Physique d`Astroparticule 3eme cours
publicité
Physique d’Astroparticule 3eme cours Jürgen Brunner CPPM / Luminy Plan de cours (24 h) • • • • • • • 19/12/06 (mar) 10/01/07 (mer) 22/01/07 (lun) 25/01/07 (jeu) 31/01/07 (mer) 01/02/07 (jeu) 07/02/07 (mer) 4h 2h 4h 4h 4h 4h 4h 8:00 – 12:00 8:00 – 10:00 8:00 – 12:00 14:00 – 18:00 8:00 – 12:00 14:00 – 18:00 8:00 – 12:00 (JB) (perdu) (JB) EK EK temperature of universe Big Bang Equilibrium n/p ends Nucleosynthesis begins 1010 K Neutral hydrogen forms universe transparent to light fossil photon radiation frozen 3000 K nuclei 100 s atoms 3 105 y time after big bang Description de l’univers Équation de la relativité générale Gab : Einstein Tensor - description de la déviation de la géométrie par rapport à la géométrie Euclidienne Tab : Énergie/stress Tensor: description de la matière a,b,µ,ν : indices (0,1,2,3) κ : constante de proportionnalité, définie par correspondance avec loi de la gravitation classique G : constant de la Gravitation c : vitesse de la lumière Metriques Definition de g : Règles de sommation : Règles de dérivation : Metriques-Exemples ∆s 2 = ∆x 2 + ∆y 2 1 0 g µν = Coordonnées Cartésiennes (2-dimensionnel) 0 1 Courbature 0 1 0 g µν = 2 0 x 1 R2 g µν = 0 2 2 2 2 ∆s = ∆r + r ∆Φ Coordonnées Polaires (2-dimensionnel) Courbature 0 2 2 2 2 2 2 2 ∆s = R ∆Θ + R sin Θ ∆Φ 0 2 2 2 R sin x1 Coordonnées Polaires (2-dimensionnel) Courbature 0 MetriquesEspace/temps Minkowski xµ = [ x0 , x1, x2 , x3 ] (relativité restreinte) x µ = [ x0 ,− x1,− x2 ,− x3 ] Convention des coordonnées 1 0 0 0 0 − 1 0 0 g µν = g µν = 0 0 − 1 0 0 0 0 − 1 1 0 µ gνµ = gν = 0 0 0 0 0 1 0 0 0 1 0 0 0 1 ∆s 2 = g µν x µ xν = g µν xµ xν = gνµ x µ xν ∆s 2 = ∆x02 − ∆x12 − ∆x22 − ∆x32 = ∆(ct ) 2 − ∆x12 − ∆x22 − ∆x32 Einstein tensor Tenseur de Riemann Tenseur de Ricci bc abcd R = g ad R Tenseur d’Einstein Scalaire de Ricci R = g ab ab R Tenseur d’énergie/tension (angl.stress) T00 = densité d’énergie T0i = flux d’énergie = Quantité de mouvement Tii = flux de quantité de de mvt (stress ou pression) Tij = shear stress Courbature d’espace/temps Distribution de la matière (aussi : radiation, énergie etc) déforment l’espace/temps Visualisation pour un monde 2-dimensionnel La constante cosmologique Problème: Cette équation n’a pas de solutions stables. L’univers stationnaire n’est pas possible. Explication naïve: force gravitationnelle est toujours positive, chaque distribution de masses initiales s’effondra (par attraction) Version modifiée Elle permet des solutions stationnaires mais instables dés lors qu’on s’écarte de l’état d’équilibre Λ : constante cosmologique peut être vu comme “pression du vacuum, qui contrebalance la force gravitationnelle Model d’univers Conditions basées sur observations et/ou des arguments philosophiques L’univers est homogène, ça veut dire invariant par translation, “il n’y a pas d’endroit particulier” (Ex.: structure cristalline ) L’univers est isotrope, ca veut dire invariant par rotation “dans tous les directions on voit la même chose” (Ex.: on imagine des sphères concentriques contenues les unes dans les autres ) La structure visible aujourd'hui est la résultat des petits fluctuations primordiales Friedman-Lemaitre-Robertson-Walker metrique Solution pour l’univers decrit au-dessus a(t) : paramètre d’échelle, décrit l’évolution du taille d’univers k = -1,0,1 : type de la géométrie (hyperbolique, plat, sphérique) H : taux d’expansion Acceleration d’expansion ρ : densité de la matière Hubble 1920-1930 – Measure of red shift for many distant galaxies – Conclusion: – the Universe expands ! – galaxies receding the faster the further they are Redshift Hubble’s law Today: H0 = 71 ± 4 (km/s) / Mpc Slope = H0 (Hubble constant) Once upon a time... our