The Solar Interior - The Standard Model. Topics to be covered: o Solar interior. Radiative Zone. Convective Zone

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1 Lecture 1 - The Slar Interir Tpics t be cvered: Slar interir Cre Radiative zne Cnvectin zne Lecture 1 - The Slar Interir The Slar Interir - The Standard Mdel Cre Energy generated by nuclear fusin (the prtn-prtn chain). Radiative Zne Energy transprt by radiatin. Cnvective Zne Energy transprt by cnvectin. Lecture 1 - The Slar Interir

2 The Slar Interir Christensen-Dalsgaard, J. et al., Science, 272, , (1996). Lecture 1 - The Slar Interir The Slar Cre R: R sun T(r): 15-8 MK!(r): g cm -3 Temperatures and densities sufficiently high t drive hydrgen burning (H->He). Ultimate surce f energy in the Sun and Sun-like stars. Lecture 1 - The Slar Interir

3 The Slar Cre What is the temperature and pressure in the cre? Assume hydrstatic equilibrium: dp dr = " GM# r 2 and mass cnservatin: Divide t cancel! s => Therefre, LHS => and RHS => " # M 0 dm dr = "4#r2 $ dp dr / dm dr = dp dm = " GM 4#r 4 dp dm dm = P C " P S M GM # 4"r dm = GM "r 4 " P C = P S + GM 2 8#r 4 P C = pressure at cre P S = pressure at surface Lecture 1 - The Slar Interir The Slar Cre Assuming P S << P C and setting r = R, Using the Ideal Gas Law k = Bltzmann s cnst n = number density atms/cm 3! = density = M/4"R 3 P C = nkt = "kt m H P C ~ GM 2 8"R 4 The cre temperature is therefre T C ~ GMm H kr Which gives T c ~ 2.7 x 10 7 K (actual value is ~1.5 x 10 7 K). Lecture 1 - The Slar Interir

4 The Slar Cre Culmb barrier between prtns must be vercme fr fusin t ccur. T vercme Culmb barrier, particles must have sufficient thermal kinetic energy t exceed Culmb repulsin: 3 e2 kt > 2 r nuc => T > 2e2 3kr nuc =10 10 K! Particles have Maxwell-Bltzmann distributin: P(E)dE " Ee # E kt de There is a high-energy tail, but nt sufficient need quantum mechanics. Lecture 1 - The Slar Interir The Slar Cre Frm Heisenberg Uncertainty Principle ("x"p # h /2) a prtn f a given (insufficient) energy may be lcated within nucleus f neighburing prtn. Cmbined with high-energy M-B tail, we get the Gamw Peak. S prtns in 3-10 kev energy range can vercme the Culmb barrier (i.e., T>15MK). Fusin can therefre ccur. Lecture 1 - The Slar Interir

5 Prtn-prtn cycle The p-p cycle ccurs in three main steps. Step 1: 1 H + 1 H! 2 H + e + + " (Q = 1.44 MeV) Might then expect a 2 H + 2 H reactin, but because f the large numbers f 1 H, the fllwing is mre prbable: Step 2: 2 H + 1 H! 3 He + # (Q = 5.49 MeV) 3 He can then react with 1 H, but the resultant 4 Li is unstable (i.e. 3 He + 1 H! 4 Li! 3 He + 1 H). The final step is then: Step 3: 3 He + 3 He! 4 He H + # (Q = MeV) The net result is: 4 1 H! 4 He + 2e " (Q = 26.7 MeV) Lecture 1 - The Slar Interir Prtn-prtn cycle (cnt.) ~99% f the Sun s energy is prduced via the p-p cycle. The remaining ~1% is prduced by the Carbn-Nitrgen-Oxygen (CNO) cycle. CNO cycle is mre imprtant in mre massive stars. Lecture 1 - The Slar Interir

6 Prtn-prtn vs.. CNO Lecture 1 - The Slar Interir The Radiative Zne R: R sun T(r): MK!(r): g cm -3 Hydrgen burning cuts ff abruptly at r ~ 0.25 R sun. Interir becmes ptically thin r transparent as density decreases. Energy transprted radiatively. Phtns cannt be absrbed in the radiative zne as the temperature are t high t allw atms t frm. Therefre n mechanism fr the absrptin f phtns. Lecture 1 - The Slar Interir

7 The Radiative Zne Fr T = 15MK Wien s displacement law implies # max = 0.19 nm i.e., the center f the Sun is full f X-rays. Phtns d 3D randm walk ut f Sun. Assume phtn mves l between interactins (mean free path) and takes a ttal number f steps N. On average it will have mved a distance d = l N As t difusin = N l / c and => t diffusin >10 4 yrs! R = l N => t diffusin = R 2 /lc Lecture 1 - The Slar Interir Slar Interir Ttal radiative energy inside Sun is: # 4 & E = at 4 % 3 "R3 ( $ ' J where a = 4$/c is the radiatin cnstant. Can thus estimate slar luminsity frm, E L = = 16" t diffusin 3 #T 4 Rl W Which gives, L ~ 3 x W. Actual value is actually 4 x W. Lecture 1 - The Slar Interir

8 The Cnvective Zne R: R sun T(r): 0.5 MK K.! <0.01 g cm -3 Phtns nw absrbed as temperature is sufficiently lw t allw atms t frm. Gas is ptically thick r paque. Cntinuus absrptin f phtns by lwer layers causes a temperature gradient t build up between the lwer and upper layers. Plasma becme cnvectively unstable, and large cnvective mtins becme the dminant transprt mechanism. T C T H r T H > T C Lecture 1 - The Slar Interir The Cnvective Zne Lecture 1 - The Slar Interir

9 Advanced Stellar Physics / Office: 3.17A. 80%: Final exam. 20%: 2000 wrd essay and 10-min presentatin. Deadline and presentatin: Last lecture (March 9) Claire: The Crnal Heating Debate Brian: The Slar Activity Cycle Lecture 1 - The Slar Interir