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NUCLEOSYNTHESISNUCLEOSYNTHESIS Also Known As Fromfrom Thethe Bigbig Bangbang Toto Todaytoday NUCLEOSYNTHESISNUCLEOSYNTHESIS also known as fromfrom thethe BigBig BangBang toto TodayToday Summer School on Nuclear and Particle Astrophysics Connecting Quarks with the Cosmos I George M. Fuller Department of Physics University of California, San Diego The man who discovered how stars shine made many other fundamental contributions in particle, nuclear, and condensed matter physics, as well as astrophysics. In particular, Hans Bethe completely changed the way astrophysicists think about equation of state and nucleosynthesis issues with his 1979 insight on the role of entropy. Bethe, Brown, Applegate, & Lattimer (1979) Hans Bethe There is a deep connection between spacetime curvature and entropy (and neutrinos) Curvature (gravitational potential well) Entropy content/transport by neutrinos Entropy fundamental (disorder) physics of the weak interaction Entropy entropy per baryon (in units of Boltzmann's constant k) of the air in this room s/k ~ 10 entropy per baryon (in units of Boltzmann's constant k) characteristic of the sun s/k ~ 10 entropy per baryon (in units of Boltzmann's constant k) for a 106 solar mass star s/k ~ 1000 entropy per baryon (in units of Boltzmann's constant k) of the universe s/k ~ 1010 total entropy of a black hole of mass M 2 ⎛ ⎞ ⎛ ⎞ 2 M 77 M S /k = 4π⎜ ⎟ ≈10 ⎜ ⎟ ⎝ mpl ⎠ ⎝ Msun ⎠ 1 where the gravitational constant is G = 2 mpl 22 and the Planck mass is mpl ≈1.221×10 MeV EntropyEntropy S = k logΓ a measure of a system’s disorder/order LowLow EntropyEntropy 12 12 free nucleons C nucleus NucleosynthesisNucleosynthesis TheThe BigBig PicturePicture Drive toward Nuclear Statistical Equilibrium (NSE) Freeze-Out from Nuclear Statistical Equilibrium FLRW Universe (S/k~1010) Neutrino-Driven Wind (S/k~102) The Bang Temperature Outflow from Neutron Star Weak Freeze-Out T= 0.7 MeV T~ 0.9 MeV Weak Freeze-Out n/p>1 n/p<1 Alpha Particle Formation T~ 0.1 MeV T~ 0.75 MeV Alpha Particle Formation Time PROTON NEUTRON The nuclear and weak interaction physics of primordial nucleosynthesis (or Big Bang Nucleosynthesis, BBN) was first worked out self consistently in 1967 by Wagoner, Fowler, & Hoyle. This has become a standard tool of cosmologists. Coupled with the deuterium abundance it gave us the first determination of the baryon content of the universe. BBN gives us constraints on lepton numbers and new neutrino and particle physics. BBN is the paradigm for all nucleosynthesis processes which involve a freeze-out from nuclear statistical equilibrium (NSE). R. Wagoner, W. A. Fowler, & F. Hoyle (from D. Clayton’s nuclear astrophysics photo archive at Clemson University) Suzuki (Tytler group) 2006 So where are the nuclei heavier than deuterium, helium, and lithium made ??? W. A. Fowler G. Burbidge M. Burbidge B2FH (1957) outlined the basic processes in which the intermediate and heavy elements are cooked in stars. F. Hoyle 10 Photon luminosity of a supernova is huge: L ~ 10 Lsun (this one is a Type Ia) Type Ia – C/O WD incineration to NSE Fe-peak elements, complicated interplay of nuclear burning, neutrino cooling, and flame front propagation