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2014/3/6

Lithium problem in big bang nucleosynthesis and its solutions by exotic nuclear reactions. Motohiko Kusakabe Korea Aerospace University Soongsil University. 2014/3/6. Content. Introduction to big bang nucleosynthesis (BBN) Standard cosmology Time evolution of nuclear abundances

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2014/3/6

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  1. Lithium problem in big bang nucleosynthesis and its solutions by exotic nuclear reactions Motohiko Kusakabe Korea Aerospace University Soongsil University 2014/3/6

  2. Content • Introduction to big bang nucleosynthesis (BBN) • Standard cosmology • Time evolution of nuclear abundances • Li problem • Effects of long-lived exotic particles on BBN • Strongly interacting particle • Negatively-charged particle • Radiatively decaying particle (sterile n)

  3. Introduction 1. Solar abundance Ryan (2000) H,He (BBN) Ne, Si, S, Ca (C, O, Si burning) Fe(NSE: supernova Ia) s(AGB), r(supernova), p(supernova) Li,Be,B (spallation+…)

  4. 2. Thermal history of the universe • Big Bang Theory  It was hot in the early universe • Signatures maybe left on elemental abundances ħ=c=kB≡1 1MeV=1.1605×1010 K Big Bang 200 MeV 1-0.01MeV 0.3eV 0.2meV Recombination of Nuclei with e- Decoupling of g and e- Temperature Big Bang Nucleosynthesis Quark Hadron Transition [Components] Neutrino Background Leptons & quarks ? Abundances Observation! Any signature of new physics? Gauge boson Observation! Photon 3K Background Exotic particles

  5. 3. Cosmic expansion • Freedmann equation (flat LCDM model) a(t): scale factor at time t K: curvature L: cosmological constant Hubble parameter critical density • Cosmic microwave background radiation • cosmological parameters [LCDM model (WMAP 9 data only)] H0=70.0 ± 2.2 km s-1 Mpc-1 Wb=0.0463 ± 0.0024 Wc=0.233 ± 0.023 Wm=0.279 ± 0.025 WL=0.721 ± 0.025 Wr=8.54×10-5 Dark matter Dark energy WMAP Science Team density parameter for species i=b, g, e±, n, …

  6. 3. Cosmic expansion • Freedmann equation (flat LCDM model) • BBN occurs in a radiation dominated universe at a~10-9, (T~T0/a~109 K) T0=2.7255 K (Fixsen 2009) • Freedmann equation during BBN: r: energy density p: pressure Total # of relativistic degrees of freedom (mi<<T) density parameter for species i=b, g, e±, n, …

  7. 4. Initial condition (T>>1 MeV, t<<1 s) • (n/p) ratio is determined by the weak interactions • If weak reaction rates GW are rapid compared to the expansion rate H • chemical equilibrium obtains, Q≡mn-mp=1.293 MeV [ reaction rate] • Asymptotic functions: (for T << Q, me) (for T >> Q, me) • Comparing G to cosmic expansion rate H, we find (for T ≳me) (n/p) ratio is equal to its equilibrium value for T ≳ 0.8 MeV

  8. 5. Light element synthesis Step 1) Weak freeze-out (t=1 s, T=TF~1 MeV) • n’s decouple from the plasma • Weak reactions for n↔p conversion freeze-out (G<H) • After this freeze-out, n abundance slowly decreases due to the b-decay Step 2) Nuclear reaction freeze-out (t=1-3 min, T=0.3-0.1 MeV) • At T~0.1 MeV, abundances of D, 3H, 3He large • almost all neutrons are quickly bound into 4He Final mass fraction of 4He at T ~ 0.1 MeV • Small amounts of 7Li and 7Be are produced via 4He(t, g)7Li & 4He(3He, g)7Be • 7Be/H > 7Li/H for h ≳ 3×10-10 • D and 3He remain after BBN at A/H ~O(10-5)

  9. 6. Important parameters • Neutron lifetime tn =880.0±0.9 s • smaller weak reaction rates G∝T5/tn  earlier freeze-out • Baryon-to-photon number ratio h • Relativistic degrees of freedom g* (additional light n species) • H(T)∝g*1/2T2 • larger g* fast expansion • earlier freeze-out •  Upper limit Neff < 4 Mangano & Serpico (2011)

  10. 7. Reaction Network L. Kawano, Fermilab-Pub-92/04-A proton # Z N neutron #

  11. 8. Standard Big Bang nucleosynthesis (SBBN) • n↔p equilibrium(n/p)EQ=exp(-Q/T) Q≡mn-mp=1.293MeV • t~1sec,T=TF~1MeV(week interaction freeze-out) • nn e+e- gg • n↔p • e±gg (T~me/3) (n/p)freeze-out=exp(-Q/TF)~1/6 (1MeV=1.16×1010 K) Kawano code (1992) Rates…Smith et al. (1993) +Descouvemont et al. (2004) +Cyburt & Davids (2008) tn=881.9s (Mathews et al. 2005) h=nb/ng=6.3×10-10 WMAP(Dunkley et al. 2008) 7Li(p,a)4He 7Be7Li e--capture after recombination 6Li(p,a)3He T(a,g)7Li 3He(a,g)7Be D(a,g)6Li T9≡T/(109K)