Universe was smaller Primordial singularity !!! => BIG BANG How far in time ? • Extrapolating backwards the present expansion speed towards the big bang T 1/H0 ~ 14 billion years (note that the present best estimate, with a lot of complicated physics inside, is T = 13.7 ± 0.2 Gyr) • Consistent with the age of the oldest stars Implosion Implosion du ofnoyau core of d’étoile red giant Explosion Explosion of star d’étoile Expansionduof matter Expansion matière shock wave⇒∼ accélération 0.5 c onde de choc Hubble law in 2003: supernovae Supernova Supernova Supernova Remnant Restes du Supernova SNIa occurs at Chandra mass, 1.4 Msun ⇒ ‘Standard Candle’ measure brightness → distance: B = L / 4π π d2 measure host galaxy redshift → get recession velocity test Hubble’s Law: v = H d, at large distances effective magnitude → brightness → distance Expansion with Supernovae Ia Acceleration of universe expansion non-linear v = H(t) d redshift → recession velocity Deviation from Hubble’s law The expansion accelerates ΩΛ ~ 0.7 Time & temperature (=energy) • Once upon a time, our Universe was hotter – Expansion requires work (and this is the most adiabatic expansion one can imagine, so the work comes from internal energy) 15 9 T ~ 10 K t γ ↔ particles+antiparticles γ ↔ proton-antiproton γ ↔ electron-positron (…) then matter became stable Two epochs Time Decoupling Energy versus temperature • L’univers peut être décrit comme corps incandescent Spectre typique comme mesure dans les lampe Dépendance de la température du longueur d’onde Formule du Planck – début de la théorie quantique E=hν Relation entre énergie et fréquence pour photons k– constante de Boltzman E ~ kT relation entre energie et temperature dans un gas ideal Back to thermal history Density perturbations (inflation?) t = 10-35 s t ~ 2000 yrs t ~ 300000 yrs Matter domination Recombination: p+e- → H+γγ Matter: Gravitational collapse Photons: Free propagation observable obs ble a v er Galaxies, clusters CMB End of opaque Universe Cannot see further back Multiple scatterings of γ on e- produces “thermal” spectrum at T = 3000 K (z ~ 1100 = a0 / arec) “Uniform” background at T0 = 2.7 K Discovery Discovered in 1965 as “excess noise” (Noble Prize in 1978) 25 years later Bell Labs COBE 1992 Bell Labs Wilson Penzias (+ Robert Dicke) COBE project 1990-1994 George F. Smoot John C. Mather Nobel prize 2006 "for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation". COBE-IRAS spectrum Excellent accord avec formule de Planck L’univers est un corps incandescent beaucoup plus précise que une lampe ordinaire COBE-IRAS spectrum Déviation du theorie au niveau 10-3 seulement COBE sky maps T = 2.7 K ∆T = 3.4 mK (after subtraction of constant emission) ∆T = 18 µK (after subtraction of dipole) COBE sky maps scale 0-4 K: very isotrope → cosmological origin Yet, regions > 1° apart never in causal contact z t LSS 103 x 3.105 θLSS ~ rad ~1° 9 14.10 Inflation ? t now COBE sky maps Doppler effect due to motion of Earth w.r.t. CMB (v = 370 km/s towards Virgo) Anisotropies : potential wells Early seeds for structure formation? (+ foregrounds) Anisotropies • Before recombination, Universe = plasma of free e- and protons • Presented as a power spectrum cosmology l(l-1)Cl (power) • Oscillations due to opposite effects of - gravity - pressure l ~ 200/θθ (deg) Max. scale of anisotropies Limited by causality (remember?) → maximum scale ⇒ Max scale relates to total content of Universe Ωtot (= ΩM+Ω ΩΛ) 2nd generation satellite COBE (7 degree resolution) WMAP (0.25 degree resolution) (l < 20) (l < 700) WMAP WMAP on its way to L2 Back to back primary mirrors shield • Very low temperature signal ⇒ Need shielding from Sun, Earth, Moon, (Jupiter) • Lagrange point L2: position