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Big Bang Nucleosynthesis

Big Bang Nucleosynthesis. (BBN) Eildert Slim. Timeline of the Universe. Baryon Asymmetry. Baryon abundance parameter η B = (n B - n ̅B )/n γ η B very small: η 10 = 10 10 η B Matter-antimatter asymmetry: η 10 = 10 10 (n B /n γ ) 0 = 274 Ω B h 2 η 10 ≈ 6. Neutron-Proton Reactions.

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Big Bang Nucleosynthesis

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  1. Big Bang Nucleosynthesis (BBN) Eildert Slim

  2. Timeline of the Universe

  3. Baryon Asymmetry Baryon abundance parameter ηB = (nB - n ̅B)/nγ ηB very small: η10 =1010ηB Matter-antimatter asymmetry: η10 =1010 (nB/nγ)0= 274ΩBh2 η10 ≈ 6

  4. Neutron-Proton Reactions Weak interactions: n ↔ p + e- +  ̅ν ν + n ↔ p + e- e+ + n ↔ p + ̅ν nγ >> nB

  5. Rate of Weak Reactions: Г • Integrate square of matrix element • Weigh by phase-space densities • Enforce four-momentum conservation For T > me: Г/H ~ (T/0.8 MeV)3

  6. Expansion rate H at BBN Friedman equation: H2 = (8π/3)GN ρTOT Prior to BBN: ρTOT = ργ + ρe + 3ρν = (43/8)ργ During SBBN:ρTOT = ργ + 3ρν = 1.68ργ

  7. Nuclear Statistical Equilibrium I Kinetic equilibrium: • Particles have same temperature Chemical equilibrium: • Same forward and reverse reaction rates • Applies if Г >> H Valid until T ≈ 0.8MeV Implies μn + μν= μp + μe

  8. Nuclear Statistical Equilibrium II Number density nA of non-relativistic nuclear species A(Z): nA = gA (mAT/2π)3/2 exp((μA – mA)/T) Chemical potential μA of A(Z): μA = Zμp + (A – Z)μn

  9. Nuclear Statistical Equilibrium III Number density nA of A(Z): nA = gAA3/22-A(2π/mNT)3(A-1)/2npZnnA-Z exp(BA/T) With binding energy BA: BA = Zmp + (A – Z)mn – mA

  10. Mass Fraction Total nucleon density: nN = nn + np + Σi(AnA)i Mass fraction contributed by A(Z): XA = nAA/nN ΣiXi = 1

  11. Neutron-Proton ratio in Equilibrium Until T ≈ 0.8 MeV: nn/np = Xn/Xp = exp [-Q/T + (μe – μν)/T] Where Q = mn – mp = 1.293 MeV Assume (μe – μν)/T small: (nn/np)EQ = exp(-Q/T)

  12. Equilibrium vs non-Equilibrium I

  13. Neutron-Proton Ratio T >> 0.8 MeV: Xn = Xp T > 0.8 MeV: Xn/Xp calculated by NSE (n/p)freeze-out = exp (-Q/TF) ≈ 1/6 → TF ≈ 0.7 MeV

  14. Basic Fusion Processes I Fusion reaction: A + B → C + … Possible reactions: - Need maximum of 2 particles A and B - A or B must exist in sufficient quantity 2-particle reactions: p + n → 2H 2H + p → 3He 3He + n → 4He

  15. Basic Fusion Processes II

  16. Light elements’ isotopes

  17. Energy vs Entropy I Energy: Binding Energy of 2H = 2,2 MeV At T < 2,2 MeV 2H is energetically favoured Entropy: Number of photons >> number of baryons Many photons higher than average energy High energy photons break up 2H Thermodynamics combines energy and entropy

  18. Energy vs Entropy II Estimate T at which 2H becomes thermodynamically favoured: TNUC = (BA/(A – 1))/(ln(η-1) + 1.5ln(mN/T)) 2H: TNUC = 0.07MeV 3He: TNUC = 0.11MeV 4He: TNUC = 0.28 MeV

  19. Production of Light Elements I t = 10-2 sec, T = 10 MeV - Very small abundance of light nuclei - High energy photons destroy light nuclei immediately Xn, Xp = 0.5

