1. Three-Year WMAP Observations: Method and Results
Eiichiro Komatsu
Department of Astronomy
HEP Seminar, April 27, 2006

2. David Wilkinson (1935~2002)
Science Team Meeting, July, 2002

3. 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.

4. WMAP Spacecraft 60K 90K 300K 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:
- instrument electronics
medium gain antennae
- attitude control/propulsion
- command/data handling
deployed solar array w/ web shielding
- battery and power control
MAP990422

5. WMAP Focal Plane 10 DAs (K, Ka, Q1, Q2, V1, V2, W1-W4)
Beams measured by observing Jupiter.

6. WMAP Goes To L2 June 30, 2001 July 30, 2001 October 1, 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
Earth
Y (AU)
0.000 L2
-0.005
-0.010
1.000
1.005
1.010
X (AU)

7. K band (22GHz)

8. Ka Band (33GHz)

9. Q Band (41GHz)

10. V Band (61GHz)

11. W Band (94GHz)

12. Intensity Mask

13. 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.

14. WMAP 3-yr Power Spectrum

15. Physics of CMB Anisotropy
SOLVE GENERAL RELATIVISTIC BOLTZMANN EQUATIONS TO THE FIRST ORDER IN PERTURBATIONS

16. Use temperature fluctuations, Q=DT/T, instead of f:
Expand the Boltzmann equation to the first order in perturbations:
where
describes the Sachs-Wolfe effect: purely GR fluctuations.

17. For metric perturbations in the form of:
Newtonian potential
Curvature perturbations
the Sachs-Wolfe terms are given by
where g is the directional cosine of photon propagations.
The 1st term = gravitational redshift
The 2nd term = integrated Sachs-Wolfe effect
h00/2
(higher T)
Dhij/2

18. Small-scale Anisotropy (<2 deg)
Collision term describing coupling between photons and baryons via electron scattering.
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.)

19. Boltzmann Equation to Hydrodynamics
Multipole expansion
Energy density, Velocity, Stress
Monopole: Energy density
Dipole: Velocity
Quadrupole: Stress

20. Photon Transport Equations
CONTINUITY
EULER
Photon-baryon coupling
f2=9/10 (no polarization), 3/4 (with polarization)
FA = -h00/2, FH = hii/2
tC=Thomson scattering optical depth

21. Baryon Transport
Cold Dark Matter

22. The Strong Coupling Regime
SOUND WAVE!

23. The Wave Form Tells Us Cosmological Parameters
Higher baryon density
Lower sound speed
Compress more
Higher peaks at compression phase (even peaks)

24. Weighing Dark Matter
where g is 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.

25. Weighing Dark Matter Smaller dark matter density
More time for potential to decay
Higher first peak

26. Measuring Geometry
Sound cross. length
W=1
W<1

27. K Band (23 GHz)
Dominated by synchrotron; Note that polarization direction is perpendicular to the magnetic field lines.

28. Ka Band (33 GHz)
Synchrotron decreases as n-3.2 from K to Ka band.

29. Q Band (41 GHz)
We still see significant polarized synchrotron in Q.

30. 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.

31. 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.

32. Polarization Mask
fsky=0.743

33. Jargon: E-mode and B-mode
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

34. Polarized Light Un-filtered
Polarized Light Filtered

35. 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

36. 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.)

37. 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.

38. Photon Transport Equation
Monopole
Dipole
Quadrupole
f2=3/4
FA = -h00/2, FH = hii/2
tC=Thomson scattering optical depth

39. Primordial Gravity Waves
Gravity waves create quadrupolar temperature anisotropy -> Polarization
Directly generate polarization without kV.
Most importantly, GW creates B mode.

40. Power Spectrum
Scalar T
Tensor T
Scalar E
Tensor E
Tensor B

41. 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

42. 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

43. Polarization from Reioniazation
“Reionization Bump”

44. Masking Is Not Enough: Foreground Must Be Cleaned
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
Rough fit to BB FG in 60GHz

45. 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)

46. 3-sigma detection of EE.
The “Gold” multipoles: l=3,4,5,6.
BB consistent with zero after FG removal.

47. Parameter Determination: 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

48. Constraints 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.

49. What Should WMAP Say About Inflation Models?
Hint for ns<1
Zero GW
The 1-d marginalized constraint from WMAP alone is ns=
GW>0
The 2-d joint constraint still allows for ns=1 (HZ).

50. What Should WMAP Say 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.

51. What Should WMAP Say 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.

52. What Should WMAP Say About Neutrino Mass?
WMAP alone (95%):
- Total mass < 2eV
WMAP+SDSS (95%)
- Total mass < 0.9eV
WMAP+all (95%)
- Total mass < 0.7eV

53. Summary Understanding of Analysis techniques
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.
Summary
To-do list for the next data release:
Understand FG and noise better.
We are still using only 1/2 of the polarization data.
These improvements, combined with more years of data, would further
reduce the error on tau.
Full 3-yr would give delta(tau)~0.02
Full 6-yr would give delta(tau)~0.014 (hopefully)
This will give us a better estimate of the tilt, and better constraints on inflation.