Stellar Nucleosynthesis

What makes the sun shine? Gravitaonal contracon Chemical reacons Nucleosynthesis Stellar Nucleosynthesis The PP chain The CNO cycle The Triple alpha process …and on to Fe Stellar Spectra Blackbody spectrum Connuum Emission and absorpon lines What makes the Sun Shine

• Luminosity of Sun measured to be: – 3.8x1026W (from measured flux W m-2 and distance) • Gravitaonal contracon (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 reacons: – 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 reacon 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 contracon • 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 reacon rates. • For the MO. < 1.3 pp dominates. • For MO. > 1.3 CNO will dominate. Beyond Helium: Triple alpha

• Major bole neck due to instability (low binding energy) of elements with atomic numbers 5-8

Progression depends on reversible reacon. 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 • Hoer star spectra peak at bluer wavelengths = BLUE • Colder star spectra peak at red or near-IR wavelengths= RED • Overall a hoer 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 connuous 'blackbody' spectrum

2) A hot transparent gas emits an emission-line spectrum - a series of bright spectral lines, plus a faint superimposed connuous spectrum.

3) A cool transparent gas in front of a connuous-spectrum source produces an absorpon-line spectrum - a series of dark spectral lines superimposed upon the connuous 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 Absorpon and Emission Lines Hydrogen oen seen in both emission and absorpon. Hydrogen series

UV OPTICAL NIR FIR mm/RADIO Rydberg Formulae for Hydrogen

1 % 1 1 ( = R#' 2 $ 2 * " & n1 n2 )

! Each element has a characterisc spectral paern Cold, low-mass, red

Examples of stellar spectra

Hot, high-mass, Blue