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Stellar Structure

0. Hydrostatic Equilibrium:. Stellar Structure. Radiation. Mass. Gas. Energy. Generation. Density. Transport. Temperature. Radiative. Composition. Convective. 0. Hydrostatic Equilibrium. A. F p. D m. D F g. D r. F’ p. 0. The Pressure Integral. A. m = cos q. q. D A.

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Stellar Structure

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  1. 0 Hydrostatic Equilibrium: Stellar Structure Radiation Mass Gas Energy • Generation • Density • Transport • Temperature Radiative • Composition Convective

  2. 0 Hydrostatic Equilibrium A Fp Dm DFg Dr F’p

  3. 0 The Pressure Integral A m = cosq q DA p v Dx

  4. 0 Overcoming the Coulomb Barrier → kTcl ~ 1010 K Ucl = (3/2) kTcl Ut = (3/2) kTt → kTcl ~ 107 K rt ~ ldeBrogle = h/p

  5. 0

  6. 0

  7. 0

  8. 0 The PP Chain

  9. 0 The CNO Cycle p 42He g 126C ne 137N p 157N e+ 136C p ne 158O g e+ 147N g p

  10. 0 Binding energy per nucleon Endothermic Energy can be liberated via nuclear fission Exothermic Energy can be liberated via nuclear fusion

  11. 0 Convection Adiabatic expansion: P = K*rg

  12. 0 Favorable Conditions for Convection • Large Opacities → Large |dT/dr|rad • Partial Ionization Zones → Brings g close to 1 → small |dT/dr|ad • Low g → small |dT/dr|ad = g/Cp • Strongly T-dependent energy generation (CNO cycle!) → large |dT/dr|

  13. 0 Stellar energy transport structure as a function of stellar mass R/R* 1 M/M0 90 0.08 0.25 1.2 1.3 Sun-like stars (0.25 M0 < M < 1.2 M0): Radiative core; convective envelope High-Mass stars (M > 1.3 M0): Convective core; radiative envelope Low-mass stars (M < 0.25 M0): Completely convective

  14. 0 Vogt-Russell Theorem The mass and composition of a star uniquely determine its radius and luminosity, internal structure, and subsequent evolution. => Almost 1-dimensional Zero-Age Main Sequence (ZAMS)

  15. 0 Masses of Stars in the Hertzsprung-Russell Diagram Masses in units of solar masses 40 18 The higher a star’s mass, the more luminous (brighter) it is: High masses 6 3 L ~ M3.5 1.7 1.0 High-mass stars have much shorter lives than low-mass stars: Mass 0.8 0.5 tlife ~ M-2.5 Sun: ~ 10 billion yr. Low masses 10 Msun: ~ 30 million yr. 0.1 Msun: ~ 3 trillion yr.

  16. Summary: Stellar Structure 0 Convective Core, radiative envelope; Energy generation through CNO Cycle Sun Mass Radiative Core, convective envelope; Energy generation through PP Cycle

  17. 0 Energy Transport Structure Inner convective, outer radiative zone Inner radiative, outer convective zone CNO cycle dominant PP chain dominant

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