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Stellar Interior

Stellar Interior. Radius: R  = 7  10 5 km = 109 R E Mass : M  = 2  10 30 kg M  = 333,000 M E Density: r  = 1.4 g/cm 3 (water is 1.0 g/cm 3 , Earth is 5.6 g/cm 3 ). Composition: Mostly H and He Temperature: Surface is 5,770 K Core is 15,600,000 K Power:

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Stellar Interior

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  1. Stellar Interior

  2. Radius: R = 7  105 km = 109 RE Mass : M = 2  1030 kg M = 333,000 ME Density: r = 1.4 g/cm3 (water is 1.0 g/cm3, Earth is 5.6 g/cm3) Composition: Mostly H and He Temperature: Surface is 5,770 K Core is 15,600,000 K Power: 4  1026 W Solar Facts

  3. Solar Layers • Core • 0 to 0.25 R • Nuclear fusion region • Radiative Zone • 0.25 to 0.70 R • Photon transport region • Convective Zone • 0.70 to 1 R • Fluid flow region

  4. Equilibrium • A static model of a star can be made by balancing gravity against pressure. • Need mass density and pressure Ft Fg Fb

  5. The particles in a star form a nearly ideal fluid. Classical ideal gas Quantum fluid The particles quantum states can be found by considering the particle in a box. Dimension L Wave vector (kx, ky, kz) Particles and States note:

  6. The internal energy depends on the quantum states. Density of states g(p)dp Energy of each state ep Number in each state f(ep) The distribution depends on the type of particle Fermion or boson Reduces to Maxwell Internal Energy

  7. The energy is related to the thermodynamic properties. Temperature T Pressure P Chemical potential m The pressure comes from the energy. Related to kinetic energy density Pressure

  8. The calculation for the ideal gas applied to both non-relativistic and relativistic particles. For non-relativistic particles For ultra-relativistic particles Relativity Effects

  9. A classical gas assumes that the average occupation of any quantum state is small. States are g(p)dp State occupancy gs Maxwellian f(ep) The number N can be similarly integrated. Compare to pressure Equation of state True for relativistic, also Ideal Gas

  10. The equation of state is the same for both non-relativistic and relativistic particles. Derived quantities differ For non-relativistic particles For ultra-relativistic particles Particle Density

  11. Electrons are fermions. Non-relativistic Fill lowest energy states The Fermi momentum is used for the highest filled state. This leads to an equation of state. Electron Gas

  12. Relativistic electrons are also fermions. Fill lowest energy states Neglect rest mass The equation of state is not the same as for non-relativistic electrons. Relativistic Electron Gas

  13. Electron Regimes • Region A: classical, non-relativistic • Ideal gases, P = nkT • Region B: classical, ultra-relativistic • P = nkT • Region C: degenerate, non-relativistic • Metals, P = KNRn5/3 • Region D: degenerate, ultra-relativistic • P = KURn4/3 T(K) 1015 B 1010 A 105 C D n(m3) 1025 1030 1035 1040 1045

  14. Particle equilibrium is dominated by ionized hydrogen. Equilibrium is a balance of chemical potentials. Hydrogen Ionization ep = p2/2m n = 3 n = 2 n = 1

  15. The masses in H are related. Small amount en for degeneracy Protons and electrons each have half spin, gs = 2. H has multiple states. The concntration relation is the Saha equation. Saha Equation

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