1. 1 Lecture-04 Big-Bang Nucleosysthesis http://power.itp.ac.cn/~hep/cosmology.htm Ping He ITP.CAS.CN 2006.03.04

2. 2 H, He, Li, … Light-elements are produced by big-bang nucleosysthesis (BBN); Heavy metals (<Fe) are created in stars; Super-heavy metals (>Fe) are generated in SNs. Basic Ideas of Nucleosynthesis

3. 3 4.0 Preliminaries In nuclear physics For pre-exponential factors:

4. 4 4.1 Nuclear Statistical Equilibrium (NSE) When thermal equilibrium, for nuclear species A, the number density is

5. 5 Moreover, chemical equilibrium Eq-3.1 also applies to n, p, hence we have

6. 6 Definition of binding energy of the nuclear species A(Z) Substituting Eq-3.3 into 3.1, the abundance of A is: Table-1

7. 7 Define total nucleon density: So Eq-3.5 becomes: Baryon-to-photon ratio So in NSE, the mass fraction of species A, 丰度：质量百分比 n B =n N

8. 8 4.2 Initial Conditions (T>>1MeV, t<<1sec) Key points: neutron-to-proton ratio The balance of neutron and proton is maintained by the weak interactions: IfChemical equilibrium

9. 9 So, we have: Based upon charge neutrality, we have: Similarly:

10. 10 The equilibrium n/p ratio: T → high n/p → 1

11. 11 Rates for interactions between neutrons and protons, for example In terms of neutron lifetime

12. 12 Lifetime of neutron Since So half-life of neutron: In fact:

13. 13 So, we have: where In high- and low-Temperature limits:

14. 14 By comparing to the expansion rate,, we have: Thus when T>0.8MeV, n/p -> equilibrium value, from (Eq-3.12), T->high, n/p ->1 At T>1MeV, rates of nuclear reactions for building up the light elements are also high -->NSE

15. 15 Consider the following light elements: n, p, D-2, He-3, He-4, C-12, in NSE, the mass fractions are:

16. 16 From Eq-3.7, when X T nuc (MeV) D-20.07 He-30.11 He-40.28 C-120.25 Table-2

17. 17 4.3 Production of the Light Elements: 1-2-3 The weak rates are much larger than the expansion rate H, so (n/p)=(n/p) eq ~1, and light elements are also in NSE. From Eq-3.20 to Eq-3.25 4.3.1 step 1 ( t= sec, T=10MeV)

18. 18 4.3.2 step 2 ( t= 1sec, T=T F =1MeV) The weak interactions that interconvert n and p freeze out ( ) Not really constant due to residual weak interactions. The deviation of n/p from its equilibrium value becomes significant by the time nucleosynthesis begins. (See Fig.4.1) (See Fig.4.1) At this time, the light nuclei are still in NSE.

19. 19 4.3.3 step 3 ( t= 1 to 3 minutes, T=0.3 to 0.1 MeV) Major nuclear reactions: due to occasional weak interactions

20. 20 is very low, due to a). low abundances for D-2, He-3, and H-3, their NSE values: The light-element bottleneck Deuterium bottleneck: NSE that is, there are 109-1010 photons around one nucleon. So when T=0.1MeV, t=3min, not enough high-energy photons (E>2.2MeV) to disassociate D-2.

21. 21 b). Coulomb-barrier suppression: : thermally-averaged cross section times relative velocity. If abundances of D-2, He-3, H-3  1 at T NUC =0.1MeV Bottleneck is broken

22. 22 Li-7: An abundance of the order, is predicted by: H/p and He-4 are in dominative amounts; Nuclei of A=5 and 8 are unstable, and with high Coulomb-barrier suppression, BBN is stopped at He-4, so that no heavier elements produced. Substantial amounts of both D-2 and He-3 are left: So:

23. 23 So, T should not be too high, i.e., T<0.1MeV, t=3min otherwise, photon disassociation However, T should not be too low, i.e., T>0.02MeV, t~1hr otherwise, kinetic energy not high enough to penetrate Coulomb potential.

24. 24 4.4 Primordial Abundances: Predictions What affect primordial nucleosynthesis?

25. 25 An accurate analytic fit for primordial mass fraction of He-4 Primordial He-4 abundance Li-7 production process-I Li-7 production process-II

26. 26 4.5 Primordial Abundances: Observations Primordial nucleosynthesis: 3min  1hr Age of the universe: 13.8 billion years The difficulty of measurement: contaminants from astrophysical processes, such as stellar production and destruction. Specifically: 4.5.1 measurement of D a) via the UV absorption studies of the local interstellar medium (ISM) in the solar system. Atmosphere of Jupiter : (DCO, DHO) Consistent with Hard task

27. 27 b) high-z QSO absorption line Since deuteron is weakly-bound  easy to be destroyed Primordial NSE value of D/H < 10^(-13), only when “the deuterium bottleneck” is broken, deuteron can be accumulated in great amount. In a star, more dense, so in NSE  D/H < 10^(-13) See Fig-4.4, constrain  :

28. 28 4.5.2 measurement of He-3 hotter interiors: He-3 is destroyed cooler outer layers: He-3 is preserved low mass star : new He-3 from hydrogen burning Notice that in a star, the processes for He-3 more complicated: a) measure of oldest meteorites: b) measure of solar wind: Also provides constraint to 

29. 29 4.5.3 measurement of He-4 He-4 can also be synthesis in stars Hence, low Z  low Y  Primordial abundance

30. 30 Predicted He-4 abundance Present observations suggest that:

31. 31 4.5.4 measurement of Li-7 Lithium abundances versus metallicity (from a compilation of stellar observations by V.V. Smith.)

32. 32 Problem?

33. 33 4.6 Primordial Nucleosynthesis as a Probe a) non-baryonic form of matter From the concordance of D, He-3, He-4, Li-7 abundances, we derive From dynamical determinations Dark matter

34. 34 b) Number of light neutrino flavors present observation or cold components

35. 35 4.7 Final Words Primordial nucleosynthesis: agreement between theory and observation indicating the standard cosmology is valid back to 10- 2 sec, or T=10MeV; Works as a probe for cosmology (  B), and particle physics (  v), etc; More precise observations for D, He-3, He-4, Li- 7 are of great importance.

36. 36 References E.W. Kolb & M.S. Turner, The Early Universe, Addison-Wesley Publishing Company, 1993 L. Bergstrom & A. Goobar, Cosmology and Particle Astrophysics, Springer, 2004 M.S. Longair, Galaxy Formation, Springer, 1998 俞允强，热大爆炸宇宙学，北京大学出版社， 2001 范祖辉， Course Notes on Physical Cosmology, See this site.this site