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Lecture 3: the Microwave Background 1 Lecture 3: The Microwave Background 1. The Cosmic Microwave Background – Prediction of a Black Body spectrum – Preservation of Black Body spectrum with expansion – Discovery of Black Body spectrum (1978 Nobel Prize) – COBE measurements (2006 Nobel Prize) – The Cosmic dipole 2. The photon-to-baryon ratio 3. CMB Anisotropies: - Sacks-Wolfe effect - Baryonic Acoustic Oscillations - Sunyaev-Zeldovich 4. CMB missions: - WMAP - PLANCK 5. BAO experiments (2dFGRS, SDSS, WiggleZ, BOSS) Course Text: Chapter 9 Wikipedia: CMB, COBE, WMAP, PLANCK (Spacecraft), BAO Periods in the early-Universe • Big Bang – initial singularity (abundant energy appearing from nowhere, ???) • Inflation – rapid exponential expansion phase • Matter-antimatter annihilation (with symmetry breaking) – High photon-to-baryon ratio established • The quark soup – All possible particles in co-existence, bubbling in and out of existence • Baryogeneis (quark confinement) – Reduction to neutrons and protons • Nucleosynthesis (plasma era) – Plasma of charged nuclei (75%H, 25%He)+electrons • Recombination – Neutral atoms – Matter and radiation decouple (Universe transparent) – The surface of last scattering (the cosmic microwave background) • Reionisation • Galaxy formation The Plasma Era • After Nucleosynthesis: charge-neutral plasma – 12H++He+++14e-+109photons • Thompson scattering of photons by electrons: • Electrons and photons exchange energy • Maintains thermal equilibrium and coupling (same T) between radiation and matter. Plasma Era • Universe opague: • When U cools so that H++e-àH, photons no longer scattered and travel (mostly) uninterupted across the Universe. Cosmic background radiation • The photons will have a perfect BB distribution at a T~3000K (equivalent to ~1:109 photons having >13.6eV)* 13.6eV /20 T = " 3000K 3kb 9 [NB: x20 comes from Nγ/Nb for 1:10 photons > 13.6eV as before. * 13.6eV = energy required to inoise Hydrogen atom.] ! BB shape preserved • In an adiabatic expansion (no energy loss) BB shape preserved: 8$h # 3 "# d# = 3 d# c exp(h# /kBT) %1 with expansion : T&'# & ) Shape dependent on exponential term only ν ε i.e., dv r4 dv "v1 1 = "vo o if r is the expansion factor between v1 and v0 Energy density ( ! Frequency (ν) Discovery of CMB • 1948 George Gamov predicted that if a Big Bang occurred a perfect black body spectrum should exist with T~5K [paper universally ignored] • No attempt to look for this was made until 1964 – Dicke radiometer • In 1964 Penzias & Wilson discovered a background radiation at 3.5K • Latter obs. showed it had a perfect BB spectrum • Nobel prize 1978 COBE satellitte Launch: 1989 Aim to map entire sky from near-Earth orbit in microwave (1micron-5mm) 3 instruments - DMR - FIRAS - DIRBE 4yr mission All sky CMB maps CMB dipole --> Milky Way velocity !T v 1 " # v " 600 km s$ T c Near perfect BB spectrum reported withTpeak~2.7K COBE team awarded Nobel Prize 2006 Energy density of Universe 8$h # 3 "# d# = 3 d# c exp(h# /kBT) %1 Integrating over all frequency can show : 8$ 5k 4 " = B T 4 = 7.565 &10%16(2.725)4 15h 3c 3 " ' = = 4.5 &10%31 kgm%3 R c 2 ! Photon-to-baryon ratio Photon energy density ! 4.5"10#31 kgm#3 Energy of mean photon ! 3kBT=0.00023eV Photon density ! 1.9 "10#27 Baryon mass density ! 2 "10#28 kgm#3 Energy of mean baryon ! 936MeV Baryon density ! 2.1"10#36 Photon # to # baryon ratio ! 109 This ratio is unexpected as in early Universe we expect the levels to be roughly equal. Symmetry breaking In very early Universe (T>>1015K) when all reactions/particles are possible have equal numbers of everything. If heavy particles (e.g., Higgs Boson) have two decay paths which are not perfectly balanced, e.g, _ _ X " a(qq) + (1# a)(q l) _ _ _ X " b(qq) + (1# b)(ql) if a > b, more quark than anti- quarks We can get a build-up of matter over anti-matter. ! If a-b~10-9 a we might get: 109+1 Quarks + 109 AntiQuarks Annihlation 1Quark+109photons CMB Anisotropies • The CMB is not perfectly smooth but contains anisotropies on scales of 1:105 • These are the seeds from which all structure grows. • The exact form of these anisotropies have spawned a cottage industry in cosmological parameter extraction. • Main physical basis for anisotropies – Sachs-Wolfe effect – Doppler effect – Sunyaev-Zoldivich effect Causes of CMB Anistropy • Sachs-Wolfe effect (large scale anisotropies) – Photons must do work to escape from very large over-dense regions • Doppler effects (medium scale anistropies) – The peculiar motions and flows giving rise to over/under densities on specific scales (Set by the time between Big Bang and decoupling) • Sunyaev-Zeldovich – The interaction of CMB photons with intervening plasma (cluster halo gas) as they travel through space • Integrated Sachs-Wolfe effect – As CMB photons travel through space they will pass into and out