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Lecture-04 Big-Bang Nucleosysthesis Ping He ITP. CAS. CN 2006. 03. 04 http: //power. itp. 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 Basic Ideas of Nucleosynthesis • H, He, Li, … Light-elements are produced by big-bang nucleosysthesis (BBN); • Heavy metals (Fe) are generated in SNs. 2

4. 0 Preliminaries In nuclear physics For pre-exponential factors: 3 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 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 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. 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 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 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 So, we have: Based upon charge neutrality, we have: Similarly: 9

The equilibrium n/p ratio: T n/p → high → 1 10 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 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 Lifetime of neutron Since So half-life of neutron: In fact: 12

So, we have: where In high- and low-Temperature limits: 13 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. 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 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. 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 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 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 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 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 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 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, 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 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 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 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 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 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 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 Predicted He-4 abundance Present observations suggest that: 30

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

Problem? 32 Problem? 32

4. 6 Primordial Nucleosynthesis as a Probe a) non-baryonic form of matter From the 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 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 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 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