1. Polarized Light in the Cosmic Microwave Background: WMAP Three-year Results Eiichiro Komatsu (UT Austin) Colloquium at U. of Minnesota November 3, 2006

2. Full Sky Microwave Map Penzias & Wilson, 1965 Uniform, “ Fossil ” Light from the Big Bang -Isotropic -Unpolarized Galactic Center Galactic Anti- center

3. A. Penzias & R. Wilson, 1965

4. CMB T = 2.73 K Helium Superfluidity T = 2.17 K

5. COBE/FIRAS, 1990 Perfect blackbody = Thermal equilibrium = Big Bang

6. COBE/DMR, 1992 Gravity is STRONGER in cold spots:  T/T~  Isotropic?

8. COBE, “Followed-up” by WMAP COBE WMAP COBE 1989 WMAP 2001 [COBE’s] measurements also marked the inception of cosmology as a precise science. It was not long before it was followed up, for instance by the WMAP satellite, which yielded even clearer images of the background radiation. Press Release from the Nobel Foundation

9. David Wilkinson (1935~2002) Science Team Meeting, July, 2002 Plotted the “ second point ” (3.2cm) on the CMB spectrum –The first confirmation of a black-body spectrum (1966) Made COBE and MAP happen and be successful “ Father of CMB Experiment ” MAP has become WMAP in 2003

10. So, It ’ s Been Three Years Since The First Data Release in 2003. What Is New Now?

11. POLARIZATION DATA!! Not only anisotropic, but also polarized.

12. The Wilkinson Microwave Anisotropy Probe A microwave satellite working at L2 Five frequency bands –K (22GHz), Ka (33GHz), Q (41GHz), V (61GHz), W (94GHz) –Multi-frequency is crucial for cleaning the Galactic emission 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. POLARIZATION DATA!!

13. WMAP Three Year Papers

14. K band (22GHz)

15. Ka Band (33GHz)

16. Q Band (41GHz)

17. V Band (61GHz)

18. W Band (94GHz)

19. The Angular Power Spectrum CMB temperature anisotropy is very close to Gaussian (Komatsu et al., 2003); thus, its spherical harmonic transform, a lm, is also Gaussian. Since a lm is Gaussian, the power spectrum: completely specifies statistical properties of CMB.

20. WMAP 3-yr Power Spectrum

21. What Temperature Tells Us Distance to z~1100 Baryon- to-Photon Ratio Matter-Radiation Equality Epoch Dark Energy/ New Physics?

22. CMB to Cosmology &Third Baryon/Photon Density Ratio Low Multipoles (ISW)

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

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

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

26. 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.

27. 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.

28. Polarization Mask f sky =0.743

29. Jargon: E-mode and B-mode Polarization has directions! One can decompose it into a divergence- like “E-mode” and a vorticity-like “B-mode”. E-modeB-mode Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky, Stebbins (1997)

30. Polarized Light Filtered Polarized Light Un-filtered

31. Physics of CMB Polarization Thomson scattering generates polarization, if and only if … –Temperature quadrupole exists around an electron –Where does quadrupole come from? Quadrupole is generated by shear viscosity of photon-baryon fluid. electron isotropic anisotropic no net polarization net polarization

32. Boltzmann Equation Temperature anisotropy, , can be generated by gravitational effect (noted as “SW” = Sachs-Wolfe, 1967) Linear polarization (Q & U) is generated only by scattering (noted as “C” = Compton scattering). Circular polarization (V) is not generated by Thomson scattering.

33. Primordial Gravity Waves Gravity waves also create quadrupolar temperature anisotropy -> Polarization Most importantly, GW creates B mode.

