Transcript Structure
Stellar Structure • 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 Theoretical “Hyashi” Tracks Proto-stellar evolution on the H-R diagram. Hydrostatic Equilibrium Gravity versus Pressure Force due to Gravity FG = mGM/R2 Force due to Radiation and Gas Pressures Pgas = rkT Pg ~ sT4 gas pressure radiation pressure Equilibrium FG = Pgas + Pg Stellar Structure Laws Stellar Zoo Luminosity L = 4pR2 sT4 Mass Chemical Composition H-R Diagram Fusion of Hydrogen • Fusion of Hydrogen into Helium • Efficient Storage, Inefficient Consumption • At the temperature in the core of the sun… Energy Required to overcome proton-proton repulsive barrier • Tsurface = 5800 K • Tcore = 15,000,000 K Number Number ofofHH Nuclei Nuclei 99.999% of H Is not tapped Energy Energy Proton-Proton Chain Proton-Proton Chain + e+ + n (positron + neutrino) • 1H + 1H 2H • 1H + 2H 3He • 3He + 3He +g 4He (photon) + 1H + 1H + g • Net effect: – 4 H nuclei (protons) form 1 He nuclei (alpha) + photons Energy Generation DE = Dm c2 mHe = 3.97 mH Dm = 0.03 mH Four protons weigh more than one alpha. Conservation of Mass??! Einstein says Mass is converted into energy. DE = Dmc2 = 6x1018 ergs/gram 1 gram of H Power DE = Dm c2 = 6x1018 ergs/gram 1 gram of H The human body requires 109 ergs/sec to live. 1 gram of hydrogen nuclei fused into helium nuclei will release enough energy to power a human for 200 years. Energy Generation • 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 Consumption 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. Stellar Masses P = Pg + Pgas radiation pressure and gas pressure M/Msolar 0.1 1 (sun) 10 100 Pg/P Pgas/P 0.0016 0.9984 0.1160.894 0.570 0.430 0.850 0.150 Stellar Mass Range Upper Limit for Stability The most massive stars would have enough radiation pressure to counteract gravity and literally blow themselves apart. M < 100 Msolar Lower Limit for Stability Need to have T = 1.5 x 106 K for Hydrogen fusion M > 0.05 Msolar In order to have nuclear fusion. Stellar Lifetimes Stellar Masses 0.05 Msolar < M < 100 Msolar Core Mass 0.01 Msolar < M < 10 Msolar LUMINOSITY 10-4 Lsolar < L < 104 Lsolar Lifetimes: t ~ Mass/Luminosity Stellar Lifetimes Stellar Masses 0.05 Msolar < M < 100 Msolar Core Mass 0.01 Msolar < M < 10 Msolar LUMINOSITY 10-4 Lsolar < L < 104 Lsolar Lifetimes: t ~ Mass/Luminosity tstar = 10 tsolar/104 = 10-3 tsolar Burn out quick tstar = 0.01 tsolar/10-4 = 100 tsolar Longevity Stellar Life Times 3.05 1.10 1.00 1.04 Main Sequence Lifetime Main Sequence Histogram