results from three- year wmap observations eiichiro komatsu (ut austin) tev ii particle astrophysics...
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Results from Three-Results from Three-Year WMAP Year WMAP
ObservationsObservations
Eiichiro Komatsu (UT Austin)Eiichiro Komatsu (UT Austin)TeV II Particle AstrophysicsTeV II Particle Astrophysics
August 29, 2006August 29, 2006
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Why Care About WMAP?Why Care About WMAP?• WMAP observes CMB. This is a conference about “Te
V” particle astrophysics. Why care about CMB? – The present-day temperature of CMB is 2.725K, or 2.35 m
eV.– The temperature at decoupling (where the most of CMB is
coming from) was ~3000K, or 0.26 eV. – The temperature at matter-radiation equality was ~9000K,
or 0.8 eV. • CMB is a nuisance for many particle astrophysicists:
it attenuates cosmic-ray particles traveling through the universe. (GZK)
• Why am I here?
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What Can CMB Offer?What Can CMB Offer?• Baryon-to-photon ratio in the universe
– Sound speed and inertia of baryon-photon fluid• Matter-to-radiation ratio in the universe
– Dark matter abundance– “Radiation” may include photons, neutrinos as well as any other relativi
stic components.• Angular diameter distance to decoupling surface
– Peak position in l space ~ (Sound horizon)/(Angular Diameter Distance) • Time dependence of gravitational potential
– Integrated Sachs-Wolfe Effect, Dark energy• Primordial power spectrum (Scalar+Tensor)
– Constraints on inflationary models• Optical depth
– Cosmic reionization
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Full Sky Microwave MapFull Sky Microwave Map
COBE/FIRAS: T=2.725 K
Uniform, “Fossil” Light from the Big Bang
Cosmic Microwave Background Radiation
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COBE/FIRAS, 1990COBE/FIRAS, 1990Perfect blackbody = Thermal equilibrium = Big Bang
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COBE/DMR, 1992COBE/DMR, 1992
Gravity is STRONGER in cold spots: T/T~
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The Wilkinson Microwave The Wilkinson Microwave Anisotropy ProbeAnisotropy 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.
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K band (22GHz)K band (22GHz)
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Ka Band (33GHz)Ka Band (33GHz)
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Q Band (41GHz)Q Band (41GHz)
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V Band (61GHz)V Band (61GHz)
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W Band (94GHz)W Band (94GHz)
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The Angular Power SpectrumThe 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.
*lmlml aaC
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WMAP 3-yr Power SpectrumWMAP 3-yr Power Spectrum
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Physics of CMB AnisotropyPhysics of CMB Anisotropy
• SOLVE GENERAL RELATIVISTIC BOLTZMANN SOLVE GENERAL RELATIVISTIC BOLTZMANN EQUATIONS TO THE FIRST ORDER IN EQUATIONS TO THE FIRST ORDER IN PERTURBATIONSPERTURBATIONS
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Use temperature fluctuations, =T/T, instead of f:
Expand the Boltzmann equation to the first order in perturbations:
where
describes the Sachs-Wolfe effect: purely GR fluctuations.
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For metric perturbations in the form of:
ds2 a2 1 h00 d 2 ij hij dx idx j the Sachs-Wolfe terms are given by
where is the directional cosine of photon propagations.
Newtonian potential Curvature perturbations
1. The 1st term = gravitational redshift
2. The 2nd term = integrated Sachs-Wolfe effect
h00/2
hij/2
(higher T)
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• 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 shear viscosity.
• So, the problem can be formulated as “hydrodynamics”. (c.f. The Sachs-Wolfe effect was pure GR.)
Small-scale Anisotropy (<2 deg)Small-scale Anisotropy (<2 deg)
Collision term describing coupling between photons and baryons via electron scattering.
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Boltzmann Equation to HydrodBoltzmann Equation to Hydrodynamicsynamics
Monopole: Energy density
Dipole: Velocity
Quadrupole: Stress
• Multipole expansion
• Energy density, Velocity, Stress
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Photon Transport EquationsPhoton Transport Equations
f2=9/10 (no polarization), 3/4 (with polarization)
A = -h00/2, H = hii/2
C=Thomson scattering optical depth
CONTINUITY
EULER
Photon-baryon coupling
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Baryon TransportBaryon Transport
Cold Dark Matter
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The Strong Coupling RegimeThe Strong Coupling Regime
SOUND WAVE!
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The Wave Form Tells Us The Wave Form Tells Us Cosmological ParametersCosmological Parameters
Higher baryon density
Lower sound speed
Compress more
Higher peaks at compression phase (even peaks)
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What CMB MeasuresWhat CMB MeasuresA
mpl
itud
e of
tem
pera
ture
flu
ctua
tion
s at
a g
iven
sca
le, l
400 80020040 10010Multipole moment l~ Small scalesLarge scales
Ang.Diam. Distance
Baryon-to-photon Ratio
Mat-to-Radiation Ratio
ISW
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CMB to ParametersCMB to Parameters
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Measuring Matter-Radiation RatioMeasuring Matter-Radiation Ratio
where is the directional cosine of photon propagations.
