1. Stellar Interiors Physical Astronomy Professor Lee Carkner Lecture 10

2. Kelvin-Helmholtz Timescale   Very roughly, the amount of gravitational energy in a sphere of mass M and radius R is E ~ -(3/10)(GM 2 /R)   Also for non-fusion objects like planets and brown dwarfs  Can only provide solar luminosity for ~10 7 years

3. Fusion   Fusion of lighter elements into heavier ones   u = 1 atomic mass unit = 1.66053873X10 -27 kg  E= mc 2 = 26.731 MeV per reaction  Enough energy to power the sun for ~10 10 years

4. Fusion and Mass  Stars fuse elements in order of mass   Only massive stars can fuse heavier elements   More massive reactions are faster  H burning phase long, each subsequent phase shorter and shorter

5. Proton-Proton Chain  4 H → 4 He + 2e + + 2 e +2    No heavier catalysts involved  Dependant on T 4

6. Three Chains  In PPI chain, 2 H and 3 He formed as intermediate products   In PPII chain, 8 B and 8 Be formed as intermediate products

7. CNO Cycle   Temperature dependant as T 20   Only available in stars with CNO present  Does not work for first generation stars

8. Triple Alpha  4 He + 4 He → 8 Be 8 Be + 4 He → 12 C +    8 Be decays rapidly back into 4 He, so three alpha particles have into collide almost simultaneously

9. Heavier Elements  12 C + 4 He → 16 O +  16 O + 4 He → 20 Ne +   Other reactions can occur at higher mass   Even more super massive stars can fuse oxygen into silicon, phosphorus, and sulfur

10. Limits of Fusion  Fusion of elements up to atomic mass 56 can liberate energy   Elements heavier than iron produced in supernovae

11. Fusion and The Main Sequence   Stars that burn hydrogen don’t change much since hydrogen burning is slow   Since H burning rate depends on core temperature, high mass stars have the shortest main sequence lifetime

12. Radiation Pressure   For a star of temperature T, the radiation pressure at the surface can be written as: P rad = (4  /3c)T 4  Note that P rad is strongly temperature dependant

13. Eddington Luminosity   Occurs at the Eddington Luminosity: L Ed = (4  GcM/  )   ~0.034 for very luminous stars   Puts upper limits on stellar size and accretion events

14. Main Sequence Evolution   This increases the fusion rate and the luminosity   Faint young Sun problem

15. Solar Interior   60% of mass is inside 1/3 radius  Inner 25% of sun generates almost all energy   Outer ¼ of Sun is convective 

16. Next Time  Read 11.2-11.3  Homework: 10.21, 11.5a, 11.12, 11.15