ISP205 Lecture #20, March 22, 2001

  1. Announcements:
    1. Homework extension of set 6 to 3-27
      (next Tuesday)
  2. How the sun works
    1. The sun emits  3.8 x 1026 W since about 4.5 billion years
      (DEMO)
      1 Professor Power: ......
      1 Horse Power     : 746 W
    2. Early ideas about the suns energy source:
      1. Fossil fuels: would last ~1000 years
      2. Meteorites: increase in sun's mass would change
        earths period by 2s/year
      3. Contraction (like Neptune): would last ~100 mio years
        (by  Lord Kelvin and Hermann von Helmholtz ~1850)
    3. Sir Arthur Eddington 1920 nuclear energy released from 
          conversion of hydrogen into helium
      Later worked our by Hans Bethe (1938,1939): fusion of hydrogen into helium
         
      Ingredients:
      1. Relativity
        (Albert Einstein, 1905)
                      E = mc2
           
        examples:
        Helium atom weighs ~0.7% less than 4 hydrogen atoms
        0.7% of hydrogen mass is converted to energy if all 
                 is fused into helium
        1kg hydrogen:  E = 1 kg * 0.007 * c2 = 6 x 1014 J

        What can fusion of 1kg hydrogen do ?
        My heater: 1350 Watts = 1350 J/s can run 
                           15000 years !
        Sun: 4 x 1026 Watts can run ~1 pico second
                (1000th of a billionth second)
          
        But: sun has about ~1030 kg hydrogen and could
                therefore run for billions of years
          
      2. High density: at center of the sun 100 g/cm3
                       increases likelihood of collisions
      3. High temperature: at center of the sun 15 million K
               helps protons to overcome the repulsion of their
               positive charges (DEMO model)
      4. Not enough ! Need Quantum mechanics
               protons overcome remaining 
               repulsion by tunneling
      5. Once protons touch, the strong nuclear force binds
        them together. 
      6. Sequence of reactions converting hydrogen into
        helium is called pp chain.
        (pictures)
          
        Summary: 4 protons ---> 1 helium + 2 positrons 
                                                 + 2 neutrinos
          
      7. Conditions are only fulfilled in the core of the sun
        (inner 200,000 km  - 30% of radius) 
        it is there where the energy is generated
      8. Evidence that theory is correct:
        1. Helioseismology (surface vibrations) determines
          conditions in suns interior (Temperature to better than
          0.1 %) - we know that fusion has to happen
        2. Neutrinos have been detected coming from the sun
          (neutrinos can escape the interior of the sun directly -
          photons need millions of years - they therefore
          reflect current state of suns interior)
      9. Problem: There is a slight deficit in neutrionos 
        compared to predictions (factor 2-3) - "solar neutrino problem"
        Solution is most likely that neutrinos change into
        different kinds of neutrinos that the experiments
        were not sensitive to.
           
    4. Heat Transport to the surface
      1. There are in principle 3 forms of heat transport
        1. Conduction (DEMO) not important in sun
        2. Radiation (DEMO) important in inner part of sun
          (72% of radius)
        3. Convection (DEMO) important in outer part of sun
          (outer 28%) (picture inner sun, picture of granules)
               
    5. Stars need energy generation too !
      1. The pressure of a gas is proportional to the temperature
      2. The energy generated in the star heats the gas in its
        interior so that the pressure can balance gravity
        (DEMO)
      3. From the fact that the sun is not collapsing we can 
        determine the temperature at its center !
          
  3. The Magnitude Scale
    1. Hipparchus introduced it ~150 B.C. (picture)
      brightest stars: magnitude 1
      faintest stars: magnitude 6
      later quantified
    2. Logarithmic scale - difference of 5 in magnitude
      corresponds to a factor of 100 change in brightness

      difference of 1 is about a factor of 2.5 change
    3. The fainter the bigger the magnitude !
    4. Examples:
      Sun -26.2
      Venus (at its brightest) -4.4
      brightest star (Sirius A) -1.5
      faintest object visible with naked eye 6
      faintest object visible with binoculars 10
      faintest object visible with Hubble or Keck 30


  4. Stellar Spectra
    1. Stars have different temperatures and therefore colors
      1. Example for a red star: Betelgeuse (upper left in Orion)
      2. Example for a blue star: Rigel (lower right in Orion)
    2. Photosphere absorption lines can be observed not only
      in the sun but in a huge number of stars
      First discovered by Joseph Fraunhofer 1823
    3. Stars can show very different absorption line spectra
      (picture)
    4. The differences in absorption lines come NOT from
      different composition but from different temperatures.
      Example: H-atom (picture)
      1. At different temperatures the same atom produces different absorption lines
      2. Only in a certain temperature range a material
        produces visible (on earth) absorption lines
    5. Stars are classified according to the visible absorption lines
      (fig 16.5)
      Classes are: O B A F G K M with
           O hottest (bluest) star,     (>28000 K)
           M coolest (reddest) star   (<3500 K)
      Memorize: "Oh Be A Fine Girl Kiss Me"
      or               "Oh Be A Fine Guy Kiss Me"
    6. The sun is a G type star
      1. 5000-6000 K
      2. Mainly ionized Calcium lines, weak hydrogen lines
        (fig)