1. The 1st term = gravitational redshift
2. The 2nd term = integrated Sachs-Wolfe effect
h00/2
hij/2
(higher T)
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.
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Matter-Radiation RatioMatter-Radiation Ratio
• More extra radiation component means that the equality happens later.• Since gravitational potential decays during the radiation era (free-fall
time scale is longer than the expansion time scale during the radiation era), ISW effect increases anisotropy at around the Horizon size at the equality.
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How Many (Effective) Neutrinos?How Many (Effective) Neutrinos?
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So, It’s Been Three Years Since So, It’s Been Three Years Since The First Data Release. What Is The First Data Release. What Is
New Now?New Now?
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POLARIZATION DATA!!POLARIZATION DATA!!
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K Band (23 GHz)K Band (23 GHz)Dominated by synchrotron; Note that polarization direction is perpendicular to the magnetic field lines.
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Ka Band (33 GHz)Ka Band (33 GHz)Synchrotron decreases as -3.2 from K to Ka band.
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Q Band (41 GHz)Q Band (41 GHz)We still see significant polarized synchrotron in Q.
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V Band (61 GHz)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.
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W Band (94 GHz)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.
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Polarized Light Filtered
Polarized Light Un-filtered
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Jargon: E-mode and B-modeJargon: 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
Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky, Stebbins (1997)
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Physics of CMB PolarizationPhysics 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.
electronisotropic
anisotropic
no net polarization
net polarization
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Boltzmann EquationBoltzmann Equation
• Temperature anisotropy, , 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.)
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Primordial Gravity WavesPrimordial Gravity Waves• Gravity waves create quadrupolar temperatu
re anisotropy -> Polarization• Directly generate polarization without kV.• Most importantly, GW creates B mode.
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Power SpectrumPower SpectrumScalar T
Tensor T
Scalar E
Tensor E
Tensor B
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Polarization From ReionizatioPolarization From Reionizationn
• CMB was emitted at z~1088.• Some fraction of CMB was re-scattered in a reionized u
niverse.• The reionization redshift of ~11 would correspond to 3
65 million years after the Big-Bang.
z=1088, ~ 1
z~ 11, ~0.1
First-star formation
z=0
IONIZED
REIONIZED
NEUTRAL
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Measuring Optical DepthMeasuring 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
Ne =
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Polarization from ReioniazationPolarization from Reioniazation
“Reionization Bump”
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• Outside P06– EE (solid)– BB (dashed)
• Black lines– Theory EE
• tau=0.09– Theory BB
• r=0.3
• Frequency = Geometric mean of two frequencies used to compute Cl
Masking Is Not Enough: Masking Is Not Enough: Foreground Must Be CleanedForeground Must Be Cleaned
Rough fit to BB FG in 60GHz
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Clean FGClean FG
•Only two-parameter fit!
•Dramatic improvement in chi-squared.
•The cleaned Q and V maps have the reduced chi-squared of ~1.02 per DOF=4534 (outside P06)
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BB consistent with zero after FG removal.
3-sigma detection of EE.
The “Gold” multipoles: l=3,4,5,6.
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Parameter Determination: Parameter Determination: First Year vs Three YearsFirst Year vs Three Years
• The simplest LCDM model fits the data very well.– A power-law primordial power spectrum– Three relativistic neutrino species– Flat universe with cosmological constant
• The maximum likelihood values very consistent– Matter density and sigma8 went down slightly
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What Should WMAP Say What Should WMAP Say About Flatness?About Flatness?
Flatness, or very low Hubble’s constant?
If H=30km/s/Mpc, a closed universe with Omega=1.3 w/o cosmological constant still fits the WMAP data.
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Constraints on GWConstraints on GW• Our ability to
constrain the amplitude of gravity waves is still coming mostly from the temperature spectrum.– r<0.55 (95%)
• The B-mode spectrum adds very little.
• WMAP would have to integrate for at least 15 years to detect the B-mode spectrum from inflation.
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What Should WMAP Say What Should WMAP Say About Inflation Models?About Inflation Models?
Hint for ns<1
Zero GW The 1-d marginalized constraint from WMAP alone is ns=0.95+-0.02.
GW>0The 2-d joint constraint still allows for ns=1 (HZ).
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What Should WMAP Say What Should WMAP Say About Dark Energy?About Dark Energy?
Not much!
The CMB data alone cannot constrain w very well. Combining the large-scale structure data or supernova data breaks degeneracy between w and matter density.
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What Should WMAP Say What Should WMAP Say About Neutrino Properties?About Neutrino Properties?
3.04)
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• Understanding of– Noise,– Systematics,– Foreground, and
• Analysis techniques • have significantly improved
from the first-year release.
• A simple LCDM model fits both the temperature and polarization data very well.
• CMB offers constraints on:
• Neutrino properties: the number of species and mass
• Dark matter abundance
• Dark matter abundance and properties
• Inflationary models (flatness and spectral index)
• Reionization of the universe
• We are now working on the 5-year data…
SummarySummary