Three-Year WMAP Obser Three-Year WMAP Obser
vations:
vations:
Method and Results Method and Results
Eiichiro Komatsu (UT Austin) Eiichiro Komatsu (UT Austin)
Physics Seminar at UTSA Physics Seminar at UTSA
April 28, 2006
April 28, 2006
David Wilkinson (1935~2002) David Wilkinson (1935~2002)
• Science Team Meeting, July, 2002
Full Sky Microwave Map Full Sky Microwave Map
COBE/FIRAS : T=2.725 K
Uniform, “Fossil” Light from the Big Ban g
Cosmic Microwave Background Radiatio
n
COBE/FIRAS, 1990 COBE/FIRAS, 1990
Perfect blackbody = Thermal equilibrium = Big Bang
G. Gamow, 1948
G. Gamow, 1948
Determination of Physical Conditions in the Determination of Physical Conditions in the
Early Universe Early Universe
n+pD+
Why was it so important?
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-3 now. 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:
K 5 cm ~
10
cm K 10
10
~
3 / 1 3 - 18
-3 9 -7
0
⎟⎟
⎠
⎜⎜ ⎞
⎝
T ⎛
R. Alpher & R. Herman, 1949 R. Alpher & R. Herman, 1949
Log TIME (sec)
~5K
~10
Deuterium 9K
formation
A. Penzias & R. Wilson, 1965
A. Penzias & R. Wilson, 1965
COBE/DMR, 1992 COBE/DMR, 1992
Gravity is STRONGER in cold spots: T/T~
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The Wilkinson Microwave Anisotr The Wilkinson Microwave Anisotr
opy Probe opy 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 polari zation modes.
• Temperature anisotropy is measured by single differenc e.
• Polarization anisotropy is measured by double differenc e.
WMAP WMAP Spacecraft Spacecraft
MAP990422
thermally isolated instrument cylinder
secondary reflectors
focal plane assembly feed horns back to back Gregorian optics, 1.4 x 1.6 m primaries
upper omni antenna line of sight
deployed solar array w/ web shielding medium gain antennae
passive thermal radiator
warm spacecraft with:
- instrument electronics - attitude control/propulsion - command/data handling - battery and power control
60K
90K
300K
WMAP Focal Plane WMAP Focal Plane
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• 10 DAs (K, Ka, Q1, Q2, V1, V2, W1-W4)
• Beams measured by observing Jupiter.
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WMAP Goes To L2 WMAP Goes To L2
• 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
0.010
0.005
0.000
-0.005
-0.010
1.000 1.005 1.010
X (AU)
Earth L2
Y (AU)
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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Intensity Mask Intensity Mask
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The Angular Power Spectrum The Angular Power Spectrum
• CMB temperature anisotropy is very clos e to Gaussian; thus, its spherical harm onic transform, a
lm, is also Gaussian.
• Since a
lmis Gaussian, the power spectru m:
completely specifies statistical proper ties of CMB.
* lm lm
l a a
C =
WMAP 3-yr Power Spectrum WMAP 3-yr Power Spectrum
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Physics of CMB Anisotropy Physics of CMB Anisotropy
• SOLVE GENERAL RELATIVISTIC BOLTZMANN SOLVE GENERAL RELATIVISTIC BOLTZMANN EQUATIONS TO THE FIRST ORDER IN
EQUATIONS TO THE FIRST ORDER IN PERTURBATIONS
PERTURBATIONS
Use temperature fluctuations, =T/T, instead of f:
Expand the Boltzmann equation to the first order in perturbat ions:
where
describes the Sachs-Wolfe effect: purely GR fluctuations.
For metric perturbations in the form of:
€
ds
2= a
2[ ( −1+ h
00) dτ
2+ ( δ
ij+ h
ij) 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)
• When coupling is strong, photons and baryons move togethe r and behave as a perfect fluid.
• When coupling becomes less strong, the photon-baryon flui d acquires shear viscosity.
• So, the problem can be formulated as “hydrodynamics”.
(c.f. The Sachs-Wolfe effect was pure GR.)
Small-scale Anisotropy (<2 d Small-scale Anisotropy (<2 d
eg) eg)
Collision term describing coupling between photons and baryons
via electron scattering.
Boltzmann Equation to Hydro Boltzmann Equation to Hydro
dynamics dynamics
Monopole: Energy density Dipole: Velocity
Quadrupole: Stress
• Multipole expansion
• Energy density, Velocity, St
ress
Photon Transport Equations Photon 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
Baryon Transport Baryon Transport
Cold Dark Matter
The Strong Coupling Regime The Strong Coupling Regime
SOUND WAVE!
The Wave Form Tells Us Cosmolog The Wave Form Tells Us Cosmolog
ical Parameters ical Parameters
Higher baryon density
Lower sound speed
Compress more
Higher peaks at com pression phase (eve n peaks)
Weighing Dark Matter Weighing Dark Matter
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 c annot grow (the expansion of the Universe is too fast); thus, dar k matter potential gets shallower and shallower as the Universe expands --> potential decay --> ISW --> Boost Cl.
