Lecture 3: Big Bang Nucleosynthesis The First Three Minutes Last time: particle anti-particle soup --> quark soup --> neutron-proton soup p / n ratio at onset of 2 D formation Today: Form 2 D and 4 He Form heavier nuclei? Discuss primordial abundances X p, Y p, Z p. Constrain baryon density
Onset of Big Bang Nucleosynthesis Deuterium production delayed until the high energy tail of blackbody photons can no longer break up D. Binding energy: E = 2.2 MeV. E / k T ~ ln N γ n + p D + γ ( N ) B = ln 10 9 k T ~ 0.1 MeV ( T ~ 10 9 K t ~ 400 s ) Thermal equilibrium + neutron decay: N p / N n ~ 7 Thus, at most, N D / N p = 1/6 ( ) ~ 20 Deuterium readily assembles into heavier nuclei.
Key Fusion Reactions product: Total binding energy: n + p D + γ Deuterium (pn) 2.2 MeV D + D 3 He ++ + n$ % p + D 3 He ++ + γ & n + D T + γ $ ' D + D T + p % ' n + 3 He ++ T + p& 3 He (ppn) 7.72 MeV Tritium (pnn) 8.48 MeV n + 3 He ++ 4 He ++ + γ $ ' D + 3 He ++ 4 He ++ + p ' p + T 4 He ++ + γ % 4 He (ppnn) 28.3 MeV D + T 4 He ++ ' + n ' 3 He ++ + 3 He ++ 4 He ++ + 2p& '
Binding Energies
Deuterium Bottleneck Note: 1) D has the lowest binding energy of any nucleon (2.2 MeV) hence D is the easiest to break up 2) Nuclei with A > 2 can t form until D is produced and stable as this would require 3-body collisions (unlikely) à Deuterium bottleneck - Nucleo-synthesis is delayed until D forms and stable - Then nuclei quickly progress to 4 He.
What about Heavier Nuclei? Z = number of protons A = atomic weight = protons + neutrons As protons increase, neutrons must increase faster for stable nuclei. Nuclei with Z > 83 or >126 neutrons UNSTABLE. e.g. α-decay (emit 4 He) β-decay (emit e - )
Lose 2 neutrons and 2 protons α decay Photon emission
β decay n => p + e - Positron emission p => n + e + Electron capture p + e - => n
Valley of stability
BBN stalls The main problem: 4 He very stable, 28 MeV binding energy. Nuclei with A = 5 are unstable! Further fusion is rare (lower binding energies): 3 He ++ + 4 He ++ 7 Li +++ + e + + γ 3 He ++ + 4 He ++ 7 Be 4 + + γ 7 Be 4 + + n 7 Li +++ + p 7 Li +++ + p 2 4 He ++ In stars, fusion proceeds because high density and temperature overcome the 4 He binding energy.
BBN reactions in full All paths lead to He 4 because of stability
Temperature- and time- line 1:5 neutron decay à Helium surge à 1:7 Helium abundance dependent on neutrons remaining. Residual Deuterium dependent on mean density.
Primordial Abundances Because 4 He is so stable, all fusion pathways lead to 4 He, and further fusion is rare. To first order: all neutrons end up in 4 He, and residual protons remain free. [i.e., p+p à 2 He does not occur] Therefore, given, N p / N n ~ 7, [Lecture 2] X p Y p mass in H total mass = N p N n N p + N n = 6 8 = 0.75 mass in He total mass = 2N n N p + N n = 2 8 = 0.25 Primordial abundances of H & He (by mass, not by number).
Primordial Metals In astronomy all nuclei with A > 4 (or with Z > 2) are known as metals Residual D, T, 7 Li, 7 Be. Z p mass of metals total mass ~ 0 Since the 1960 s, computers simulating Big Bang Nucleosynthesis, using known reaction rates, give more detailed abundance predictions: X p = 0.75 Y p = 0.25 Z p = 5x10-5
Big Bang Nucleosynthesis Expansion, cooling T R t 1 1/ 2 X p 0.75 Y p 0.25 Thermal equilibrium n n n p & exp $ % ( m n m k T p ) c 2 #! " Reactions freeze out due to expansion Z p 5 10 5 neutrons decay into protons
Sensitivity to Parameters Abundances depend on two parameters: 1) photon-baryon ratio (T at which D forms) 2) cooling time vs neutron decay time (proton - neutron ratio) If cooling much faster, no neutrons decay and N p / N n ~ 5 à X p = 4/6 = 0.67 Y p = 2/6 = 0.33. If cooling much slower, all neutrons decay à X p = 1 Y p = 0.
Baryon Density Constraint Abundances (especially D) sensitive to these 2 parameters. Why? Fewer baryons/photon, D forms at lower T, longer cooling time, more neutrons decay ==> less He. At lower density, lower collision rates, D burning incomplete ==> more D. Conversely, higher baryon/photon ratio ==> more He and less D. Photon density is well known, but baryon density is not. à The measured D abundance constrains the baryon density!! A very important constraint. Ω b 0.04
Baryon Density Constraint Observed He/H matches! Observed D/H requires: ρ crit # H Ω 0 & b % ( $ 70 ' = 0.040 ± 0.004 2 ~4% baryons Less Deuterium at higher densities Confirmed by an independent result from the CMB ripples.
Observational constraints on primordial abundances à
Primordial gas Observations can check the predictions, but must find places not yet polluted by stars. - D/H ratio from Lyman-alpha clouds: Quasar spectra show absorption lines. Line strengths give D/H abundance in primordial gas clouds (where few or no stars have yet formed). - He/H ratio from nearby low-metalicity dwarf galaxies: High gas/star ratio and low metal/h in gas suggest that interstellar medium still close to primordial
Primordial D/H measurement Lα (+Deuterium Lα) line in quasar spectrum:
Deuterium measurements
Primordial He/H measurement Emission lines from H II regions in lowmetalicity galaxies. Measure abundance ratios: He/H, O/H, N/H, Stellar nucleosynthesis increases He along with metal abundances. Find Y p by extrapolating to zero metal abundance.
Baryon density constraints
The elemental abundance of the solar system (Sun)
Summary Mostly H (75%) and 4 He (25%) emerge from the Big Bang, plus a few metals (~0%) up to 7 Li. The strong binding energy of 4 He largely prevents formation of heavy metals. Observed primordial abundances confirm predictions, and measure the baryon density Ω b 0.04 Next time: Matter-radiation decoupling Formation of the CMB
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