  12. Effects of long-lived exotic particles 1. BBN theory and observation • Standard big bang nucleosynthesis (BBN) • parameter: baryon-to-photon ratio h • Observation of CMB constraint on h • Observation of metal-poor stars(MPSs) • 7Li abundance is smaller than theory • by a factor of ~3 • Primordial abundances of Be, B, … • are not detected yet. WMAP7 WMAP Science Team Signature of new physics? Kawasaki & MK, PRD 86, 063003 (2012)

  13. 2. Li problem • 7Li/H in MPSs < 7Li/H in SBBN • 7Li/H=(1.1-1.5)×10-10fit of LiI 6708 A line • (Spite & Spite 1982, Ryan et al. 2000, Melendez & Ramirez 2004, Asplund et al. 2006, Bonifacio et al. 2007, Shi et al. 2007, Aoki et al. 2009, Sbordone 2010) log(Li/H)+12 Sbordone et al. (2010) 7LiBBN Aoki et al. (2009) Asplund06 Li problem Aoki09 Sbordone10 Gonzalez Hernandez08 Old stars ~ primordial

  14. 3. Li spectrum Inoue et al. (2005) • [Liabundance analysis] • Isotopic ratio is estimated • spectral fit of LiI 6708 A line • 6Li in 9 stars are detected: 6Li/H ≈ 6×10-12(Asplund et al. 2006) • 3D effect in stellar atmosphere  the number of 6Li detections reduces (94) but nonzero(Garcia Perez et al. 2009) • 6Li/7Li from 3D NLTE analysis for atmosphereno detection • 6Li/H < 9.5×10-12 (the highest lower limit of Lind et al. 2013)

  15. 4. Standard stellar model for surface Li abundance Hertzsprung-Russell diagram (M=0.75 M8, Z=10-4, a=1.1) Fully convective pre-main sequence giant branch Deliyannis et al. (1990)

  16. 4. Standard stellar model for surface Li abundance Temperature at the base of the convection zone. ① (p, a) reaction ④ convection zone mixes with Li-depleted region • ② Shallow convective zone  low Tb • gravitational settling is efficient • Li is drained from the convective zone ③ Rapid deepening of convective zone dredge-up of diffused Li Deliyannis et al. (1990)

  17. 4. Standard stellar model for surface Li abundance Main-sequence 7Li isochrones (t=16-20 Gyr; best fit) & 6Li isochrones(6Li/7Li=1 was assumed) =log(NLi/NH) + 12 Z=10-4 Z=10-3 Deliyannis et al. (1990)

  18. 5. Best fit stellar model with an adhoc mixing Korn et al. (2007) g burning • First detection of stellar evolution of Fe abundance by observations of stars in metal poor globular cluster NGC6397 ([Fe/H] ≈ -2) • Stellar evolution model including atomic diffusion, extra-mixing below the convective zone  Li, Mg, Ca, Ti, Fe abundances are explained.

  19. 6. Possible existence of exotic particles • Astronomical observations indicate Dark Matter • beyond the standard model (e.g. SUSY, extra-dimensions) • exotic particles Wikipedia contributors. Standard Model [Internet]. Wikipedia, The Free Encyclopedia; 2014 Jan 27, 14:33 UTC [cited 2014 Feb 18]. Available from: http://en.wikipedia.org/w/index.php?title=Standard_Model&oldid=592640485.

  20. 6. Possible existence of exotic particles • Long-lived exotic particles might have affected light element abundances Liproblem? • 1. Nuclear reactions of exotic atoms • 2. Nuclear reactions of exotic nuclei (Cahn & Glashow 1981) (Pospelov 2007, Kohri & Takayama 2007, Kawasaki et al. 2007-, Hamaguchi et al. 2007, MK et al. 2007-) (Dover et al. 1979) X-nucleus (MK et al. 2009, Kawasaki & MK 2011, MK & Takesako 2012) X-nucleus X- X0 nuclide A nuclide A

  21. I-1) Effect of long-lived exotic strongly interacting massive particle (SIMP) X • X binds to nuclei by strong force  nuclear reactions of X-nuclei • [Assumption] • X (spin 0, charge 0, mass mX>>1 GeV) • X interacts as strongly as nucleons • Nuclear potential • 1)nucleon+X: well reproducing the binding energy of d • 2)other nuclides: Woods-Saxon • (V0=50MeV, a=0.6fm, R=<rm2>1/2) • Schrödinger equation • binding energies and wave functions • rates for formations of X-nuclei & nuclear reactions of X-nuclei X-nucleus r X0 nuclideA

