Three-Year WMAP Observations: Method and Results Eiichiro Komatsu (UT Austin) Physics Seminar at UTSA April 28, 2006
David Wilkinson (1935~2002) • Science Team Meeting, July, 2002
Full Sky Microwave Map COBE/FIRAS: T=2.725 K Uniform, “Fossil” Light from the Big Bang Cosmic Microwave Background Radiation
COBE/FIRAS, 1990 Perfect blackbody = Thermal equilibrium = Big Bang
Why was it so important? • Gamow has shown that the baryon number density was ~1018 cm-3, when temperature was 109 K. • It’s ~10-7 cm-3now. What is temperature now? • Since the baryon number density scales as (radius of the universe)–3 ~(temperature)3, we get for the present-day temperature:
R. Alpher & R. Herman, 1949 ~5K ~109 K Deuterium formation Log TIME (sec)
COBE/DMR, 1992 Gravity is STRONGER in cold spots: DT/T~F
The Wilkinson Microwave Anisotropy Probe • A microwave satellite working at L2 • Five frequency bands • K (22GHz), Ka (33GHz), Q (41GHz), V (61GHz), W (94GHz) • The Key Feature: Differential Measurement • The technique inherited from COBE • 10 “Differencing Assemblies” (DAs) • K1, Ka1, Q1, Q2, V1, V2, W1, W2, W3, & W4, each consisting of two radiometers that are sensitive to orthogonal linear polarization modes. • Temperature anisotropy is measured by single difference. • Polarization anisotropy is measured by double difference.
WMAP Spacecraft upper omni antenna back to back line of sight Gregorian optics, 1.4 x 1.6 m primaries 60K passive thermal radiator focal plane assembly feed horns secondary 90K reflectors thermally isolated instrument cylinder 300K warm spacecraft with: medium gain antennae - instrument electronics - attitude control/propulsion - command/data handling deployed solar array w/ web shielding - battery and power control MAP990422
WMAP Focal Plane • 10 DAs (K, Ka, Q1, Q2, V1, V2, W1-W4) • Beams measured by observing Jupiter.
WMAP Goes To L2 0.010 • June 30, 2001 • Launch • Phasing loop • July 30, 2001 • Lunar Swingby • October 1, 2001 • Arrive at L2 • October 2002 • 1st year data • February 11, 2003 • 1st data release • October 2003 • 2nd year data • October 2004 • 3rd year data • March 16, 2006 • 2nd data release 0.005 Earth Y (AU) L2 0.000 -0.005 -0.010 1.000 1.005 1.010 X (AU)
The Angular Power Spectrum • CMB temperature anisotropy is very close to Gaussian; thus, its spherical harmonic transform, alm, is also Gaussian. • Since alm is Gaussian, the power spectrum: completely specifies statistical properties of CMB.
Physics of CMB Anisotropy • SOLVE GENERAL RELATIVISTIC BOLTZMANN EQUATIONS TO THE FIRST ORDER IN PERTURBATIONS
Use temperature fluctuations, Q=DT/T, instead off: Expand the Boltzmann equation to the first order in perturbations: where describes the Sachs-Wolfe effect: purely GR fluctuations.
For metric perturbations in the form of: Newtonian potential Curvature perturbations the Sachs-Wolfe terms are given by wheregis the directional cosine of photon propagations. • The 1st term = gravitational redshift • The 2nd term = integrated Sachs-Wolfe effect h00/2 (higher T) Dhij/2
Small-scale Anisotropy (<2 deg) • When coupling is strong, photons and baryons move together and behave as a perfect fluid. • When coupling becomes less strong, the photon-baryon fluid acquires shearviscosity. • So, the problem can be formulated as “hydrodynamics”. (c.f. The Sachs-Wolfe effect was pure GR.) Collision term describing coupling between photons and baryons via electron scattering.
Boltzmann Equation to Hydrodynamics • Multipole expansion • Energy density, Velocity, Stress Monopole: Energy density Dipole: Velocity Quadrupole: Stress
CONTINUITY EULER Photon-baryon coupling Photon Transport Equations f2=9/10 (no polarization), 3/4 (with polarization) FA = -h00/2, FH = hii/2 tC=Thomson scattering optical depth
Baryon Transport Cold Dark Matter
The Strong Coupling Regime SOUND WAVE!
The Wave Form Tells Us Cosmological Parameters Higher baryon density • Lower sound speed • Compress more • Higher peaks at compression phase (even peaks)
Weighing Dark Matter wheregis the directional cosine of photon propagations. • The 1st term = gravitational redshift • The 2nd term = integrated Sachs-Wolfe effect h00/2 (higher T) Dhij/2 During the radiation dominated epoch, even CDM fluctuations cannot grow (the expansion of the Universe is too fast); thus, dark matter potential gets shallower and shallower as the Universe expands --> potential decay --> ISW --> Boost Cl.
Weighing Dark Matter • Smaller dark matter density • More time for potential to decay • Higher first peak
Measuring Geometry Sound cross. length • W=1 • W<1
K Band (23 GHz) Dominated by synchrotron; Note that polarization direction is perpendicular to the magnetic field lines.
Ka Band (33 GHz) Synchrotron decreases as n-3.2 from K to Ka band.
Q Band (41 GHz) We still see significant polarized synchrotron in Q.
V Band (61 GHz) The polarized foreground emission is also smallest in V band. We can also see that noise is larger on the ecliptic plane.
W Band (94 GHz) While synchrotron is the smallest in W, polarized dust (hard to see by eyes) may contaminate in W band more than in V band.
Polarization Mask fsky=0.743
Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky, Stebbins (1997) Jargon: E-mode and B-mode • Polarization is a rank-2 tensor field. • One can decompose it into a divergence-like “E-mode” and a vorticity-like “B-mode”. E-mode B-mode
Polarized Light Un-filtered Polarized Light Filtered
Physics of CMB Polarization • Thomson scattering generates polarization, if… • Temperature quadrupole exists around an electron • Where does quadrupole come from? • Quadrupole is generated by shear viscosity of photon-baryon fluid, which is generated by velocity gradient. electron isotropic no net polarization anisotropic net polarization
Boltzmann Equation • Temperature anisotropy, Q, can be generated by gravitational effect (noted as “SW” = Sachs-Wolfe) • Linear polarization (Q & U) is generated only by scattering (noted as “C” = Compton scattering). • Circular polarization (V) would not be generated. (Next slide.)
Sources of Polarization • Linear polarization (Q and U) will be generated from 1/10 of temperature quadrupole. • Circular polarization (V) will NOT be generated. No source term, if V was initially zero.
Monopole Dipole Photon Transport Equation Quadrupole f2=3/4 FA = -h00/2, FH = hii/2 tC=Thomson scattering optical depth
Primordial Gravity Waves • Gravity waves create quadrupolar temperature anisotropy -> Polarization • Directly generate polarization without kV. • Most importantly, GW creates B mode.
Power Spectrum Scalar T Tensor T Scalar E Tensor E Tensor B
Polarization From Reionization • CMB was emitted at z~1088. • Some fraction of CMB was re-scattered in a reionized universe. • The reionization redshift of ~11 would correspond to 365 million years after the Big-Bang. IONIZED z=1088, t～1 NEUTRAL First-star formation z～11, t～0.1 REIONIZED z=0
Measuring Optical Depth • Since polarization is generated by scattering, the amplitude is given by the number of scattering, or optical depth of Thomson scattering: which is related to the electron column number density as