Notes
Slide Show
Outline
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Astro 1050     Wed. Oct. 16, 2002
  •    Today:  Chapter 9: Formation & Structure
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Spectral Measurements
  • Use spectra of stars
  • Ignore broad (“high pressure” stellar lines


  • Very narrow (low pressure) lines from interstellar gas
    • This one Ca II  = Ca+1
  • Stronger in more distant stars
  • Stronger when looking through interstellar gas clouds


  • Hydrogen hard to measure
    • remember Balmer rules

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Measurements at other Wavelengths
  • Infrared “Cirrus”
    • really slightly warm dust
  • X-Rays of hot gas near exploded stars (supernova)
  • Radio observations of “Molecular Clouds”
    • Called that because cool and dense enough for molecules to form
    • H2 also hard to detect
    • CO common and easy to detect
    • Densest have 1000 atoms/cm3
    • T as low as 10 K
    • Location of star formation

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Collapse of
 Molecular Clouds
  • Barely stable against collapse:
  • Imagine slightly compressing cloud
    • Gravity goes up because material is packed more tightly (R in 1/R2 is smaller)
      • Tends to make cloud want to collapse


    • Pressure goes up because material is packed more tightly (P µ rT) and r higher
      • Tends to make cloud want to expand


    • For smaller clouds Pressure wins (stable)
    • For larger clouds Gravity wins (collapse)
  • As it collapses and becomes denser, smaller and smaller parts become unstable
  • Shock wave can trigger collapse
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What will a forming star look like in HR diagram?
  • Temperature changes relatively simple
    • Starts out large and relatively cool Must be on red side of diagram
    • It heats up as it contracts Must towards the blue


  • Luminosity more complicated because it depends on T and R
    • Not much energy to start with Luminosity must start out low
    • Collapse releases grav. energy Luminosity will rise
    • Fusion begins, releases more energy Luminosity at a peak
    • Collapse slows, only have fusion now Luminosity declines

  • Finally stabilizes on the main sequence
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How does mass affect collapse?
  • More massive protostars have stronger gravity
  • Collapse speed will be much faster


  • Fast collapse and short lifetime means massive stars reach end of lifetime while low mass stars in cloud are just forming
    • Supernova shocks may come from earlier generation of stars
      • Sequential Star Formation

    • Energy from supernova and other effects eventually disrupts cloud – prevents further collapse.
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Observations of collapse
  • Young cluster “NGC 2264”
    • Few million years old

  • High mass stars have reached
    main sequence
  • Lower mass stars are still approaching main sequence


    • T Tauri stars


  • Naming of classes of stars:  Usually named after first star in class:  T Tauri
    • Stars with letters (RR Lyrae) are typically “variable” stars


  • Earlier stages hidden by dust


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More details of stellar structure and energy generation

  • Alternatives to the proton-proton chain


  • Fusion of Helium to heavier elements


  • Proton-proton reaction slow because:
    • Need two rare events at once
      • High energy collision of 2 protons
      • Conversion of p Þn during collision
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The CNO Cycle
  • Gives way around need for p ®n during the collision


  • Still must happen later – but don’t need to rare events simultaneously


  • Trade off is need for higher energy collisions  (T>16 million K)


  • Add p to some nucleus where new one is still “stable”
  • Wait for p ® n while that nucleus just “sits around”


  • The net effect is still   4  1H ®  4He
  • C just acts like a “catalyst”
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Heavy Element Fusion
  • Triple Alpha process
    • 4He + 4He ® 8Be + g
    • 8Be + 4He ® 12C  + g

  • Similar type reactions create heavy elements above 600 Million K


  • Plot to left gives:
    • x:   # of neutrons
    • y:   # of protons


    • Right one – add neutron
    • Up     one – add proton
    • Diagonal  –  p ® n or reverse
    • Jumps:        add 4He or more
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Models of Stellar Structure
  • Divide star into thin shells,calculate how following vary from shell to shell
     (i.e. as function of radius r)
    • P (Pressure)
    • T (Temperature)
    • r (Density)
  • To do this also need to find:
    • M (Mass) contained within any r
    • L (Luminosity) generated within any r


  • P example:



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Numerical Stellar Models
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Why don’t stars collapse?
  • Limiting case:  Assume no nuclear fusion so only energy source is gravity.


  • Star is “almost” in hydrostatic equilibrium
    • Star radiates energy:  If nothing else happened T would drop, P would drop, star would shrink.
    • Star does shrink, but in doing so gravitational energy is converted to heat, preventing T from continuing to drop.
    • In fact, since star is now more compact, gravity is stronger and it actually needs higher P (so higher T) to prevent catastrophic collapse


  • As star shrinks, ½ of gravitational energy goes into heating up star, ½ gets radiated away


  • Rate at which it radiates energy, so rate at which it shrinks, is limited by how “insulating” intermediate layers are
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Why do we get steady fusion rates?
  • Strange counterintuitive result:
    • As star radiates away thermal energy it actually heats up
      (because as it shrinks gravity supplies even more energy)


  • Star continues to shrink till it gets hot enough inside for fusion (rather than gravity) to balance energy being radiated away.


  • Nuclear thermostat
    • If fusion reactions took place in a “box” with fixed walls:
      • Fusion Þ more energy Þhigher T Þ more fusion    (explosion)


    • If fusion reactions take place in sun with “soft gravity walls”:
      • If fusion rate is too high T tries to go up but star expands and actually ends up cooling off – slowing down fusion.  (steady rate)



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Mass-Luminosity relationship
  • L µ M3.5 Why?


  • Higher mass means higher internal pressure
  • Higher pressure goes with higher temperature
  • Higher temperature means heat leaks out faster
  • Star shrinks until T inside is high enough for
    fusion rate (which is very sensitive to temperature)
    to balance heat leak rate




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Lifetime on Main Sequence
  • L µ M3.5 T µ fuel / L = M/M3.5 = M-2.5
  • Example:  M=2 MSun      L = 11.3 LSun        T =1/5.7  TSun


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How about a 0.5 solar mass star?
  • M = 0.5 Msun
  • Time =
  • Luminosity =


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How about a 0.5 solar mass star?
  • M = 0.5 Msun
  • Time = 5.7 times solar lifetime
  • Luminosity = 0.09 solar luminosity


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Width of Main Sequence – and Stellar Aging
  • As star converts H to He you have more massive nuclei
    • Pressure related to number of nuclei
    • Gravity related to mass of nuclei
      • Pressure would tend to drop unless something else happens
  • Temperature must rise (slightly) to compensate
  • Luminosity  must  rise (slightly) as heat leaks out faster



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Orion Nebula: A Star-Forming Region
  • Red light = Hydrogen emission
  • Blue light = reflection nebula
  • Dark lanes = dust


  • Astronomy Picture of the Day:
    http://antwrp.gsfc.nasa.gov/apod
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Protoplanetary Disks in the Orion Nebula

  • Dusty disk seen in silhouette


  • Central star visible at long wavelengths
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Herbig-Haro objects: The angular momentum problem

  • As clouds try to collapse angular momentum makes them spin faster
  • A disk forms around the protostar
  • Material is ejected along the rotation axis


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Herbig-Haro 34 in Orion

  • Jet along the axis visible as red


  • Lobes at each end where jets run into surrounding gas clouds
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Motion of Herbig-Haro 34 in Orion

  • Can actually see the knots in the jet move with time


  • In time jets, UV photons, supernova, will disrupt the stellar nursery