e-939.6 MeVdeuteron d+3669 e-1875 MeVhelium α++7292 e-3727 MeVn p+ + e- + ν + 0.8 MeVn + ν p+ + e- + 0.8 MeVp+ n + e+ + ν – 1.8 MeVp+ + p+ p+ + n + e+ + ν -1.8 MeV d+ + e+ + ν + 1.4 MeV4p+ α++ + 2e+ + 2ν + 26.6 MeVThe rate of fusionIf we know the rate of energy generation, and the amountof energy generated for each helium nucleus made, wecan calculate the rate at which helium nuclei are made.helium nuclei made / second energy made / second= ------------------------------------------------ energy made / helium nucleus madeQuizA 100 Watt light bulb uses 100 Joules (102 J) of electrical energyeach second. (1 Watt = 1 Joule / second)A typical photon from a light bulb has about 10-19 J of energy.How many photons does a 100 W light bulb emit each second?A. 10-21B. 10-17C. 1017D. 1021Fusion of hydrogen to make helium1 hydrogen atom: 1.673 x 10-27 kg4 hydrogen atoms: 6.693 x 10-27 kg1 helium atom: 6.646 x 10-27 kgMass lost: 0.047 x 10-27 kg (0.7% of 6.693x10-27)Energy created = Mass lost x c2:4.29 x 10-12 J / He atom formedTotal power (energy radiated per second) from Sun:3.90 x 1026 J / sHelium atoms formed / s = (Energy / s) / (Energy / He atom):9.09 x 1037 He atoms formed / sMass destroyed / s = (Energy generated / s) / c2:4.33 x 109 kg / s = 4.33 x 106 tonnes / sIs it ‘Just a Theory’?Fusion only occurs very close to the center of the Sun.How can we be sure this is how the Sun generates energy?The neutrinos created when protons became neutrons andpositrons during fusion are very unlikely to collide withanything while leaving the Sun.When they get to the Earth they can cause neutrons tobecome protons and electrons.Since 1965 Ray Davis and others have been observing thesolar neutrinos through the conversion of neutrons intoprotons in a tank of dry cleaning fluid (C2Cl4) in a goldmine in South Dakota.He received the Nobel prize in Physics for this work.Detection of Solar Neutrinosn + ν p+ + e-37Cl + ν 37Ar + e-…with a half-life of 34 days37Ar + e- 37Cl + ν + 0.82 MeVBy bubbling Ar through the tank of cleaning fluid everyweek or so, the 37Ar can be collected and measuredthrough its radioactive decay.But the number of neutrinos detected is only about 1/3 thenumber expected.What happened to the other neutrinos?Is there less nuclear fusion in the Sun than we thought?Neutrino OscillationsThe favored explanation for the lack of solar neutrinos isthat they changed to something else before getting toDavis’s tank of dry cleaning fluid.There are 3 families of leptons (light-weight particles):electron e-νemuon µ−νµtau τ−ντJust like there are 3 families of quarks:u ds ct bMaybe some of the electron neutrinos turn into the othertypes on their way here.Quantum Field TheoryNeutrinos can transform from one type into another if theneutrinos formed from electrons, muons, and taus arenot the mass eigenstates (the normal modes) of theneutrino field.Whatever that
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