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Big Bang Nucleosynthesis BIG BANG NUCLEOSYNTHESIS Elisabetta Caffau GEPI 0.1 Chemical elements? ? = ) SBBN .. 30.08.2017 1.1 Primordial Nucleosynthesis Production of nuclei other than H in a period 1s t 300s after Big Bang ≤ ≤ The prediction of the Standard Model on the production of D, 3He, 4He, 7Li is overall in good agreement with the observations BBN started with the work of Gamow, Alpher and Herman in the 1940s who predicted connection between the elements formation and the 3 K background radiation they predicted the production of all elements, not only the light ones; with the discovery of the instability of the Z=5 element it revealed clear that this is not possible SBBN .. 30.08.2017 2.1 Primordial Nucleosynthesis Standard Model of the very early Universe simple and determined by three milestones: expansion governed by General Relativity; particle interactions governed by Standard Model; particle distribution governed by statistical physics. SBBN depends on only ONE parameter: nb baryon-to-photon ratio η = (baryons: protons, neutrons and nuclei) or nγ baryon density Ωb (dimensionless quantity) the 4He abundance depends also on expansion rate SBBN .. 30.08.2017 3.1 Baryon to photon ratio η baryon-to-photon ratio η = nb nγ η baryon-to-photon ratio η10 = 10−10 The predicted abundance of light elements depends only on η Number of photon nγ in the present Universe known from the cosmic background temperature (411 2 photons per cm3) ± the number of photons has not changed in time (emission from stars is negligible) SBBN .. 30.08.2017 4.1 Baryon to photon ratio Present: Ωb;0 2 −3 Ωb;0h = 3:65 10 η10 h present expansion× rate: H0 h = 100kms−1Mpc−1 with R_ 0 H0 = , H0 present Hubble constant. R0 R(t) cosmic scale factor, evolving in time and describing expansion of the Universe; with t the cosmic time 2 R_ 0 2 1 8πG = H (t) = 2 = ρ(t) with ρ(t) the energy of the Universe, G R0 8t 3 Newton constant. SBBN .. 30.08.2017 5.1 Cosmic nb at the BBN time is the same as at the recombination time nγ ( 40000 yr after BB) ∼ Abundances of primordial elements, in the Standard Model context, can be derived by using the Cosmic Microwave Background (CMB) radiation derived by Planck 2 By using for the CMB the Planck observations Ωb;0h = 0:02226 0:00023, the primordial elements are (68% confidence): ± primordial fraction of baryons consisting of 4He: Yp = 0:2471 0:0005 primordial abundance± ratio of D with respect to H: D=H = (2:414 0:047)=105 primordial abundance± ratio of 3He with respect to H: 3He=H = (1:110 0:022)=105 primordial abundance± ratio of 7Li: A(7Li=H) = 2:745 0:021 (with A(7Li=H) = log (7Li=H) + 12) ± 10 SBBN .. 30.08.2017 6.1 Big Bang first modelled time According to Standard Model at t = 0 s, the instant of the Big Bang, matter and radiation of the Universe were condensed in a point First time that can be modelled at t = 10−43 s gravitational, strong, weak, electromagnetic forces were undistinguished there are particle of matter and antimatter in equal proportion particles create radiation and are created from radiation SBBN .. 30.08.2017 7.1 At t ∼ 10−34 s tiny excess of matter over antimatter (one matter particle surviving over 109 particles to annihilate with antimatter) SBBN .. 30.08.2017 8.1 SBBN .. 30.08.2017 9.1 Big Bang first times At t ∼ 10−5 s Protons and neutrons builded Remaining antimatter (in form of positrons e+) disappeared significantly when energy below level to create couples e+ + e− SBBN .. 30.08.2017 10.1 Early Universe Early times: T ∼ 1012 K, t ∼ 10−4 s Universe filled by gas extremely hot and dense matter completely dissociated matter in equilibrium with radiation As Universe evolve: T (t) changes due to expansion in timescale-order H(t): _ −1 H−1(t) = R0 R0 Particles couple directly or indirectly with with photons, rate of interaction: Γ = nhσvi with n number density of target particles v relative velocity σ interaction cross section for Γ(t) > H(t) interactions can maintain equilibrium SBBN .. 30.08.2017 11.1 Early Universe t <1 s At T > 1010 K and t < 1 s there is statistical and thermal equilibrium inter-conversion between neutron and proton: n + ν ! p + e− n + e+ ! p + ν n ! p + e− +ν ¯ n Q p = exp − T will be maintained as long as n−p reactions are rapid enough (Q = 1:293 MeV) as the temperature is such that Γ(T ) < H(T ) n=p ratio get frozen only the β-decay, n −! p + e− +ν ¯, continues n 1 this happens for T ∼ 0:8 MeV at t ∼ 1 s, and p ∼ 6 n p slowly decreases (occasional weak interactions, dominated by n decay) n 1 p ∼ 7 at the time nucleosynthesis begins SBBN .. 