Topic 3 Primordial nucleosynthesis Evidence for the Big Bang ! Back in the 1920s it was generally thought that the Universe was infinite ! However a number of experimental observations started to question this, namely: • Red shift and Hubble’s Law • Olber’s Paradox • Radio sources • Existence of CMBR Red shift and Hubble’s Law ! We have already discussed red shift in the context of spectral lines (Topic 2) ! Crucially Hubble discovered that the recessional velocity (and hence red shift) of galaxies increases linearly with their distance from us according to the famous Hubble Law V = H0d where H0 = 69.3 ±0.8 (km/s)/Mpc and 1/H0 = Age of Universe Olbers’ paradox ! Steady state Universe is: infinite, isotropic or uniform (sky looks the same in all directions), homogeneous (our location in the Universe isn’t special) and is not expanding ! Therefore an observer choosing to look in any direction should eventually see a star ! This would lead to a night sky that is uniformly bright (as a star’s surface) ! This is not the case and so the assumption that the Universe is infinite must be flawed Radio sources ! Based on observations of radio sources of different strengths (so-called 2C and 3C surveys) ! The number of radio sources versus source strength concludes that the Universe has evolved from a denser place in the past ! This again appears to rule out the so-called Steady State Universe and gives support for the Big Bang Theory Cosmic Microwave Background ! CMBR was predicted as early as 1949 by Alpher and Herman (Gamow group) as a “remnant heat” left over from the very hot and dense initial Universe ! They predicted that after the Big Bang the Universe should “glow” in the gamma ray part of the spectrum ! This will subsequently cool as the Universe expands shifting the wavelength of this “last light” to a temperature of ~5K ! Eventually observed in 1965 by Penzias and Wilson ! The CMBR is now a very powerful tool for cosmologists ! Recent experiments such as COBE and WMAP have measured the CMBR anisotropies at the 10-5 level ! Gives us information on Big Bang, Dark Matter, etc. αβγ theory (Origin of Chemical Elements) ! Actually Alpher & Gamow: Bethe included (by Gamow) as a joke ! Proposed an early Universe that was hot and dense ! Assumed that the Early Universe consisted only of neutrons ! As the temperature fell neutron decay to protons was possible ! Subsequently they proposed a single process for all elemental abundances in the Universe - that of neutron capture - ! Protons via β-decay: n → p + e + νe ! First step: p + n → 2H + γ αβγ theory νe νe αβγ theory - abundances ! Successive neutron For these capture creates heavier calculations elements capture cross-sections ! At each step the progress measured at controlled by the balance Los Alamos between the rate of during World War II production and the rate of were used destruction (1 MeV ! By setting up and solving a neutrons sequence of differential =1010K) equations of this type, a distribution could be dNA/dt = F(S,T)[σ A-1NA-1 - σANA] produced in reasonable F is collision frequency (function of agreement with the trend of thermodynamic state variables) the observed abundances NA is the no. of atoms with atomic no. A σA is the neutron capture cross-section Cross-sections (quick revision) ! Consider the simple case in which a beam of particles is incident on nuclei of some type, then the cross-section is the probability of a particular process occurring per target nucleus, per incident particle ! The total area “blocked out” is the ! In neutron capture the rate at (number of nuclei per unit volume) x (the which the reaction is occurring volume) x (σ). Thus the fraction of the depends upon the relative beam which is removed by the reaction is: velocity v of the particles and target nuclei and is given by the dN/N = - nσ dx product of particle density, the relative velocity, the cross where n = number density x beam area section and the total number of Integration yields target nuclei. N = N exp(- nσx) ! We shall discuss neutron 0 capture further in understanding or N = N0 exp(- x /λ ) the production of elements where λ is the mean free path heavier than Iron αβγ theory - success and failure ! Abundance for He agrees well with observation ! By splitting the elements into 15 “groups” by atomic weight and using an average cross-section for each group gives a reasonable fit to abundance data ! BUT predicted abundances for heavier elements were incorrect ! Problem getting past A=4 due to lack of stable elements with A=5, 8 ! Results carved the way for calculations of thermonuclear fusion ! Discussion is relevant to neutron capture topic later This is an extract from the “Chart of nuclides” Big Bang: Underlying principles I ! Universe expanded some 14 billion years ago from a singularity ! At extremely high temperatures elementary particles can simply be created from thermal energy kT = mc2 (essentially E = mc2) ! After the BB the Universe expands and cools ! As temperatures fall below the threshold temperature for particle production then annilihilation rate > creation rate Big