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Stellar Nucleosynthesis

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Stellar Nucleosynthesis Stellar Nucleosynthesis What makes the sun shine? Gravitaonal contrac7on Chemical reac7ons Nucleosynthesis Stellar Nucleosynthesis The PP chain The CNO cycle The Triple alpha process …and on to Fe Stellar Spectra Blackbody spectrum Connuum Emission and absorp7on lines What makes the Sun Shine • Luminosity of Sun measured to be: – 3.8x1026W (from measured flux W m-2 and distance) • Gravitaonal contrac7on (Kelvin-Helmholtz): – Grav. Energy is u=M.GM/R = 4 x1041J (if all mass placed at surface) – Sufficient to fuel sun for 33 million years – Oldest rocks dated to be ~4billion years • Chemical reac7ons: – Burning Coal releases: 10-19 J per atom – Luminosity implies a mass loss of 2x1026 kg per year – Sufficient for sun to last 10 thousand years • Nuclear Fusion (Einstein): – E=mc2 implies E=1.8x1047J – Sufficient to fuel sun for 15,010 billion years Stellar Nucleosynthesis Base fuel is hydrogen (and some helium with traces of CNO) • Three key reac7on chains: – Proton-proton chain – Carbon-Nitrogen-Oxygen cycle – Triple-Alpha process • But fusion requires high temperatures… Core Temperature of Sun • Assuming the Sun is in hydrostac equilibrium the thermal pressure is sufficient to resist gravitaonal contrac7on • Crudely, consider the mass (m) pressing on the core: m = !AR GmM G!AM Assumes constant F = = R2 R density so not quite right but true answer F !GM P = = based on more precise c A R equaons which !GM incorporate the density Pc V = nkTc = variaon is close: R 15 million K nmpGM mpGM Tc = = Enough to overcome nkR kR the Coulomb Force to allow Fusion to occur Tc = 23 million K The p-p chain CNO cycle • Another way to progress Hydrogen to Helium • Requires Carbon to be present which acts as a catalyst To pp or to CNO? Efficiency depends on temperature of the core, which govern the reac7on rates. • For the MO. < 1.3 pp dominates. • For MO. > 1.3 CNO will dominate. Beyond Helium: Triple alpha • Major bohle neck due to instability (low binding energy) of elements with atomic numbers 5-8 Progression depends on reversible reac7on. High density and abundant energy required For triple-alpha to occur = High mass stars only Triple-α only occurs in massive stars Beyond Helium Numerous paths exist to progress up the valley of stability if other elements are already present but generally require even more temperature/pressure to occur Typically only happen in very Massive stars or during SN Explosion (see later lecture). CNO cycle Nucleon Binding Energies Valley of Stability Stellar spectra • Stars are hot gas balls and behave like any hot gas: – Black body spectrum 3 2h! h! • Intensity kT in Wm-2Hz-1ster-1 I(!,T) = 2 (e !1) c 4" u(!,T) = I(v,T) • Energy density c in Wm-3Hz-1 – Wien’s displacement Law "3 2.9 !10 !MAX = T – Stephan-Boltzmann Law ! • From integrang the energy density ! = " AT 4 = " u(v,T)dv 0 • or for spherically symmetrical systems: L = 4# R2"T 4 Surface Temp of Sun • The Sun’s black body spectrum peaks at 500nm use Wein’s Law to get temperature? 2.9 !10"3 T = = 5800K Surface 500 10"9 ! – Surface temperature is 5800K – Core temperature is 15 million K – Nuclo-synthesis only occurs in the solar core • Core radius ~20-25% of the Solar Radius Implied solar radius • Can use Stefan-Boltzmann Law to measure implied solar radius, using known Luminosity and Temp. L 3.8!1026 R = = 4!"T 4 4!(5.67!10"8 )57434 R = 7.0 !108 m – Note have used slightly more accurate value of Temp Black body spectrum • Hoher star spectra peak at bluer wavelengths = BLUE • Colder star spectra peak at red or near-IR wavelengths= RED • Overall a hoher objects gives off more energy (integral under curve) Solar spectrum v Black Body General connuum shape OK but lots of lines on top, why? Kirchhoff’s laws Spectral analysis shows us: 1) A hot opaque body, such as a hot dense gas, emits light at all wavelengths - i.e. it produces a con7nuous 'blackbody' spectrum 2) A hot transparent gas emits an emission-line spectrum - a series of bright spectral lines, plus a faint superimposed con7nuous spectrum. 3) A cool transparent gas in front of a con7nuous-spectrum source produces an absorp7on-line spectrum - a series of dark spectral lines superimposed upon the con7nuous spectrum. Kirchhoff’s laws of spectral analysis 3. Continuous + absorption-line spectrum blackbody Cloud of gas prism prism prism 2. Emission-line spectrum + weak continuum 1. Continuous spectrum Absorp7on and Emission Lines Hydrogen oqen seen in both emission and absorp7on. Hydrogen series UV OPTICAL NIR FIR mm/RADIO Rydberg Formulae for Hydrogen 1 % 1 1 ( = R#' 2 $ 2 * " & n1 n2 ) ! Each element has a characteris7c spectral paern Cold, low-mass, red Examples of stellar spectra Hot, high-mass, Blue .
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