1. Cosmic Rays during BBN to Solve Lithium Problems
Mingming Kang
Collaborators : Yang Hu, Hongbo Hu, Shouhua Zhu
College of physical science and technology, Sichuan University
KIAA-WAP Ⅱ, Aug. 18, 2016

2. Contents Brief introduction to BBN The Lithium Problems1
The Lithium Problems 2
Our method – MeV cosmic rays in BBN 3
Calculation and Results 4
Conclusion 5

3. A brief introduction to BBN The theory
Big Bang Nucleosynthesis(BBN, for short) refers to the production of nuclei other than those of the lightest isotope of hydrogen(1H) during the early phases of the universe.
BBN is believed to have taken place from tens of seconds to 20 minutes after the Big Bang.
It is calculated to be responsible for the formation of most of the universe's 4He, along with small amounts of the deuterium(2H or D), 3He, and a very small amount of the lithium isotopes 7Li(decay from 7Be) and 6Li.

4. A brief introduction to BBN The main nuclear reaction chains in BBN
Before the epoch of nucleosynthesis, there are electrons,
positrons, neutrinos, neutrons and protons(heavier nuclei are
almost absent) in the plasma. It was hot and dense enough
for these particles to be in kinetic and chemical equilibrium.
As the Universe expansion proceeds(the temprature was
going down), neutrinos freeze out, the n/p density ratio departs
from its equilibrium value and freezes out at the value n/p = 1/7.
When the photon temperature become below the deuterium
binding energy, deuterium formed via n + p → 2H + γ process.
Once 2H starts forming, a whole nuclear process
network sets in, leading to heavier nuclei production
until BBN eventually stops.

5. The Lithium Problems Primordial nuclide abundance
Our knowledge of the abundances of light
elements in the early Universe has relied on
measurements of the chemical content of old
stars in the Milky Way’s halo.
Theoretical predictions of the primordial
abundances of light elements are based
on the precise determination of the cosmic
ratio of baryons to photons.
The measured primordial amounts of
hydrogen(H, D) and helium(4He, 3He(only upper
limit)) match the predictions.
But that of lithium does not.
PDG 2014

6. The Lithium Problems The Spite plateau
The chance to link primordial 7Li with the standard BBN abundance was first proposed by Spite & Spite (1982).
They showed that the lithium abundance in the metal-poor dwarfs was independent of metallicity for [Fe/H] < -1.5.
This constant lithium abundance is commonly called “the Spite plateau”.
The Spite plateau suggests that this may be the lithium abundance in pre-Galactic gas provided by the standard BBN.
Spite plateau

7. The Lithium Problems What are the “Lithium Problems”?
The BBN predicted abundance of 7Li is higher than that of observations.
The BBN predicted abundance of 6Li is lower than that of observations.
Observational abundance
7Li/H = (1 ～2) × 10-10
6Li/H ～6 × 10-12
Theoretical abundance
7Li/H = ( ) × 10-10
6Li/H ～ 10-14

8. The Lithium Problems Some methods solving the problems
Modification to the BBN scenario:
--Particle Decay, Evaporate, Annihilate, Catalyze
--Variable constants (effective couplings; neutron lifetime …)
The observed Lithium abundance is not primordial
--Astrophysical origin
Comments:
Updated observations show that the second way are moving farther and farther
away from the target.
Some of the first solutions can solve the lithium-7 problem, but they will let the
lithium-6 problem worse.

9. Our method – MeV cosmic rays in BBN
Reasons for the existence of cosmic rays in BBN
The absolute thermal equilibrium can’t be maintained because
of the rapid cosmic expansion.
Plasma turbulence acceleration?
The field seeds born in the electroweak phase transition epoch
evolve into BBN?
Deviating from the thermal equilibrium because of the original
perturbation?
Anyway, we give the hypothesis that
there are non-thermal energetic particles(BBNCR) in the BBN period !

10. e+, e- × quickly thermalized n × not easy to be accelerated p, d, t √
Our method – MeV cosmic rays in BBN Candidates for cosmic ray particles in BBN
e+, e × quickly thermalized
ϒ × quickly thermalized
n × not easy to be accelerated
p, d, t √
4He, 3He, etc √
The nucleon energy loss due to Coulomb collisions;
The electron energy loss due to Compton scattering and synchrotron.

11. Our method – MeV Cosmic rays in BBN BBN cosmic ray(BBNCR) spectrum
The highest energy of energetic hydrogen isotopes is a model parameter, named Eupper.
Assuming that electric-charged particles are accelerated by electromagnetic force, and that the gain energy is proportional to the electric charge, then Eupper(He) = 2Eupper .
The proportion of energetic particles to the thermal ones is set as the other free paremeter, named ε, which is unchanging during the BBN period.
The explicit expression of energy distribution
with a “knee” and “GZK” cutoff：

12. Our method – MeV Cosmic rays in BBN The critical nuclear reactions
For 7Li problem：
7Be + p -> 4He + 3He + p Eth = MeV
2H + p -> n + 2p Eth = MeV
For 6Li problem：
4He + 3He -> p + 6Li Eth = MeV
2H + 4He -> n + p + 4He Eth = MeV
We introduce energetic particles into BBN to open the endothermic reactions to account for the lithium problems.
The endothermic reactions with the lowest threshold energy destroying 7Be and producing 6Li are 7Be(p, pα)3He and 3He(α, p)6Li, respectively.
The reactions with the lowest threshold energy destroying D by proton and 4He are D(p, n)2H and 4He(d, α)np, respectively.
The highest threshold energy of these 4 reactions is MeV, if BBNCRs really work all reactions with a threshold below this energy will occur!.
There are nearly 200 such reactions associated with light nuclides(isotopes of hydrogen, helium and lithium)! We have to pick out those important ones ignoring those that have no
effect on the abundances of light elements.

