1. Slide 1 Test 2 results Test 2 average: 77 (test 1: 82) Test 2 median: 79 (test 1: 87)

2. Slide 2 SOHO: The Solar and Heliospheric Observatory 1.5 million km from the Earth at the L1 point

3. Slide 3 The Lagrange Points L4,5: Trojans (stable points) L1: SOHO L2: WMAP L3: empty (unstable points)

4. Slide 4 Gravitational potential in the corotating frame

5. Slide 5 What we want to know: Internal structure and composition Source of energy Lifetime

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7. Slide 7 Life of stars: Gravity is everything Stars are born due to gravitational collapse of gas clouds Star’s life is a battle between thermal pressure generated by nuclear reactions and gravity Eventually, a star loses this battle, and gravity overwhelms

8. Slide 8 Gravity is balanced by thermal gas pressure Stars are held together by gravity. Gravity tries to compress everything to the center. What holds an ordinary star up and prevents total collapse is thermal and radiation pressure. The thermal and radiation pressure tries to expand the star layers outward to infinity.

9. Slide 9 Stars are gravitating spheres: they are held together by their own gravity. The gravity force acting on each volume element of a star is exactly balanced by gas pressure (Hydrostatic equilibrium) This balance is steady gravity gas pressure No gravity: the Sun will disperse in 1 day No gas pressure: the Sun will collapse in 20 minutes Central pressure ~ 10 10 atmospheres

10. Slide 10 Hydrostatic equilibrium Temperature in the center of a star A =1 m 2 =

11. Slide 11 Internal structure Central temperature T c  1.5  10 7 K Surface temperature T c  5800 K Heat transfer from the center to the surface! Heat transfer determines both the internal composition and the luminosity of the Sun

12. Slide 12 Internal source of energy Gravitational energy? Chemical energy? Nuclear reactions? The Sun’s luminosity is L = 4x10 26 Watt. Where does this energy come from?

13. Slide 13 Chemical energy? This is the energy associated with breaking chemical bonds in molecules 1. Typical energy released per proton is ~ 1-10 eV 2. There are M/m p ~ 10 57 protons in the Sun Total available energy is E chem ~ 10x10 57 = 10 58 eV ~ 2x10 39 J Chemical energy will be radiated away during the time But the Sun’s age is at least 4.6 billion years! Also, there is too hot for molecules in the sun

14. Slide 14 Note: If E is total energy stored in the sun (in J); L is luminosity, or the rate with which this energy is spent (in J/sec); Then the time it takes to spend all energy is T = E/L sec

15. Slide 15 Gravitational energy? As the Sun radiates its thermal energy to outer space, it shrinks, and the central temperature is increased (!) The energy source is the gravitational energy of a star If the energy is radiated away with luminosity L = 4x10 26 J/s, The Sun would radiate all its energy during the time But the Sun’s age is at least 4.6 billion years!

16. Slide 16 Nuclear reactions?

17. Slide 17 Nuclear reactions? Fission: decay of heavy nuclei into lighter fragments Fusion: synthesis of light nuclei into a heavier nucleus Energy released per proton is ~10-20 MeV!!

18. Slide 18 Energy is released in fusion reaction if the sum of masses of initial nuclei is larger that the mass of the final nucleus m p + m p M D + m e < 2 m p Deuterium Positron (antielectron) neutrino Deuterium has larger binding energy than protons (more tightly bound)  M = 2 m p - M D - m e Energy released E =  M c 2 Famous Einstein’s relation: E = mc 2 hydrogen

19. Slide 19 What is binding energy? It exists due to attractive forces between parts of a compound system: protons and neutrons in a nucleus, electrons and ion in an atom, Earth and moon, etc. Binding energy is negative!: U b = -|U b | Total energy of a system is the sum of energies of its parts plus binding energy: E = E 1 + E 2 + U b = E 1 + E 2 - |U b |

20. Slide 20 Energy is released in fission reaction if the mass of an initial nucleus is larger that the sum of masses of all final fragments M U > M Rb + M Cs + 3 m n Rubidium and Cesium are more tightly bound, or have larger binding energy than Uranium. It is energetically favorable for Uranium to split. When is the energy released in fission reactions?  M = M U – (M Rb + M Cs + 3 m n ) Energy released E =  M c 2 Famous Einstein’s relation: E = mc 2