of potential wells, as these are expanding more work is done climbing out than falling in. • Baryonic Acoustic Oscillations – A characteristic scale set by the outflow of photons from overdense regions visible in the galaxy distribution today COBE 1994 WMAP 2004 PLANCK 2009 PLANCK Measured anisotropies (pre-Planck) CMB peaks Any over-density will try to collapse under gravity and overshoot then collapse back setting up an oscillation which damps. If at the moment of photon-baryon de-coupling the photon-baryon fluid is caught in a collapsed state it will give-rise to an over-density etc. This sets up a series of damped peaks. The largest peak is from the largest area which can collapse in the time since the Big Bang and decoupling Precise form of Anisotropies depend on cosmological params. Baryonic Acoustic Oscillations • Baryon-photon fluid at maximum extension sets up an over-density of matter on a specific scale. • This is detectable in the galaxy distribution today as a BAO peak. Baryons Photons Baryon Amplitude Baryon Linear scale (Mpc) Photons and baryons expand together outward from an over-density Baryonic Acoustic Oscillations • Baryon-photon fluid at maximum extension sets up an over-density of matter on a specific scale. • This is detectable in the galaxy distribution today as a BAO peak. Baryons Photons Baryon Amplitude Baryon Linear scale (Mpc) Photons and baryons expand together outward from an over-density Baryonic Acoustic Oscillations • Baryon-photon fluid at maximum extension sets up an over-density of matter on a specific scale. • This is detectable in the galaxy distribution today as a BAO peak. Baryons Photons Baryon Amplitude Baryon Linear scale (Mpc) Photons and baryons expand together outward from an over-density Baryonic Acoustic Oscillations • Baryon-photon fluid at maximum extension sets up an over-density of matter on a specific scale. • This is detectable in the galaxy distribution today as a BAO peak. Baryons Photons Baryon Amplitude Baryon Linear scale (Mpc) Once decoupling occurs, the photons push outward and mass is left behind Baryonic Acoustic Oscillations • Baryon-photon fluid at maximum extension sets up an over-density of matter on a specific scale. • This is detectable in the galaxy distribution today as a BAO peak. Baryons Photons Baryon Amplitude Baryon Linear scale (Mpc) Photons continue expanding outwards, mass now stationary Baryonic Acoustic Oscillations • Baryon-photon fluid at maximum extension sets up an over-density of matter on a specific scale. • This is detectable in the galaxy distribution today as a BAO peak. Baryons Photons Baryon Amplitude Baryon Linear scale (Mpc) Photons smearing out, mass starts to self-gravitate Baryonic Acoustic Oscillations • Baryon-photon fluid at maximum extension sets up an over-density of matter on a specific scale. • This is detectable in the galaxy distribution today as a BAO peak. Baryons Photons Baryon Amplitude Baryon Linear scale (Mpc) Baryons show an excess peak at a characteristic scale (150Mpc) BAO • BAOs now seen in all major surveys – 2dFGRS, SDSS, 6df, WiggleZ Summary so far • Copernican Principle • Olber’s paradox and permanency • Discovery of the Expansion • Adoption of General Relativity • Conflict between Big Bang and Steady State • George Gamov – Explanation of the 4He abundance – Prediction of a Microwave Background • 1964 Discovery of CMB • 1990-2010s detailed mapping of CMB anisotropies • 2000s+ Discovery of Baryonic Acoustic Oscillations Numbers so far v Hubble constant: H = r o d ! "R some characteristic length today % Expansion Redshift: (1+ z) = observed ! $ o = ' !laboratory # R some characteristic length in the past& 4 " R % (4 (31 (3 Radiation: "rad,z=0 = $ ' "rad,z = (1+ z) "rad,z = 4.5)10 kgm #Ro & 3 " R % (3 (28 (3 Baryonic Matter: "baryons,z=0 = $ ' "baryons,z = (1+ z) "baryons,z = 2.0 )10 kgm #Ro & 3 " R % (3 (27 (3 Total Matter: "matter,z=0 = $ ' "matter,z = (1+ z) "matter,z = 2.0 )10 kgm [10x as much Dark Matter as baryons] #Ro & (1 Temperature: Tz=0 = (1+ z) Tz = 2.7K N Photon-to-baryon ratio: # =109 Nb Abundances: XP = 0.75,YP = 0.25, ZP = 0.00 Redshift • An expansion implies a stretching of space-time. • The more space-time there is between you and an object the faster it will appear to be moving away. • It is the expansion which causes a galaxy’s spectrum to be REDSHIFTED: STATIONARY: DOPPLER SHIFT: REDSHIFT: Dark Matter • E.g., A galaxy with absolute magnitude -20.0 mag has stars rotating at v=220km/s at a radius of 15kpc: 10 – Stellar Mass: ~2x10 MO " % f1 !0.4(M1!M2 ) !0.4(!20!(+5.6)) M1 ! M 2 = 2.5log10 $ ', or n* =10 =10 # f2 & 11 – Dynamical Mass: ~2x10 MO GMm mv2 v2r (220 !103 )2.(15!103 !3!1016 ) = , or, M= = r2 r G 6.67!10"11 – Implied Dark matter to baryonic matter ratio ~x10 Mass radiation equality ! ! rad,0 = (1+ z)!1 rad,z !matter,0 !matter,z.
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