1As hydrogen is exhausted in the(convective) core of a star(point 2)it moves away from the main sequence (point 3)What happens to the star ?• lower T Æ redder• same L Æ larger (Stefan’s L.)star becomes a red giant2For completeness – here’s what’s happening in detail (5 solar mass ZAMS star):I. Iben, Ann. Rev. Astron. Astroph. Vol 5 (1967) P. 5713What happens at hydrogen exhaustion(assume star had convective core)1. Core contracts and heatsH shell burningHe rich corecontracts andgrows from H-burning H,He mixHe rich coreÆ red giant2. Core He burning sets inHe core burningÆ lower mass stars become bluerlow Z stars jump to the horizontal branch42. a (M < 2.25 M0) Degenerate He coreH shell burning ignitesdegenerate, not burning He coreonset of electron degeneracy halts contraction then He core grows by H-shell burning until He-burning sets in.Æ He burning is initially unstable (He flash)in degenerate electron gas, pressure does not depend on temperature (why ?)therefore a slight rise in temperature is not compensated by expansion• rise temperature• accelerate nuclear reactions• increase energy productionÆ thermonuclear runaway:5Why does the star expand and become a red giant ?Because of higher Coulomb barrier He burning requires much higher temperaturesÆ drastic change in central temperatureÆ star has to readjust to a new configurationQualitative argument:• need about the same Luminosity – similar temperature gradient dT/dr• now much higher Tc– need larger star for same dT/drLower mass stars become red giants during shell H-burningIf the sun becomes a red giant in about 5 Bio years, it will almost fill the orbit of Mars6Pagel, Fig. 5.147Globular Cluster M10bluer horizontalbranch starsred giantsstill H burning8He burning overview• Lasts about 10% of H-burning phase• Temperatures: ~300 Mio K• Densities ~ 104g/cm3Reactions:4He + 4He + 4He Æ12C (triple α process)12C + 4He Æ16O(12C(α,γ))Main products: carbon and oxygen (main source of these elements in the universe)9Helium burning 1 – the 3α processα + α Æ8BeFirst step:unbound by ~92 keV – decays back to 2 α within 2.6E-16 s ! but small equilibrium abundance is establishedSecond step:8Be + α Æ12C* would create 12C at excitation energy of ~7.7 MeV1954 Fred Hoyle (now Sir Fred Hoyle) realized that the fact that there is carbon in the universe requires a resonance in 12C at ~7.7 MeV excitation energy1957 Cook, Fowler, Lauritsen and Lauritsen at Kellogg Radiation Laboratoryat Caltech discovered a state with the correct properties (at 7.654 MeV) Experimental Nuclear Astrophysics was born10How did they do the experiment ?• Used a deuterium beam on a 11B target to produce 12B via a (d,p) reaction.• 12B β-decays within 20 ms into the second excited state in 12C• This state then immediately decays under alpha emission into 8Be• Which immediately decays into 2 alpha particlesSo they saw after the delay of the b-decay 3 alpha particles coming from theirtarget after a few ms of irradiationThis proved that the state can also be formed by the 3 alpha process …Æ removed the major roadblock for the theory that elements are made in starsÆ Nobel Prize in Physics 1983 for Willy Fowler (alone !)11Third step completes the reaction:γ decay of 12Cinto its ground stateNote:Γα/Γγ> 103so γ-decay is very rare !Note: 8Be ground state is a 92 keV resonance for the α+α reaction12Calculation of the 3α rate in stellar He burningUnder stellar He-burning conditions, production and destruction reactions for 12C*(7.6 MeV) are very fast (as state mainly α-decays !)therefore the whole reaction chain is in equilibrium:α+α8Be 8Be + α12C*(7.7 MeV)The 12C*(7.6 MeV) abundance is therefore given by the Saha Equation: Q/kT2/94He22234He2/312C2MeV) 12C(7.6e22−=kTmNYkTmYAhhπρπQwith αmmc 3/12C(7.7)2−=13Q/kT34He22234He2/3MeV) 12C(7.6e23−=kTmNYAhπρ4He12C3mm ≈using Yone obtains:The total 3α reaction rate (per s and cm3) is then the total gamma decay rate(per s and cm3) from the 7.6 MeV state.This reaction represents the leakage out of the equilibrium !Therefore for the total 3α rate r:hγρΓ=ANYrMeV) 12C(7.6And with the definition><=αααρλαα222361ANYnote 1/6 because 3 identical particles !14one obtains:Q/kT34He2222/32e236−Γ⋅>=<hhγπραααkTmNNAA(Nomoto et al. A&A 149 (1985) 239)With the exception of masses, the only information needed is the gamma widthof the 7.6 MeV state in 12C. This is well known experimentally by now.15Helium burning 2 – the 12C(α,γ) rateNo resonance in Gamow window – C survives !Resonance in Gamow window- C is made !But some C is converted into O …16resonance(high lying)resonance(sub threshold)E1E1E2 DCresonance(sub threshold)E2some tails of resonancesjust make the reactionstrong enough …complications:• very low cross section makes direct measurement impossible• subthreshold resonances cannot be measured at resonance energy• Interference between the E1 and the E2 components17Therefore: Uncertainty in the 12C(α,γ) rate is the single most important nuclear physics uncertainty in astrophysicsAffects: • C/O ration Æ further stellar evolution (C-burning or O-burning ?)• iron (and other) core sizes (outcome of SN explosion)• Nucleosynthesis (see next slide)Some current results for S(300 keV):SE2=53+13-18 keV b (Tischhauser et al. PRL88(2002)2501SE1=79+21-21 keV b (Azuma et al. PRC50 (1994) 1194)But others range among groups larger !18Massive star nucleosynthesis model as a function of 12C(α,γ) rateWeaver and Woosley Phys Rep 227 (1993) 65• This demonstrates the sensitivity• One could deduce a preference for a total S(300) of ~120-220(But of course we cannot be sure that the astrophysical model is right)19End of core helium burning and beyondArnett, fig 8.7convective regions indicate burning (steep ε(T) – steep dL/dr – convection)end of coreHe burningÆ note complicated multiple burning layers !!!20Further evolution of burning conditionsν coolingdominatesυυ+→+−+eeWoosley, Heger, Weaver, Rev. Mod. Phys 74 (2002)101521Carbon burningBurning conditions:for stars > 8 Mo (solar masses) (ZAMS)T~ 600-700 Mio ρ ~ 105-106g/cm3Major reaction sequences:dominatesby farof course p’s, n’s, and a’s are recaptured … 23Mg can b-decay into 23NaComposition at the end of burning:mainly 20Ne, 24Mg, with some 21,22Ne, 23Na,
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