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Explore the foundational principles of stellar structure, from hydrostatic equilibrium to energy generation through nuclear fusion in stars. Learn about the laws governing stellar evolution and the immense energy released in the core. Discover how mass influences stellar lifetimes.
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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 gas pressure Pg~ sT4 radiation pressure Equilibrium FG = Pgas + Pg
Stellar Zoo Luminosity L = 4pR2 sT4 Mass Chemical Composition
Fusion of Hydrogen • Fusion of Hydrogen into Helium • Efficient Storage, Inefficient Consumption • At the temperature in the core of the sun… • Tsurface = 5800 K • Tcore = 15,000,000 K 99.999% of H Is not tapped Energy Required to overcome proton-proton repulsive barrier Number of H Nuclei Number of H Nuclei Energy Energy
Proton-Proton Chain • 1H + 1H 2H + e+ + n (positron + neutrino) • 1H + 2H 3He + g (photon) • 3He + 3He 4He + 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 + Pgasradiation pressure and gas pressure M/Msolar Pg/P Pgas/P 0.1 0.0016 0.9984 1 (sun) 0.116 0.894 10 0.570 0.430 100 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