cse.ssl.berkeley.edu/ Weaver & Woosley, Sci Am, 1987 NuclearNuclear BurningBurning StagesStages ofof aa 2525 MMsun StarStar Burning Temperature Density Time Scale Stage Hydrogen 5 keV 5 g cm-3 7 X 106 years Helium 20 keV 700 g cm-3 5 X 105 years Carbon 80 keV 2 X 105 g cm-3 600 years Neon 150 keV 4 X 106 g cm-3 1year Oxygen 200 keV 107 g cm-3 6 months Silicon 350 keV 3 X 107 g cm-3 1 day Core Collapse 700 keV 4 X 109 g cm-3 ~ seconds of order the free fall time “Bounce” ~ 2 MeV ~1015 g cm-3 ~milli-seconds Neutron Star < 70 MeV initial ~1015 g cm-3 initial cooling ~ 15-20 seconds ~ keV “cold” ~ thousands of years MassiveMassive StarsStars areare From core carbon/oxygen burning onward the neutrino luminosity exceeds the photon luminosity. Neutrinos carry energy/entropy away from the core! Core goes from S/k~10 on the Main Sequence (hydrogen burning) to a thermodynamically cold S/k ~1 at the onset of collapse! e.g., the collapsing core of a supernova can be a frozen (Coulomb) crystalline solid with a temperature ~1 MeV! Type II core collapse supernova Type Ib/c core collapse supernova BLUE - UV GREEN -B RED -I Caltech Core Collapse Project (CCCP) www.cfa.harvard.edu/ ~mmodjaz Fuller & Meyer 1995 Meyer, McLaughlin & Fuller 1998 PrimordialPrimordial NucleosynthesisNucleosynthesis ((BBNBBN)) Suzuki (Tytler group) 2006 WMAP cosmic microwave background satellite Fluctuations in CMB temperature give Insight into the composition, size, and age of the universe and the large scale character of spacetime. Age = 13.7 Gyr Spacetime = “flat” (meaning k=0) Composition = 23% unknown nonrelativistic matter, 73% unknown vacuum energy (dark energy), 4% ordinary baryons. (1) The advent of ultra-cold neutron experiments has helped pin down the neutron lifetime (strength of the weak interaction) (2) The CMB acoustic peaks have given a precise determination of the baryon to photon ratio This has changed the way we look at BBN - New probes of leptonic sector now possible. QuantumQuantum NumbersNumbers baryon number of universe From CMB acoustic peaks, and/or observationally-inferred primordial D/H: three lepton numbers From observationally-inferred 4He and large scale structure and using collective (synchronized) active-active neutrino oscillations (Abazajian, Beacom, Bell 03; Dolgov et al. 03): Leptogenesis Generate net lepton number through CP violation in the neutrino sector. Transfer some of this or a pre-existing net lepton number to a net baryon number. BaryonBaryon NumberNumber (from CMB acoustic peak amplitudes) -- Precision baryon number measurement -- Sets up robust BBN light element abundance predictions which, along with observations and simulations of large scale structure potentially enables probes of QCD epoch – entropy fluctuations, black holes Early nuclear evolution, cosmic rays, the first stars Neutrino mass physics (leptogenesis, mixing, etc.) Decaying Dark Matter WIMPS ThermodynamicThermodynamic PreliminariesPreliminaries Thermonuclear Reaction Rates Rate per reactant is the thermally-averaged product of flux and cross section. a+X→ Y+b or X(a,b)Y −1 rate per X nucleus is λ = ()1+ δaX σ v 1 ⎛ Z Z e2 ⎞ ~ exp⎜ −b a X ⎟ E ⎝ E ⎠ Rates can be very temperature sensitive, especially when Coulomb barriers are