30.08.2017 12.1 D formation When n − p no more in equilibrium n 1 p ∼ 6 it starts n + p −! D + γ but for T ≥ 109 K (at t ≤ 100 s) γ enough energetic for D + γ −! n + p faster than n + D −!3 H + γ and p + D −!3 He + γ tiny abundances of D, 3He and 4He SBBN .. 30.08.2017 13.1 D and He formation For T ∼ 109 K(∼ 0:1 MeV), at t ∼ 100 s) nuclei are built n + D −!3 H p + D −!3 He n + He −!4 He D + D −!4 He D is the bottleneck, the first stepping stone to build heavier elements SBBN .. 30.08.2017 14.1 Network of reactions .. 30.08.2017 15.1 Network of reactions .. 30.08.2017 16.1 At t ∼ 100 s n 1 p ∼ 7 Assuming all available n end bond in 4He Mass fraction of 4He: Y = 4nn=2 = 2n=p ∼ 0:25 nn+np 1+n=p 4 if the n number density is nn, nn=2 He can be formed. SBBN .. 30.08.2017 17.1 be T∗ temperature for Γ(T∗) = H(T∗) but Γ(T ) ∼ T 5t 1 1=2 2q8πG and H(T ) ∼ 2t ∼ g (T )T 3 so T∗ depends on g(T ), the number of degree of freedom of the radiation at T = T∗ h i g(T ) = 2 1 + (7=8 + 7=8) + − + (7=8N ) ∗ γ e +e ν Nνν¯ Nν = 3, g(T ) = 43=4, but changes if number light neutrino is different Nν = 2; 3; 4 give Y ∼ 0:227; 0:242; 0:254 SBBN .. 30.08.2017 18.1 There is no stable element for atomic mass of 5 To build elements heavier than 4He: collisions of rare D, 3H or 3He with 4He required majority D, 3H or 3He are burnt into 4He =) there is very little of heavier elements SBBN .. 30.08.2017 19.1 Universe continue to expand and cool temperature and density decrease nuclear reactions more and more rare At t ∼ 103 s nucleosynthesis is over SBBN .. 30.08.2017 20.1 Models Two main cosmological parameters on which predictions depend number of degree of freedom g (at T ∼ 1 MeV) baryon to photon ratio p 2 1=6 An increase in g increases H(T ) ∼ gT leading to higher freeze out temperature (T∗ ∼ g ) and higher He abundance. Dependence on η is more complicate =) nucleosynthesis can be followed with large number of equations (code). Wagoner (1973, ApJ 179, 343) wrote first code, improved by Kawano (1992, preprint FERMILAB Pub 92/04A). SBBN .. 30.08.2017 21.1 Primordial abundances SBBN .. 30.08.2017 22.1 SBBN .. 30.08.2017 23.1 The lithium valley 4 He(T,γ ) 7 Li 4 3 7 He( He,γ ) Be SBBN predicts an ABSOLUTE minimum for " the Li abundance SBBN .. 30.08.2017 24.1 From Coc & Vangioni 2017 Vertical strip the CMB baryonic; horizontal green areas represent the primordial abundances. SBBN .. 30.08.2017 25.1 Observations Goal would be to derive the primordial abundance of D, 3He, 4He, 7Li A good precision needed (at the limit or beyond of current capabilities) A theoretical understanding for each element of all mechanisms of production destruction Observe in the right place. SBBN .. 30.08.2017 26.1 As stars are formed, metals are synthesised in (massive) stars As massive stars explode as supernovae, ISM is enriched by metals =) metal content is an indication of age Old stars are poor in metals (metal-poor stars) Young ones are rich (Sun) Stars \produce" elements up to iron in their interior heavier in cataclysmic events no production of D, Li, Be, B D is synthesised only in BBN Li, Be and B can be produced by cosmic rays spallation Li is produced by novae and AGB stars Only 10B and 11B stable Stellar synthesis .. 30.08.2017 27.1 Elements' production .. 30.08.2017 28.1 Deuterium Never produced in stars Low binding energy: 2.2 MeV Destroyed by stellar evolution processes, via D + p −!3 He + γ + 5:49MeV Its abundance decreases with time Observations provide lower limit of its primordial value Its abundance in low-metallicity environment has to be close to BBN value D −1:6 Its primordial abundance very sensitive to Ωb (monotonic behaviour, H / η ) Deuterium .. 30.08.2017 29.1 Deuterium Historically the first determinations from Lyman limit systems D information detectable only on Lyman-α line D can be safely measured only in high red-shift, low-metallicity damped Lyman α where observations challenging Deuterium .. 30.08.2017 30.1 Difficult to derive D in old stars' atmospheres Hα in HD 84937 (6250 K/4.0/{2.1) −5 ND=NH = 4 × 10 (dotted line) ND=NH = 0 (dashed line) from Spite, Maillard, & Spite (1983) A&A 128,252 Deuterium .
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