  22. Nuclear reaction network • Up to X-bound O isotopes • X-capture: 25 • X-nuclear reaction: 147 • (b-decay:15) • X-transfer: 2 • X-decay: 38 nuclear reaction b-decay

  23. Abundance evolution Abundance • mX>>1GeV, nx=10-8nb, tx=∞ • T9~1: D abundance increases • d-capture reactions • heavy X-nuclei are produced • 9Be and B could be produced • more than SBBNpredictions • 10B/11B~105 high ratio • c.f.Galactic CR (10B/11B~0.4) • SN n-process (10B/11B<<1) X-capture MK, Kajino, Yoshida, Mathews, PRD 80, 103501, (2009) Temperature T9=T/(109 K)

  24. I-2) Effect of sub-SIMP X Investigation of elemental abundances by taking the interaction strength between X and nuclei as parameter Kawasaki & MK, PRD 83, 055011, (2011) 7Be 3He 4HeX 3He a X0 a 1H X0 a-transfer (7Be is destroyed) 4He abundance • 7Be and 7Lireduces • solution to the Liproblem temperatureT9=T/(109K)

  25. II) Effect of negatively charged massive particle (CHAMP) • CHAMP X- recombines with nuclide A, and • X-nuclide (AX) forms (Cahn & Glashow 1981) • [assumption] • X-: spin 0, charge -e, mass mX • Nuclear charge density • ex) Gaussian Root mean square charge radius X-nucleus X- Schrödinger equation r x O r’ Nucleus A Binding energies and wave functions are calculated • exotic atoms form exotic nucleosynthesis

  26. Exotic reactions induced by X- • Recombination of X- and nuclides • Nuclear reactions of X-nuclei • Radiative recombination (e.g. De Rujula et al. 1990, Dimopoulos et al 1990) g g X- A • Charge exchange reaction (MK, Kim, Cheoun, Kajino, Kino, PRD 88, 063514, 2013) p a b 7Be 7Be X- X- X- X- X- X- X- X- X- A B 8B A 8B* O(100) g emissions  the ground state • Normal reaction (e.g. Kohri& Takayama 2007) e- 7Be4+ • Resonant reaction via exotic atoms of 8BX* (Bird et al. 2008; MK et al. 2007) e- 7Be4+

  27. Abundances evolution Abundance • mX=1 TeV, nx=0.05nb, tx>>200 s MK, Kim, Cheoun, Kajino, Kino, Mathews, in preparation 7LiX(d, X-)9Be 7BeX+p8BX*a8BX+g Gaussian Woods-Saxon homogeneous 7Be(X-, g)7BeX • the resonance height of 8BX* is sensitive • to the nuclear charge distribution • amount of 7Be destruction significantly • depends on the charge distribution temperature T9=T/(109 K)

  28. III) Effect of a radiatively decaying particle • Energetic g is generated  photodisintegration of nuclei (Lindley 1979, Ellis et al. 1985-, Reno & Seckel 1988, Dimopoulos et al. 1988-, …) • Decay of X generation of very energetic g • 7Be can be destroyed But other nuclei are simultaneously destroyed • 7Li problem cannot be solved (Ellis et al. 2005) MK, Kajino, Mathews, PRD 74, 023526 (2006) decay life

  29. Model Interactions with background g and e± X (Kawasaki & Moroi 1995) g 1st AX’ AX 2nd Interactions with background g and e± (Kawasaki et al. 2005) • Assume: exoticparticle (X) decays →g generates with energy Eg0 life time abundance parameter 1. Primary (1st) process • g reacts with background nuclei (Cyburt et al. 2003) 2. Secondary (2nd) process • primary product reacts with background nuclei • 6Liproduction processes (Cyburt et al. 2003) • Destruction processes of d,t,3He,6Liproduced in 1st processes • 2H(p,pn)p • 2H(p,pn)p • 3H(p,dp)n • 3H(p,2np)p • 3He(p,dp)p • 3He(p,2pn)p • 6Li(p,3He)4He • 6Li(p,3He)4He

  30. Result • Solution: 1.59 MeV < Eg0 < 2.22 MeV • fine tuned photon energy 7Be(g, a)3He 7Lireduction without other effects MK, Balantekin, Kajino, Pehlivan, PRD 87, 085045 (2013)

  31. Result • Constraint on the mass, life time, & magnetic moment of sterile n ns nl + g best region MK, Balantekin, Kajino, Pehlivan, PRD 87, 085045 (2013)

  32. Processes affecting elemental abundances Existence of particle decay of particle • Exotic particles could have affected the light element synthesis • Future observations for abundances of Li, Be, B are important • to figure out the solution to the Li problem

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