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Lecture 1 - The Solar Interior

Lecture 1 - The Solar Interior. Topics to be covered: Solar interior Core Radiative zone Convection zone. The Solar Interior - “The Standard Model”. Core Energy generated by nuclear fusion (the proton-proton chain). Radiative Zone Energy transport by radiation. Convective Zone

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Lecture 1 - The Solar Interior

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  1. Lecture 1 - The Solar Interior • Topics to be covered: • Solar interior • Core • Radiative zone • Convection zone Lecture 1 - The Solar Interior

  2. The Solar Interior - “The Standard Model” • Core • Energy generated by nuclear fusion (the proton-proton chain). • Radiative Zone • Energy transport by radiation. • Convective Zone • Energy transport by convection. Lecture 1 - The Solar Interior

  3. The Solar Interior • Christensen-Dalsgaard, J. et al., Science, 272, 1286 - 1292, (1996). Lecture 1 - The Solar Interior

  4. The Solar Core • R: 0.0 - 0.25 Rsun • T(r): 15 - 8 MK • (r): 150 - 10 g cm-3 • Temperatures and densities sufficiently high to drive hydrogen burning (H->He). • Ultimate source of energy in the Sun and Sun-like stars. Lecture 1 - The Solar Interior

  5. The Solar Core • What is the temperature and pressure in the core? • Assume hydrostatic equilibrium: and mass conservation: • Divide to cancel ’s => • Therefore, LHS => and RHS => PC= pressure at core PS= pressure at surface Lecture 1 - The Solar Interior

  6. The Solar Core • Assuming PS<< PCand setting r = R, • Using the Ideal Gas Law k = Boltzmann’s const n = number density atoms/cm3  = density = M/4R3 • The core temperature is therefore • Which gives Tc~ 2.7 x 107 K (actual value is ~1.5 x 107 K). Lecture 1 - The Solar Interior

  7. The Solar Core • Coulomb barrier between protons must be overcome for fusion to occur. • To overcome Coulomb barrier, particles must have sufficient thermal kinetic energy to exceed Coulomb repulsion: • Particles have Maxwell-Boltzmann distribution: • There is a high-energy tail, but not sufficient … need quantum mechanics. Lecture 1 - The Solar Interior

  8. The Solar Core • From Heisenberg Uncertainty Principle a proton of a given (insufficient) energy may be located within nucleus of neighbouring proton. • Combined with high-energy M-B tail, we get the Gamow Peak. • So protons in 3-10 keV energy range can overcome the Coulomb barrier (i.e., T>15MK). • Fusion can therefore occur. Lecture 1 - The Solar Interior

  9. Proton-proton cycle • The p-p cycle occurs in three main steps. Step 1:1H + 1H 2H + e+ +  (Q = 1.44 MeV) • Might then expect a 2H + 2H reaction, but because of the large numbers of 1H, the following is more probable: Step 2:2H + 1H 3He +  (Q = 5.49 MeV) • 3He can then react with 1H, but the resultant 4Li is unstable (i.e. 3He + 1H  4Li  3He + 1H). • The final step is then: Step 3:3He + 3He  4He + 21H +  (Q = 12.86 MeV) • The net result is: 4 1H  4He + 2e+ + 2  (Q = 26.7 MeV) Lecture 1 - The Solar Interior

  10. Proton-proton cycle (cont.) • ~99% of the Sun’s energy is produced via the p-p cycle. • The remaining ~1% is produced by the Carbon-Nitrogen-Oxygen (CNO) cycle. • CNO cycle is more important in more massive stars. Lecture 1 - The Solar Interior

  11. Proton-proton vs. CNO Lecture 1 - The Solar Interior

  12. The Radiative Zone • R: 0.25 - 0.8 Rsun • T(r): 8 - 0.5 MK • (r): 10 - 0.01 g cm-3 • Hydrogen burning cuts off abruptly at r ~ 0.25 Rsun. • Interior becomes optically thin or transparent as density decreases. • Energy transported radiatively. • Photons cannot be absorbed in the radiative zone as the temperature are too high to allow atoms to form. Therefore no mechanism for the absorption of photons. Lecture 1 - The Solar Interior

  13. The Radiative Zone • For T = 15MK Wien’s displacement law implies max= 0.19 nm i.e., the center of the Sun is full of X-rays. • Photons do 3D random walk out of Sun. • Assume photon moves l between interactions (mean free path) and takes a total number of steps N. • On average it will have moved a distance • As tdifusion = N l / c and => tdiffusion >104 yrs! Lecture 1 - The Solar Interior

  14. Solar Interior • Total radiative energy inside Sun is: J where a = 4/c is the radiation constant. • Can thus estimate solar luminosity from, W • Which gives, L ~ 3 x 1026W. • Actual value is actually 4 x 1026W. Lecture 1 - The Solar Interior

  15. The Convective Zone • R: 0.8 - 1 Rsun • T(r): 0.5 MK - 6000 K. •  <0.01 g cm-3 • Photons now absorbed as temperature is sufficiently low to allow atoms to form. Gas is optically thick or opaque. • Continuous absorption of photons by lower layers causes a temperature gradient to build up between the lower and upper layers. • Plasma become convectively unstable, and large convective motions become the dominant transport mechanism. TC r TH TH > TC Lecture 1 - The Solar Interior

  16. The Convective Zone Lecture 1 - The Solar Interior

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