  20. Production of Light Elements II t ≈ 1 sec, T ≈ 1 MeV - Very small abundance of light nuclei - Weak interactions freeze out at Г < H • (n/p)freeze-out = exp (-Q/TF) ≈ 1/6 • (n/p) continues to decrease due to neutron decay Xn ≈ 1/7, Xp ≈ 6/7

  21. Production of Light Elements III t ≈ 1 min, T ≈ 0.3 MeV • 4He becomes thermodynamically favoured • High energy photons destroy 2H, 3H and 3He quickly • Coulomb-barrier suppression becomes significant → 4He production is slowed down

  22. Production of Light Elements IV t ≈ 3 min, T ≈ 0.1 MeV • 2H, 3H and 3He become thermodynamically favoured • More 4He is produced • All free neutrons are bound into 4He.

  23. Production of Light Elements V

  24. Heavy Elements • Stable at high T • Need lighter elements to form • Lighter elements have too low abundance at high T • At low T Coulomb-barrier suppression too strong

  25. Elements Produced Some D, 3He and 7Li is synthesized: 7Li/H ~ 10-10 to 10-9 D, 3He/H ~ 10-5 to 10-4 Remaining neutrons are bound into 4He: X4 ≈ 2(n/p)NUC/(1 + (n/p)NUC = (2/7)/(1 + 1/7) = 1/4

  26. Important Parameters Higher τ1/2(n): - Decreases weak rates - Causes freeze out at higher T - Larger 4He abundance Higher g*: - Faster expansion rate - Causes freeze out at higher T Higher η: - Fewer photons - 2H, 3H, 3He build up earlier - Less 2H, 3H, 3He remains unburnt

  27. Dependence on η

  28. Observations We would like to measure primordial, cosmic abundances. We can only measure present-day abundances in selected sites.

  29. Observations of 2H Properties: • Easy to destroy, hard to produce: • Observations provide lower bound Abundance has been measured: • In solar system studies • In studies of deuterated molecules - In UV absorption studies of local interstellar medium Results: • 2H/H = (1.5 to 2.9) x 10-5: • η < 10-9.

  30. Observations of 3He Properties: • Produced from 2H in stars • Difficult to destroy without producing heavier elements Abundance has been measured: • In solar system studies: • In meteorites corresponds with pre-solar 3He • In solar wind corresponds with pre-solar 2H + 3He • In galactic HII regions Results: • 3He+/H ≈ (1.2 to 15) x 10-5 • [(2H + 3He)/H] ≈ (3.6 ± 0.6) x 10-5 • Can be astrated by a factor ≤ 2: • [(2H + 3He)/H]P≤ 8 x 10-5

  31. Observations of 7Li Properties: • Produced by cosmic rays and in stars • Easily destroyed Abundance has been measured: • In unevolved halo stars with low metal abundances • Plateau in 7Li abundance was found in heavy stars: • Lower mass stars astrate 7Li Results: • Primordial 7Li abundance follows from plateau: • 7Li/H ≈ (1.1 ± 0.4) x 10-10: • η = (1 to 7) x 10-10

  32. Observations of 4He • Produced in stars • Stars produce metals too • Correlation between 4He and metals shows primordial 4He • YP ≈ 0.22 to 0.26

  33. Observations: Conclusion - Nucleosynthesis produces only 2H, 3He, 4He and 7Li. • Good agreement between predicted and observed abundances • Corresponding parameter-values: • 10.3 min ≤ τ1/2(n) ≤ 10.7 min • 4 x 10-10 ≤ η ≤ 7 x 10-10

  34. Caveats • Theorized generation of heavy stars • Could destroy 3He and 7Li • Present agreement would disappear • Xn/Xp = exp [-Q/T + (μe – μν)/T] • μν unknown • Is assumed small or equal to μe • Would affect 4He abundance if not

  35. Dark matter Assuming standard model is valid: 4 x 10-10 ≤ η ≤ 7 x 10-10 0.015 ≤ ΩB ≤ 0.016 Measurements of Ω0 suggest Ω0 = 0.2 ± 0.1 Hence a non-baryonic form of matter must account for difference.

  36. References: Graphs from “The Early Universe”, by Edward W. Kolb and Michael S.Turner Fusion image from ned.ipac.caltech.edu.

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