ISP205 Lecture #20, March 22, 2001

  1. Announcements:
    1. NEW Homework assignment: Set 7
      due: April 10
    2. This Friday and Saturday, March 30 and 31, there is 
      open viewing at the MSU observatory 9-11pm
      (weather permitting)
            
  2. Review: How the sun works
    1. Energy generation by fusion of 4 hydrogen nuclei (protons)
      into helium (pp-chain)
    2. Hydrogen fusion requires frequent collisions at high velocities
      to overcome electrostatic repulsion of protons:
      1. High temperatures (sun: 15 Million K)
      2. High densities        (sun: 100 g/cm3)
      3. Quantum mechanics (tunneling)
    3. Hydrogen burning is an efficient fuel because:
      1. Helium nucleus is 0.7% lighter and the difference
        is released as energy (E=mc2)
      2. Reason: strong nuclear force binds protons and neutrons
        together once they touch.
        It isn't called the strong force for nothing !
    4. Energy generation in the suns interior
      1. Provides solar system and earth with energy 
      2. Stabilizes sun against gravity
    5. Energy transport from sun's interior to the outside
      1. Takes millions of years
      2. First 2/3 via radiation
      3. Last 1/3 to surface via convection
             
  3. The Magnitude Scale
    1. Apparent brightness: Intensity of stars light that reaches earth
      Luminosity              : Intensity of the light that a star emits
          
    2. Hipparchos 190BC-120BC introduced Magnitude ~150 B.C.
      as a measure of the apparent brightness.
          
      brightest stars: apparent magnitude 1
      faintest stars: apparent magnitude 6
      later quantified:
               
    3. 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
      difference of 2 is about a factor of 2.5 x 2.5 =  change
      ...
    4. The fainter the bigger the magnitude !
    5. 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

       DEMO: Redshift magnitude filter
         

    6. Note: to get the stars luminosity one needs to know 
      the distance (inverse square law)

  4. Review: Stellar Spectra
    1. Stars have different temperatures and therefore:
      1. different colors
      2. different absorption spectra (because electrons
        are in different places, and atoms can have lost
        electrons [ionization])
    2. Stars are classified according to the absorption lines 
      one sees (which means according to their photospheric
      temperatures): (picture)

      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"
    3. Examples for characteristic lines are going from cool to hot:
      1. (coolest) Molecules (lots of lines very close together)
        and neutral metals, like neutral Calcium (422.5nm)
      2. (warmer) Singly ionized Calcium CaII (393.3nm, 396.8nm)
        (temperatures are high enough to ionize Calcium once)
      3. (warmer) Hydrogen (397.0, 410.1, 424.0 nm)
        (temperatures are high enough to excite hydrogen so that 
        it absorbs visible photons, but not too high so it doesn't 
        get ionized)
      4. (hot) Neutral helium
      5. (hottest) ionized helium
        (extreme temperatures are needed to ionize a noble gas like 
        helium)
                 
    4. Color Index: (picture)
    5. Characteristics of stars:
      1. Luminosity
        1. Power of electromagnetic radiation emitted by the star
        2. Obtained from measured apparent brightness and distance
          (inverse square law !)
        3. Typical Luminosities (picture)
      2. Temperature (Photosphere)
        1. From absorption spectra
      3. Mass
        1. From period and velocity observations in binary systems
          (Charon movie, Doppler demo)
          and Keplers third law:
          A3 = (M1+M2) x P2
        2. Typical masses for stars:
          least massive stars  : 1/12th solar mass (if lighter: brown dwarf or planet)
          most massive stars  : ~200 times solar mass (1/billion)
                 
      4. Size
        1. From eclipses in binary systems
          (Demo)
        2. Typical sizes:
          white dwarfs:  size of the earth (1/100 of sun)
          giants            :  10-100 times larger than the sun
          supergiants   :  several hundred times larger than sun (Betelgeuse)
            
    6. H-R Diagram
      1. Example: Exercise
      2. Hertzsprung-Russel Diagram: Temperature vs. Luminosity
        (picture)( Sirius, Betelgeuze, Rigel - redshift)
      3. Main sequence: stars that burn hydrogen lie along a narrow
        band in the H-R diagram called the main sequence.
        90% of all stars are on the Main Sequence
      4. More massive stars are  hotter and more luminous (upper
        left end of Main Sequence) 
        There are much fewer massive stars than light stars.
        What does that mean ?
      5. Giants and Supergiants are mostly red, but much
        more luminous than main sequence stars
        (they are bigger)
      6. White dwarfs are white (quite hot) but less luminous
        than main sequence stars
        (they are smaller)
                      
    7. Distance Ladder
      1. Parallax
        (blackboard, DEMO)
        1. Stars position shift slightly as the earth orbits around the sun.
          The change in angle when the earth moves 1 AU (1/4 year)
          is called parallax.
        2. The further a star is away, the smaller the parallax
        3. Largest parallax is 1.5 arc sec for Alpha Centauri
          (size of a US quarter seen from 3 miles away)
        4. 1 Parsec: Distance of a star that has a parallax of 1 arc sec
          = 3.26 light years
        5. Hipparcos satellite measured parallaxes up to 300 Ly
          (less than 1/100th of our galaxy)
      2. H-R Diagram and Luminosity classes
        1. One can determine the Luminosity of a star from the H-R
          diagram - from comparison with apparent brightness one
          obtains the distance (inverse square law)
        2. From the stars spectrum one needs to determine:
          1. Spectral class (O,B, ...)
          2. Luminosity class (dwarf, Main Sequence, Giant, ...)
            (picture)
      3. Variable Stars
        1. Cepheid Variables
          1. Pulsating stars that vary in their brightness
            (picture)
          2. discovered 1784 by John Goodricke (Delta Cephei)
          3. Typical periods: 3-50 days
          4. Henrietta Leavitt discovered 1908 that there is
            a relation between luminosity and period
            (picture) (why is that useful ?)
          5. Period can be easily measured - with the known
            period -luminosity relation this gives luminosity
          6. Cepheids are bright and can even be see in other galaxies !
            (up to 60 Million Ly)
            (1000-10000 times the sun's luminosity)
        2. RR Lyrae Stars
          1. Typical periods <1 day
          2. Luminosity: ~50 times the sun
          3. More numerous than Cepheids