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Lecture-04 Big-Bang Nucleosysthesis Ping He ITP. CAS. CN 2006. 03. 04 http: //power. itp. ac. cn/~hep/cosmology. htm 1

Basic Ideas of Nucleosynthesis • H, He, Li, … Light-elements are produced by big-bang nucleosysthesis (BBN); • Heavy metals (

4. 0 Preliminaries In nuclear physics For pre-exponential factors: 3

4. 1 Nuclear Statistical Equilibrium (NSE) When thermal equilibrium, for nuclear species A, the number density is 4

Moreover, chemical equilibrium Eq-3. 1 also applies to n, p, hence we have 5

Definition of binding energy of the nuclear species A(Z) Substituting Eq-3. 3 into 3. 1, the abundance of A is: Table-1 6

Define total nucleon density: 丰度：质量百分比 So Eq-3. 5 becomes: n. B=n. N Baryon-to-photon ratio So in NSE, the mass fraction of species A, 7

4. 2 Initial Conditions (T>>1 Me. V, t<<1 sec) Key points: neutron-to-proton ratio The balance of neutron and proton is maintained by the weak interactions: If Chemical equilibrium 8

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

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

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

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

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

By comparing to the expansion rate, , we have: Thus when T>0. 8 Me. V, n/p -> equilibrium value, from (Eq-3. 12), T->high, n/p ->1 At T>1 Me. V, rates of nuclear reactions for building up the light elements are also high -->NSE 14

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

From Eq-3. 7, when Table-2 X Tnuc (Me. V) D-2 0. 07 He-3 0. 11 He-4 0. 28 C-12 0. 25 16

4. 3 Production of the Light Elements: 1 -2 -3 4. 3. 1 step 1 ( t= sec, T=10 Me. V) 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 17

4. 3. 2 step 2 ( t= 1 sec, T=TF=1 Me. V) 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) • At this time, the light nuclei are still in NSE. 18

4. 3. 3 step 3 ( t= 1 to 3 minutes, T=0. 3 to 0. 1 Me. V) due to occasional weak interactions Major nuclear reactions: 19

Deuterium bottleneck: NSE that is, there are 109 -1010 photons around one nucleon. So when T=0. 1 Me. V, t=3 min, not enough high-energy photons (E>2. 2 Me. V) to disassociate D-2. is very low, due to a). low abundances for D-2, He-3, and H-3, their NSE values: The light-element bottleneck 20

b). Coulomb-barrier suppression: : thermally-averaged cross section times relative velocity. Bottleneck is broken If abundances of D-2, He-3, H-3 1 at TNUC=0. 1 Me. V 21

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: 22

So, T should not be too high, i. e. , T<0. 1 Me. V, t=3 min otherwise, photon disassociation However, T should not be too low, i. e. , T>0. 02 Me. V, t~1 hr otherwise, kinetic energy not high enough to penetrate Coulomb potential. 23

4. 4 Primordial Abundances: Predictions What affect primordial nucleosynthesis? 24

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

4. 5 Primordial Abundances: Observations Primordial nucleosynthesis: 3 min 1 hr Age of the universe: 13. 8 billion years Hard task 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 26

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 h: 27

4. 5. 2 measurement of He-3 a) measure of oldest meteorites: b) measure of solar wind: Notice that in a star, the processes for He-3 more complicated: hotter interiors: He-3 is destroyed cooler outer layers: He-3 is preserved low mass star : new He-3 from hydrogen burning Also provides constraint to h 28

4. 5. 3 measurement of He-4 can also be synthesis in stars Hence, low Z low Y Primordial abundance 29

Predicted He-4 abundance Present observations suggest that: 30

4. 5. 4 measurement of Li-7 Lithium abundances versus metallicity (from a compilation of stellar observations by V. V. Smith. ) 31

Problem? 32

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 33

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

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

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. 36