Weighing Dark Matter Weighing Dark Matter
• Smaller dar k matter de nsity
• More time f or potentia l to decay
• Higher firs
t peak
Measuring Geometry Measuring Geometry
Sound cross. length
θ
220
~ or deg
1
~ l
θ
θ
220 or
deg
1 >
< l
θ
• =
• <
K Band (23 GHz) K Band (23 GHz)
Dominated by synchrotron; Note that polarization direction is perpendicular to the magnetic field lines.
Ka Band (33 GHz) Ka Band (33 GHz)
Synchrotron decreases as -3.2 from K to Ka band.
Q Band (41 GHz) Q Band (41 GHz)
We still see significant polarized synchrotron in Q.
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.
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.
Polarization Mask Polarization Mask
f
sky=0.743
Jargon: E-mode and B-mode 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
Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky, Stebbins (1997)
Polarized Light Filtered
Polarized Light Un-filtered
Physics of CMB Polarization 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-bar yon fluid, which is generated by velocity gradient.
electron isotropic
anisotropic
no net polarization
net polarization
Boltzmann Equation Boltzmann Equation
• Temperature anisotropy, , can be generated by gravi tational effect (noted as “SW” = Sachs-Wolfe)
• Linear polarization (Q & U) is generated only by scat tering (noted as “C” = Compton scattering).
• Circular polarization (V) would not be generated. (Ne xt slide.)
Sources of Polarization Sources of Polarization
• Linear polarizat ion (Q and U) wi ll be generated from 1/10 of tem perature quadrup ole.
• Circular polariz ation (V) will N OT be generated.
No source term,
if V was initial
ly zero.
Photon Transport Equation Photon Transport Equation
f2=3/4
A = -h00/2, H = hii/2
C=Thomson scattering optical depth
Monopole Dipole
Quadrupole
Primordial Gravity Waves Primordial Gravity Waves
• Gravity waves create quadrupolar tempe rature anisotropy -> Polarization
• Directly generate polarization without kV.
• Most importantly, GW creates B mode.
Power Spectrum Power Spectrum
Scalar T
Tensor T
Scalar E Tensor E
Tensor B
Polarization From Reioniz Polarization From Reioniz
ation ation
• CMB was emitted at z~1088.
• Some fraction of CMB was re-scattered in a reion ized universe.
• The reionization redshift of ~11 would correspon d to 365 million years after the Big-Bang.
z=1088, ~ 1
z ~ 11, ~ 0.1
First-star formation
z=0 IONIZED
REIONIZED NEUTRAL
Measuring Optical Depth 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
Polarization from Reioniazation Polarization from Reioniazation
“Reionization Bump”
• Outside P06
– EE (solid) – BB (dashed)
• Black lines
– Theory EE
• tau=0.09
– Theory BB
• r=0.3
• Frequency = Geometri c mean of two freque ncies used to comput e Cl
Masking Is Not Enough:
Masking Is Not Enough:
Foreground Must Be Cleaned Foreground Must Be Cleaned
Rough fit to BB FG in 60GHz
Clean FG Clean 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)
BB consistent with zero after FG removal.
3-sigma detection of EE.
The “Gold” mu ltipoles: l=3,4, 5,6.
Parameter Determination:
Parameter Determination:
First Year vs Three Years First 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
Constraints on GW Constraints on GW
• Our ability to con strain the amplitu de of gravity wave s is still coming mostly from the te mperature spectru m.
– r<0.55 (95%)
• The B-mode spectru m adds very littl e.
• WMAP would have to integrate for at l east 15 years to d etect the B-mode s pectrum from infla tion.
What Should WMAP Say About What Should WMAP Say About
Inflation Models?
Inflation Models?
Hint for ns<1 Zero GW
The 1-d margin alized constrain t from WMAP al one is ns=0.95 +-0.02.
GW>0
The 2-d joint co nstraint still allo ws for ns=1 (H Z).
What Should WMAP Say About What Should WMAP Say About
Flatness?
Flatness?
Flatness, or very l ow Hubble’s const ant?
If H=30km/s/Mpc, a closed universe wit h Omega=1.3 w/o c osmological consta nt still fits the WMA P data.
What Should WMAP Say About What Should WMAP Say About
Dark Energy?
Dark Energy?
Not much!
The CMB data alone cannot c onstrain w very well. Combinin g the large-scal e structure data or supernova d ata breaks deg eneracy betwe en w and matte r density.
What Should WMAP Say About What Should WMAP Say About
Neutrino Mass?
Neutrino Mass?
WMAP alone (95%):
- Total mass < 2eV
WMAP+SDSS (95%) - Total mass < 0.9eV
WMAP+all (95%)
- Total mass < 0.7eV
• Understanding of
– Noise,
– Systematics, – Foreground, and
• Analysis techniques
• have significantly impro ved from the first-year release.
• A simple LCDM model fits both the temperature and polarization data very w