big. At high enough temperature the forward and reverse rates for nuclear reactions can be large and equal and these can be larger than the local expansion rate. This is equilibrium. If this equilibrium encompasses all nuclei, we call it Nuclear Statistical Equilibrium (NSE). In most astrophysical environments NSE sets in for T9 ~ 2. T T ≡ 9 109 K where Boltzmann's constant is kB ≈ 0.08617 MeV per T9 ElectronElectron FractionFraction InIn general,general, abundanceabundance relativerelative toto baryonsbaryons forfor speciesspecies ii mass fraction mass number Freeze-Out from Nuclear Statistical Equilibrium (NSE) In NSE the reactions which build up and tear down nuclei have equal rates, and these rates are large compared to the local expansion rate. Z p + N n A(Z,N) + γ nuclear mass A is the sum of protons and neutrons A=Z+N Z μp + N μn = μA + QA Binding Energy of Nucleus A Saha Equation Saha Equation 3 2(A−1) 7 1 ⎛ ⎞ 1−A 2(A−1) 2(A−3) 3/2 T Z N QA /T YAZ(),N ≈ []S Gπ 2 A ⎜ ⎟ Yp Yn e ⎝ mb ⎠ Typically, each nucleon is bound in a nucleus by ~ 8 MeV. For alpha particles the binding per nucleon is more like 7 MeV. But alpha particles have mass number A=4, and they have almost the same binding energy per nucleon as heavier nuclei so they are favored whenever there is a competition between binding energy and disorder (high entropy). FLRW Universe (S/k~1010) Neutrino-Driven Wind (S/k~102) The Bang Temperature Outflow from Neutron Star Weak Freeze-Out T= 0.7 MeV T~ 0.9 MeV Weak Freeze-Out n/p>1 n/p<1 Alpha Particle Formation T~ 0.1 MeV T~ 0.75 MeV Alpha Particle Formation Time PROTON NEUTRON number density for fermions (+) and bosons (-) degeneracy parameter d 3p 1 g ⎛ dΩ⎞ E 2dE (chemical potential/temperature) dn ≈ g 3 E /T −η ≈ 2 ⎜ ⎟ E /T −η ()2π e ±1 2π ⎝ 4π ⎠ e ±1 μ η ≡ where the pencil of directions is dΩ=sinθ dθ dφ T The energy density is then in extreme relativistic limit g ⎛ dΩ⎞ E ⋅ E 2dE η → 0 dε ≈ ⎜ ⎟ 2π 2 ⎝ 4π ⎠ eE /T −η ±1 now get the total energy density by integrating over all energies and directions (relativistic kinematics limit) T 4 ∞ x 3 dx ρ ≈ 2 ∫ x−η 2π 0 e ±1 ∞ x 3 dx π 4 ∞ x 3 dx 7π 4 ∫ x = and ∫ x = 0 e −1 15 0 e +1 120 π 2 ⎛ 7 ⎞ π 2 bosons ρ ≈ g T 4 and fermions ρ ≈ ⎜ g ⎟ T 4 b 30 ⎝ 8 f ⎠ 30 Statistical weight in all relativistic particles: 3 ⎛ ⎞ 3 b⎛ Ti ⎞ 7 f Tj geff = ∑gi ⎜ ⎟ + ∑g j ⎜ ⎟ i ⎝ T ⎠ 8 j ⎝ T ⎠ e.g., statistical weight in photons, electrons/positrons and six thermal, zero chemical potential (zero lepton number) neutrinos, e.g., BBN: 7 geff = 2 + 8 (2 + 2 + 6))=10.75 ν e ν e ν μ ν μ ντ ν τ SpacetimeSpacetime BackgroundBackground Relic neutrinos from the epoch when the universe was at a temperature T ~ 1 MeV ( ~ 1010 K) ~ 300 per cubic centimeter photon decoupling T~ 0. 2 eV neutrino decoupling T~ 1 MeV Relic photons. We measure 410 per cubic centimeter vacuum+matter dominated at current epoch Coupled star formation, cosmic structure evolution – Mass assembly history of galaxies, nucleosynthesis, weak lensing/neutrino mass Very Early Universe: baryo/lepto-genesis QCD epoch, BBN Neutrino physics Re-ionization: 1 in 103 baryons into stars; Nucleosynthesis? Black Holes? George Gamow Albert Einstein George LeMaitre A.
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