1. Read Your Textbook: Foundations of Astronomy –Chapter 12 Homework Problems Chapter 12 –Review Questions: 2, 3, 8, 9 –Review Problems: 3, 7-9 –Web Inquiries: 1 Stellar Structure

2. Proto-stellar evolution on the H-R diagram. Theoretical “Hyashi” Tracks

3. Gravity versus Pressure Force due to Gravity F G = mGM/R 2 Force due to Radiation and Gas Pressures P gas =  kT gas pressure P   ~  T 4 radiation pressure Equilibrium F G = P gas + P  Hydrostatic Equilibrium

4. Stellar Structure Laws

5. Luminosity L = 4  R 2  T 4 Mass Chemical Composition Stellar Zoo

6. H-R Diagram

7. Fusion of Hydrogen into Helium Efficient Storage, Inefficient Consumption At the temperature in the core of the sun… T surface = 5800 K T core = 15,000,000 K 99.999% of H Is not tapped Number of H Nuclei Energy Energy Required to overcome proton-proton repulsive barrier Fusion of Hydrogen Number of H Nuclei Energy

8. Proton-Proton Chain

9. 1 H + 1 H 2 H + e + +  (positron + neutrino) 1 H + 2 H 3 He +  (photon) 3 He + 3 He 4 He + 1 H + 1 H +  Net effect: –4 H nuclei (protons) form 1 He nuclei (alpha) + photons Proton-Proton Chain

10.  E =  m c 2 m He = 3.97 m H  m = 0.03 m H Four protons weigh more than one alpha. Conservation of Mass??! Einstein says Mass is converted into energy.  E =  mc 2 = 6x10 18 ergs/gram 1 gram of H Energy Generation

11.  E =  m c 2 = 6x10 18 ergs/gram 1 gram of H The human body requires 10 9 ergs/sec to live. 1 gram of hydrogen nuclei fused into helium nuclei will release enough energy to power a human for 200 years. Power

12. Each second the sun converts 600 million tons of Hydrogen –7000 Aircraft carriers And makes 596 million tons of Helium Yielding 4 million tons of Radiation –50 Aircraft carriers This takes place in the inner 15-25 % of the star. Energy Generation

13. Stellar Lifetimes depend on mass. High mass stars are bright and short lived, use their fuel up rapidly. Low mass stars are faint and have longevity, use fuel slowly and efficiently. Energy Consumption

14. P = P  + P gas radiation pressure and gas pressure M/M solar P  /P P gas /P 0.10.00160.9984 1 (sun)0.1160.894 100.5700.430 1000.8500.150 Stellar Masses

15. Upper Limit for Stability The most massive stars would have enough radiation pressure to counteract gravity and literally blow themselves apart. M < 100 M solar Lower Limit for Stability Need to have T = 1.5 x 10 6 K for Hydrogen fusion M > 0.05 M solar In order to have nuclear fusion. Stellar Mass Range

16. Stellar Masses 0.05 M solar < M < 100 M solar Core Mass 0.01 M solar < M < 10 M solar LUMINOSITY 10 -4 L solar < L < 10 4 L solar Lifetimes: t ~ Mass/Luminosity Stellar Lifetimes

17. Stellar Masses 0.05 M solar < M < 100 M solar Core Mass 0.01 M solar < M < 10 M solar LUMINOSITY 10 -4 L solar < L < 10 4 L solar Lifetimes: t ~ Mass/Luminosity t star = 10 t solar /10 4 = 10 -3 t solar Burn out quick t star = 0.01 t solar /10 -4 = 100 t solar Longevity Stellar Lifetimes

18. 3.05 1.10 1.001.04 Stellar Life Times

19. Main Sequence Lifetime

20. Main Sequence Histogram