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

35. Polarization From Reionization CMB was emitted at z~1100. 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. z=1100,  ～ 1 z ～ 11,  ～ 0.1 First-star formation z=0 IONIZED REIONIZED NEUTRAL e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e-

36. 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

37. Polarization from Reioniazation “ Reionization Bump ” 22

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

40. 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)

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

42. 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

43. Null Tests It’s very powerful to have three years of data. –Year-year differences must be consistent with zero signal. yr1-yr2, yr2-yr3, and yr3-yr1 We could not do this null test for the first year data. –We are confident that we understand polarization noise to a couple of percent level. Statistical isotropy –TB and EB must be consistent with zero. Inflation prior… –We don’t expect 3-yr data to detect any BB.

44. Data Combination (l<23) We used Ka, Q, V, and W for the 1-yr TE analysis. We use only Q and V for the 3-yr polarization analysis. –Despite the fact that all of the year-year differences at all frequencies have passed the null tests, the 3-yr combined power spectrum in W band shows some anomalies. EE at l=7 is too high. We have not identified the source of this anomalous signal. (FG is unlikely.) We have decided not to use W for the 3-yr analysis. –The residual synchrotron FG is still a worry in Ka. We have decided not to use Ka for the 3-yr analysis. KaQVW is ~1.5 times more sensitive to tau than QV. –Therefore, the error reduction in tau by going from the first-year (KaQVW) to three-year analysis (QV) is not as significant as one might think from naïve extrapolation of the first-year result. –There is also another reason why the three-year error is larger (and more accurate) – next slide.

45. Correlated Noise At low l, noise is not white. 1/f noise increases noise at low l –See W4 in particular. Scan pattern selectively amplifies the EE and BB spectra at particular multipoles. –The multipoles and amplitude of noise amplification depend on the beam separation, which is different from DA to DA. Red: white noise model (used in the first-year analysis) Black: correlated noise model (3-yr model)

46. Low-l TE Data: Comparison between 1-yr and 3-yr 1-yr TE and 3-yr TE have about the same error-bars. –1yr used KaQVW and white noise model Errors significantly underestimated. Potentially incomplete FG subtraction. –3yr used QV and correlated noise model Only 2-sigma detection of low-l TE.

47. High-l TE Data The amplitude and phases of high-l TE data agree very well with the prediction from TT data and linear perturbation theory and adiabatic initial conditions. (Left Panel: Blue=1yr, Black=3yr) Phase Shift Amplitude

48. High-l EE Data When QVW are coadded, the high-l EE amplitude relative to the prediction from the best-fit cosmology is 0.95 +- 0.35. Expect ~4-5sigma detection from 6-yr data. WMAP: QVW combined

49.  1st year vs 3rd year Tau is almost entirely determined by the EE from the 3-yr data. –TE adds very little. Dotted: Kogut et al.’s stand-alone tau analysis from TE Grey lines: 1-yr full analysis (Spergel et al. 2003)

50. Tau is Constrained by EE The stand-alone analysis of EE data gives –tau = 0.100 +- 0.029 The stand-alone analysis of TE+EE gives –tau = 0.092 +- 0.029 The full 6-parameter analysis gives –tau = 0.093 +- 0.029 (Spergel et al.; no SZ) This indicates that the stand-alone EE analysis has exhausted most of the information on tau contained in the polarization data. –This is a very powerful statement: this immediately implies that the 3-yr polarization data essentially fixes tau independent of the other parameters, and thus can break massive degeneracies between tau and the other parameters.

51. Degeneracy Finally Broken: Negative Tilt & Low Fluctuation Amplitude Degeneracy Line from Temperature Data Alone Polarization Data Nailed Tau Temperature Data Constrain “  8 exp(-  )” Lower  Polarization Nailed Tau Lower 3rd peak

52. 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.

53. What Should WMAP Say About Inflation Models? Hint for ns<1 Zero GW The 1-d marginalized constraint from WMAP alone is ns=0.96+-0.02. GW>0 The 2-d joint constraint still allows for ns=1.

54. 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.

55. 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.

56. What Should WMAP Say About Neutrino Mass? 3.04)

57. 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. To-do list for the next data release (now working on the 5-year data) 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. Summary Tau=0.09+-0.03