Test 2 results

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

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

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

4. Gravitational potential in the corotating frame

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

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. 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. gas pressure gravity 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 No gravity: the Sun will disperse in 1 day No gas pressure: the Sun will collapse in 20 minutes Central pressure ~ 1010 atmospheres

10. = Hydrostatic equilibrium Temperature in the center of a star A =1 m2

11. Internal structure Central temperature Tc 1.5107 K Surface temperature Tc 5800 K Heat transfer from the center to the surface! Heat transfer determines both the internal composition and the luminosity of the Sun

12. Gravitational energy? Chemical energy? Nuclear reactions? Internal source of energy The Sun’s luminosity is L = 4x1026 Watt. Where does this energy come from?

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/mp ~ 1057 protons in the Sun Total available energy is Echem ~ 10x1057 = 1058 eV ~ 2x1039 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. 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. 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 = 4x1026 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. Nuclear reactions?

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. Energy is released in fusion reaction if the sum of masses of initial nuclei is larger that the mass of the final nucleus hydrogen mp + mp hydrogen Positron (antielectron) Deuterium MD + me < 2 mp M = 2 mp- MD - me Energy released E = M c2 neutrino Famous Einstein’s relation: E = mc2 Deuterium has larger binding energy than protons (more tightly bound)

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!: Ub = -|Ub| Total energy of a system is the sum of energies of its parts plus binding energy: E = E1 + E2 + Ub = E1 + E2 - |Ub|

20. When is the energy released in fission reactions? Energy is released in fission reaction if the mass of an initial nucleus is larger that the sum of masses of all final fragments MU > MRb + MCs + 3 mn Rubidium and Cesium are more tightly bound, or have larger binding energy than Uranium. It is energetically favorable for Uranium to split. M = MU – (MRb + MCs + 3 mn) Energy released E = M c2 Famous Einstein’s relation: E = mc2

21. |Ub| There are no heavy elements on the stars

22. 0 Energy Production Energy generation in the sun (and all other stars): Binding energydue to strong force= on short range, strongest of the 4 known forces:electromagnetic, weak,strong,gravitational 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.

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

25. Einstein’s relation: E = mc2 Energy released in one reaction: (Binding energy) 0.007, or 0.7% of the rest energy of protons (4mpc2) is released This is 107 times more efficient than chemical reactions! Hans Bethe 1939

26. Does nuclear fusion provide enough energy to power the Sun? Assume 1056 protons in the core: There is more than enough nuclear fuel for 1010 years!

27. 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 600 million tons of hydrogen are fused every second on the Sun! Matter-antimatter annihilation has even higher efficiency: 100% !!

28. Proton-proton cycle

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

30. Step 1 1H + 1H --> 2H + 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. Protons should be hot!

32. But we need T > 109 K to overcome the Coulomb barrier! Such reaction is nearly impossible • Quantum tunneling helps Still, a proton has 1 chance in 10 billion years to fuse!

33. Step 2 Takes 6 seconds to occur

34. Step 3 Takes 1 million years to occur

35. The solar neutrino problem

36. Fundamental Forces : • 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. Neutrino have zero or very small mass and almost do not interact with matter 10,000 years

38. Neutrino image of the Sun

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 There are 1032 Cl atoms in a tank! Much more difficult than finding a needle in a haystack!!

40. Sudbury neutrino observatory: 1000 tons of heavy water D2O

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

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

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