Bang; Underlying Principles II ! Normal physics laws (including standard model of particle physics) ! Small matter-antimatter asymmetry ! Gravitation described by General Relativity ! Cosmological principal (Universe is homeogeneous and isotropic) Robertson- Walker metric ! Expansion of the Universe is governed by field equations of GR The Big Bang Time Space Key events after Big Bang Time Temp/Energy Event 10-43 s kT = 1019 eV Planck era, quantum gravity, prior to this all forces one, gravity first to decouple, many exotic particles 10-35 s kT = 1015 eV Inflation starts, Strong nuclear force decouples 10-10 s T = 1015 K – Free electrons, quarks, photons, -10-4 s 1012 K neutrinos all strongly interacting 10-4 s T = 1012 K – Free electrons, protons, neutrons, -101 s 1010 K photons, neutrinos all strongly interacting Key events after Big Bang Time Temp/Energy Event 101 s T = 1010 K Neutrinos “decouple” from the cosmic plasma (cross-section falls dramatically) 102 s T = 7.5-6x109 K Pair production of e+e- ceases 102 s kT = 0.8 MeV Proton:neutron ratio is frozen Next Thermal energy still high enough 300 s to photodissociate atoms Neutron decay continues, n:p ratio changing Next Primordial nucleosynthesis starts 103 s Note ions not atoms due to mean thermal energy Key events after Big Bang Time Temp/Energy Event ~ 103 s T ~ 108 or 9 K “Dark ages”: Universe is a sea of to to free nuclei, electrons and photons. 400,000 T = 3000 K Photons Thomson scatter off years electrons so Universe remains opaque to photons. Physics in this period is less well-established. 380,000 T = 3000 K Photons can no longer ionize, years photons decouple, “last scattering surface”. Origin of CMBR. Fundamental forces Cosmic Microwave Background Cosmic Microwave Background Very close to a perfect thermal (Black Body) spectrum with a temperature of 2.7K The neutron:proton ratio ! The main 3 reactions involved in determining the number of protons and neutrons in the early Universe are: + (i) n + e p + νe (+ 1.8 MeV) - (ii) p + e (+0.8MeV) n + νe - (iii) n p + e + νe (+ 0.8 MeV) ! Note that reaction (ii) is endothermic in a left- right direction i.e. requires energy into the system (KE of incoming particles) in order to proceed The neutron:proton ratio ! At T > 1010 K, kT > 1 MeV, t < 1 s, reactions (i) and (ii) maintain protons and neutrons in thermal equilibrium • When kT >> mn – mp = Δm, protons and neutrons are nearly equal in number • When Δm becomes significant compared to kT, the neutron-proton ratio is given by the Boltzmann factor exp(−Δmc2/kT) ! At T ~ 1010 K, kT ~ 0.8 MeV, t ~ 1 s, the reaction rates for (i) and (ii) become slow compared to the expansion rate of the universe • neutrinos decouple (weak interaction rate slow compared to expansion rate) • e+e− pair creation suppressed (γ energies drop below 0.511 MeV) • neutron:proton ratio “freezes out” ! Below this temperature only reaction (iii) continues The neutron:proton ratio ! We use the Boltzmann distribution to estimate the n:p ratio at this point 2 3 $ mc ' N ∝ m 2 exp& − ) % kBT ( ! hence 3 " % 2 " 2 % Nn mn (mn − mp )c = $ ' exp$ − ' N p # mp & # kBT & € 2 ! where kT = 0.8 MeV and (mn - mp) = 1.3 MeV/c € This yields a value of Nn:Np ~ 0.2 Primordial nucleosynthesis ! At this point kT is too high p + n ⇔ 2H + γ for primordial 2H + 2H ⇔ 3He + n nucleosynthesis to start 2H + 2H ⇔ 3H + p (formation of nuclei) due 3 2 4 to dissociation H + H ⇔ He + n 3He + 2H ⇔ 4He + p ! Therefore reaction (iii) continues in the left-right 2H + 2H ⇔ 4He direction – this is neutron 3He + 4He ⇔ 7Be + γ decay 3H + 4He ⇔ 7Li + γ ! After a further 300 7Be + n ⇔ 7Li + p seconds primordial 7Li + p ⇔ 24He nucleosynthesis starts Note: ions not atoms Solved problem ! If the neutron:proton ratio starts at 0.2 and the neutron continues to decay for a further 300 seconds what is the neutron:proton ratio at the end of this period given that the neutron’s lifetime is 890 seconds? ! The neutron’s lifetime is 890 seconds therefore in 300 seconds: N $ t ' $ 300' = exp& − ) = exp& − ) = 0.714 N0 % τ ( % 890( ! Therefore the fraction of neutrons that have decayed = 0.286 ! Next we write N n (1− d) " % € Nn Nn (1− d) N p $ ' = = N N + dN Nn # p & t= 300s p n 1+ d N " % p Nn Nn where = 0.2 and d=0.286 to give $ ' = 0.135 N p N # p & t= 300s € € € Abundances vs time Note that a neutron:proton ratio of 0.135:1 is equivalent to 12:88 Assuming that the 12 neutrons go to forming 4He we would expect 76% Hydrogen (1H) and 24% Helium (4He) - in excellent agreement with observation Modern day abundances ! Comparison of modern day elemental abundances from primordial nucleosynthesis can also give important cosmological information such as the baryon density or the baryon to photon ratio ! Concordance with CMB is important check on theory Summary ! Big Bang Nucleosynthesis (BBNS) successfully predicts the production of light elements shortly after the Big Bang ! The thermal history of the early Universe and nuclear physics are used to explain the sequence of events ! Light element abundances can be accurately predicted and related to cosmological parameters .