Stellar Nucleosynthesis
What makes the sun shine? Gravita onal contrac on Chemical reac ons Nucleosynthesis Stellar Nucleosynthesis The PP chain The CNO cycle The Triple alpha process …and on to Fe Stellar Spectra Blackbody spectrum Con nuum Emission and absorp on lines What makes the Sun Shine
• Luminosity of Sun measured to be: – 3.8x1026W (from measured flux W m-2 and distance) • Gravita onal contrac on (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 reac ons: – 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 reac on 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 hydrosta c equilibrium the thermal pressure is sufficient to resist gravita onal contrac on • 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 equa ons which !GM incorporate the density Pc V = nkTc = varia on 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 reac on rates. • For the MO. < 1.3 pp dominates. • For MO. > 1.3 CNO will dominate. Beyond Helium: Triple alpha
• Major bo le neck due to instability (low binding energy) of elements with atomic numbers 5-8
Progression depends on reversible reac on. 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 integra ng 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 • Ho er star spectra peak at bluer wavelengths = BLUE • Colder star spectra peak at red or near-IR wavelengths= RED • Overall a ho er objects gives off more energy (integral under curve) Solar spectrum v Black Body
General con nuum 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 con nuous 'blackbody' spectrum
2) A hot transparent gas emits an emission-line spectrum - a series of bright spectral lines, plus a faint superimposed con nuous spectrum.
3) A cool transparent gas in front of a con nuous-spectrum source produces an absorp on-line spectrum - a series of dark spectral lines superimposed upon the con nuous 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 Absorp on and Emission Lines Hydrogen o en seen in both emission and absorp on. Hydrogen series
UV OPTICAL NIR FIR mm/RADIO Rydberg Formulae for Hydrogen
1 % 1 1 ( = R#' 2 $ 2 * " & n1 n2 )
! Each element has a characteris c spectral pa ern Cold, low-mass, red
Examples of stellar spectra
Hot, high-mass, Blue