21. Slide 21 There are no heavy elements on the stars |U b |

22. Slide 22 Energy Production Energy generation in the sun (and all other stars): Nuclear Fusion = fusing together 2 or more lighter nuclei to produce heavier ones. Nuclear fusion can produce energy up to the production of iron; For elements heavier than iron, energy is gained by nuclear fission. Binding energy due to strong force = on short range, strongest of the 4 known forces: electromagnetic, weak, strong, gravitational

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24. Slide 24 Proton-proton cycle: four hydrogen nuclei fuse to form one helium nucleus Hydrogen Fusion

25. Slide 25 Einstein’s relation: E = mc 2 Energy released in one reaction: (Binding energy) Hans Bethe 1939 0.007, or 0.7% of the rest energy of protons (4m p c 2 ) is released This is 10 7 times more efficient than chemical reactions!

26. Slide 26 There is more than enough nuclear fuel for 10 10 years! Does nuclear fusion provide enough energy to power the Sun? Assume 10 56 protons in the core:

27. Slide 27 600 million tons of hydrogen are fused every second on the Sun! How much hydrogen should be fused per second to provide the Sun’s luminosity? Nuclear fusion efficiency: 0.7% of the hydrogen mass is converted into radiation in the p-p cycle Matter-antimatter annihilation has even higher efficiency: 100% !!

28. Slide 28 Proton-proton cycle

29. Slide 29 Proton-proton cycle Step 1 Step 2 Step 3 All positrons annihilate with electrons creating gamma-quanta

30. Slide 30 Step 1 1 H + 1 H --> 2 H + positron + neutrino To fuse, two protons need to be as close as 10 -15 m to each other They need to overcome the Coulomb barrier Coulomb repulsion energy:

31. Slide 31 Protons should be hot!

32. Slide 32 But we need T > 10 9 K to overcome the Coulomb barrier! Quantum tunneling helps Still, a proton has 1 chance in 10 billion years to fuse! Such reaction is nearly impossible

33. Slide 33 Step 2 Takes 6 seconds to occur

34. Slide 34 Step 3 Takes 1 million years to occur

35. Slide 35 The solar neutrino problem

36. Slide 36 Fundamental Forces : M a t t e r i s e f f e c t e d b y f o r c e s o r i n t e r a c t i o n s ( t h e t e r m s a r e i n t e r c h a n g e a b l e ) t h e r e a r e f o u r f u n d a m e n t a l f o r c e s i n t h e U n i v e r s e : g r a v i t a t i o n ( b e t w e e n p a r t i c l e s w i t h m a s s ) e l e c t r o m a g n e t i c ( b e t w e e n p a r t i c l e s w i t h c h a r g e / m a g n e t i s m ) s t r o n g n u c l e a r f o r c e ( b e t w e e n q u a r k s ) w e a k n u c l e a r f o r c e ( t h a t c h a n g e s q u a r k t y p e s ) Matter is effected by forces or interactions (the terms are interchangeable) There are four fundamental forces in the Universe: gravitation (between particles with mass) electromagnetic (between particles with charge) strong nuclear force (between quarks) weak nuclear force (that changes quark types)

37. Slide 37 10,000 years Neutrino have zero or very small mass and almost do not interact with matter

38. Slide 38 Neutrino image of the Sun

39. Slide 39 The Davis experiment 400,000 liters of perchlorethylene buried 1 mile deep in a gold mine About 1 Chlorine atom per day is converted into Argon as a result of interaction with solar neutrino Much more difficult than finding a needle in a haystack!! There are 10 32 Cl atoms in a tank!

40. Slide 40 Sudbury neutrino observatory: 1000 tons of heavy water D 2 O

41. Slide 41 32,000 ton of ultra-pure water 13,000 detectors

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44. Slide 44 Observed neutrino flux is 2 times lower than the theoretical prediction!

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46. Slide 46 The problem has been finally solved just recently: Neutrinos “oscillate”! They are converted into other flavors: mu and tau neutrinos Neutrinos should have mass Particle physics models should be modified

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