13. Our method – MeV Cosmic rays in BBN Reactions added into BBN code
D(p, n)2H Eth = destroy D
D(d, n)3He destroy D
D(d, p)T destroy D
T(d, n)4He destroy D
D(p, g)3He destroy D
4He(d, np) 4He Eth = destroy D
7Be(p, pα)3He Eth = destroy 7Be
7Be(α, 2α)3He Eth = destroy 7Be
7Be(α, p)10B Eth = destroy 7Be, produce 10B
7Li(p, n)7Be Eth = destroy 7Li
7Li(p, α)4He destroy 7Li
4He(t, g)7Li produce 7Li
4He(t, n)6Li Eth = produce 6Li
3He(α, p)6Li Eth = produce 6Li
7Li(d, t)6Li Eth = produce 6Li
7Be(d, 3He)6Li Eth = produce 6Li
4He(d, g)6Li produce 6Li
D(α, g)6Li produce 6Li
6Li(α, p)9Be Eth = destroy 6Li, produce 9Be
6Li(α, d)24He Eth = destroy 6Li
6Li(p, α)3He destroy 6Li

14. Calculation and Results The set of differential equations ruling the BBN
Definition of Hubble parameter H
Baryon number conservtion
Entropy conservtion
Boltzmann equations
for Nnuc
Universe charge
neutrality
Boltzmann equations
for neutrino species

15. Calculation and Results Modification in the BBN code – calculation of new processing rates
Each new reaction will contribute
a processing rate to the Boltzmann
equation to change the abundance
of related nuclide.

16. Calculation and Results The production and destruction rate of 7Be (7Li)
Processing rates of the reactions of
Destroying and producing 7Be(or 7Li).
The reactions with BBNCR work later than the thermal ones
The reactions with BBNCR will delay BBN.

17. Calculation and Results The production and destruction rate of 6Li
Processing rates of the reactions of
Destroying and producing 6Li.

18. Calculation and Results The evolution of light element abundance as a function of the Universe’s temperature
ε = 2x10-5
Eupper = 3.7MeV
7Be
6Li
Element abundances as a function of the Universe’s temperature. Solid lines
Denote the BBNCR results and dashed lines those for standard BBN.

19. Calculation and Results The parameter space
7Li/H = (1.3 ～1.9) × 10-10
6Li/ 7Li < and 6Li /H >
7Li/H = (1.3 ～1.9) × 10-10
6Li/ 7Li < and 6Li /H >
Because only the upper bound of 6Li is measured, we give two results
corresponding to two lower bounds.
The red area indicate the BBNCR predicted abundances fall into the observationally
allowed range.

20. Calculation and Results Abundance variation range
7Li/H = (1.3 ～1.9) × 10-10
6Li/ 7Li < and 6Li /H >
D, 7Be, and 6Li abundances as a function of the Universe’s
temperature with the observationally allowed ε and Eupper range.

21. Calculation and Results Model test
On cross-section uncertainties
-- trial cross-sections (7Be(p, pα)3He and 3He(α, p)6Li) time 1/10
-- the cross-sections are constant, using the value once the energy exceeds the threshold. (0.22 mb and 5.2 mb, respectivly)
On energy spectrum uncertainty
-- uniform distribution all through
Our hypothesis is insensitive to the amplitude or resonance peak of the
uncertain cross-sections and also insensitive to the explicit shape of the
BBNCR energy spectrum.

22. Calculation and Results Model test
The parameter space of different observations, cross-section test,
and energy spectrum test.

23. Calculation and Results Predictions
BBNCRs may promote 10B via 7Be(α, p)10B to approaching the upper limit of observations, and also produce more 9Be, isotopes of C, N, O.

24. Conclusion
The Lithium Problem is still a puzzle after 30 years, to answer this problem requires new thoughts.
We take the concept of cosmic rays into BBN for the first time and find it effective on both 7Li and 6Li problems without excessive depletion of deuterium.
The BBN cosmic ray(BBNCR) flux in the model is small enough (~10-5 relative to the background) to keep the success of standard BBN(SBBN) and the BBNCR need to be accelerated to MeV.
Our hypothesis is insensitive to the amplitude or resonance peak of the uncertain cross-sections and also insensitive to the explicit shape of the BBNCR energy spectrum.
We predict more primordial 10B and more CNO which would affect the
first generation of stars(or Population Ⅲ), precise observations may
or may not support our hypothesis.
The acceleration mechanism in BBN and possible observational consequences of BBNCR are interesting subjects to explore.

25. Thanks

26. Recent observation data

27. The spectrum of BBNCR

28. On the reaction cross sections
1， D（p，n）2H √
2， T（a，n）Li √
3， （He4（t，n）Li ） shift the data of reaction 2
4， Be7（a，p）B √
5， Be7（a，aa）He √
6， He4（He3，p）Li √
7， He4（d，np）He shift the data of reaction 1
and times 5
8， Li6（a，p）Be √
9， Li6（a，d）Be √

29. Calculation and Results The 7Be abundance with different ε

30. preliminary
preliminary

35. Calculation and Results The evolution of light nuclide abundance (with high energy H isotopes only)
ε = 1.6x10-5
Eupper = 3.5 MeV
7Be
6Li