Lecture 3: Big Bang Nucleosynthesis The First Three Minutes

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1 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

2 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.

3 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 He ++ 4 He p& '

4 Binding Energies

5 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.

6 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 - )

7 Lose 2 neutrons and 2 protons α decay Photon emission

8 β decay n => p + e - Positron emission p => n + e + Electron capture p + e - => n

9 Valley of stability

10 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 He ++ 7 Li e + + γ 3 He He ++ 7 Be γ 7 Be 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.

11 BBN reactions in full All paths lead to He 4 because of stability

12 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.

13 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).

14 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

15 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 neutrons decay into protons

16 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 = If cooling much slower, all neutrons decay à X p = 1 Y p = 0.

17 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

18 Baryon Density Constraint Observed He/H matches! Observed D/H requires: ρ crit # H Ω 0 & b % ( $ 70 ' = ± ~4% baryons Less Deuterium at higher densities Confirmed by an independent result from the CMB ripples.

19 Observational constraints on primordial abundances à

20 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

21 Primordial D/H measurement Lα (+Deuterium Lα) line in quasar spectrum:

22

23 Deuterium measurements

24 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.

25 Baryon density constraints

26 The elemental abundance of the solar system (Sun)

27 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

28 SUGGESTED TALK TITLES COSMOLOGY what is symmetry breaking, any evidence dark matter particle searches latest deuterium abundance measurements latest constraints from nearby low metallicity galaxies inhomogeneous big bang nucleosynthesis STAR-FORMATION what is alpha-enhancement and what is it telling us what is the g-dwarf problem and whats the best explanation beyond the closed box model evidence for infall and outflows the mass-metallicity relation the main sequence

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