of co-rotation with Earth ⇒ Stability of conditions • Measure of T differences • 5 frequency channels Foreground removal (< <90 GHz) Launch: Jun. 2001 First results: 2003 Cosmological parameters Ω b h2 Ω m h2 h … ns σ8 = 0.0223 +/-0.001 = 0.13 +/-0.01 = 0.73 +/- 0.03 … = 0.95 +/- 0.02 = 0.74 +/- 0.06 Typically ± 5-10% + H0 from HST Ωm = 0.24 +/- 0.04 = 0.72 +/- 0.04 ΩΛ Beyond WMAP - More frequency channels - Improved resolution 20 GHz 70 GHz 30 GHz 90 GHz 40 GHz Weighted sum background removal Planck - Freq coverage from 30 to 850 GHz (9 channels) - Polarization sensitive - Launch foreseen spring 2008 temperature of universe Big Bang Equilibrium n/p ends Nucleosynthesis begins 1010 K Neutral hydrogen forms universe transparent to light fossil photon radiation frozen 3000 K nuclei 100 s atoms 3 105 y time after big bang Which elements ? H Li Be BBN Elements METALS He Age < 1s, T > 1 MeV Collisions maintain thermal equilibrium Proton - neutron conversion Maxwell-Boltzmann distribution : 2 N ∝ m3/2 exp - mc kBT n N (neutron) = ~ e −∆mc2/kT ~ 1 p N (proton) (∆m = 1.3 MeV) n → 0 as T → 0 BUT freeze-out p n-p freeze-out - Weak reaction n ↔ p rate: Γweak = nσ σ|v| ∝ GF2 T5 - Expansion rate: . H = a/a ∝ ρ1/2 so H ∝ g* 1/2 T2 (n ∝ T3 and σ ∝ GF2 T2) with ρ ∝ g* T4 (Stefan’s law) 3 - Freeze-out when Γweak ~ H with Γweak ~ Τ H 0.8 MeV ⇒ drop-out of equilibrium at T ~ 0.8 MeV n = e −∆m/kT = e p -(1.3 MeV / 0.8 MeV) ~ 0.2 Deuterium bottleneck - nB small ⇒ 2-body reactions only - Formation of D - Binding Energy (D) = 2.2 MeV nB / nγ ~ 10-10 γ energy distribution ⇒ D photo-disintegrated Tail of high energy photons prevents formation of Deuterium until T ~ 0.1 MeV E t=1-3 mn, T=0.3-0.1 MeV - neutron decay: ⇒ n/p ~ (n/p)0 e-(∆∆t/ττ) n/p ~ 1/7 - Deuterium (all n): - Helium (all D ie. all n + equal number of p): 2n Helium abundance ~ ~ 0.25 n+p H abundance ~ 0.75 η = nB/nγ ➚ ⇒ D bottleneck lasts less ⇒ n/p ➚ ⇒ He ➚ pp-I pp-II pp-III 3He 1H 2H 4He 7Be 8Be 6Li 7Li Heavier elements - BBN No A=5, A=8 stable nuclei + 2-body reactions only Li5 → He4+p He5 → He4+n Be8 → He4+He4 BBN essentially STOPS at He4 Trace amounts of 3Li7, 4Be7 : He4+H3 → Li7+γγ He4+He3 → Be7+γγ Be7 +γγ → Li7+p Heavier elements - Stars Produced in stars (high densities ⇒ triple alpha reactions allowed) Spread in ISM by SN explosions Crab nebula (SN II) Origin of elements formed in: Big Bang Nucleosynthesis Hot stars Supernova explosions Cosmic-ray interactions on inter-stellar medium Observational constraints - Stars are net producers of He4 and metals ⇒ use metal poor stars upper limit on primordial abundance of He4 (and on η) - D weakly bound ⇒ measure in ISM lower limit on primordial abundance of D (upper limit on η) - D burnt to He3 and He3 produced by stars ⇒ D+He3 increases with time upper limit on D+He3 ie lower limit on η - Li7 very fragile, burnt in stars ⇒ use old metal poor stars, require Li6 (more fragile) Abundances Observational concordance Agreement of abundances over 10 orders of magnitude ⇓ Major success of Big-Bang CMB: nγ = 411 cm-3 η = nB/nγ = (4± ±1).10-10 nBmB ΩB = ρ B = 2 πG ρc 3H /8π η ΩB h702 ~ 0.04 BBN and neutrinos H ∝ g* 1/2 T2 (remember?) where g* includes relativistic ν’s He mass fraction so Nν ➚ ⇒ H ➚ ⇒ sooner freeze-out ⇒ n/p ➚ ⇒ He4 ➚ upper limit on He4 Nν = 3 LEP and light neutrinos Nν = 2.994 ± 0.012 Matter/Energy in the Universe Ωtotal = ΩΜ matter + ΩΛ ∼1 dark energy Matter: ΩΜ = Ωb + Ων + ΩCDM ∼ 0.27 baryons neutrinos cold dark matter Baryonic matter : Ωb ∼ 0.04 CDM Cold Dark Matter Dark Baryons stars, gas, brown dwarfs, white dwarfs Neutrinos: Ων ∼ 0.003 if Μ(ν) ∼ 0.1 eV Cold Dark Matter : ΩCDM ∼ 0.23 WIMPS/neutralinos, axions, … Luminous Stars Neutrinos Radiation Dark Energy Dark Energy
