1. Three-Year WMAP Observations: Method and Results Eiichiro Komatsu (UT Austin) Colloquium at U. of Florida October 13, 2006

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

3. POLARIZATION DATA!!

4. WMAP Three Year Papers

5. Full Sky Microwave Map COBE/FIRAS : T=2.725 K Uniform, “ Fossil ” Light from the Big Bang Cosmic Microwave Background Radiation

6. G. Gamow, 1948

7. Determination of Physical Conditions in the Early Universe n+p  D+ 

8. Why was it so important? Gamow has shown that the baryon number density was ~10 18 cm -3, when the temperature was 10 9 K. It ’ s ~10 -7 cm -3 now. What is the temperature now? Since the baryon number density scales as (radius of the universe) – 3 ~(temperature) 3, we get for the present-day temperature: Who calculated this first?

9. R. Alpher & R. Herman, 1949 Log TIME (sec) ~5K ~10 9 K Deuterium formation

10. A. Penzias & R. Wilson, 1965

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

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

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

15. 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

16. 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.

17. WMAP 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

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

19. 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 –1 st data release October 2003 –2nd year data October 2004 –3rd year data March 16, 2006 –2 nd data release 0.010 0.005 0.000 -0.005 -0.010 1.0001.0051.010 X (AU) L2 Earth Y (AU)

20. K band (22GHz)

21. Ka Band (33GHz)

22. Q Band (41GHz)

23. V Band (61GHz)

24. W Band (94GHz)

25. 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.

26. WMAP 3-yr Power Spectrum

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

28. 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.

29. For metric perturbations in the form of: 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 h 00 /2  h ij /2 (higher T)

30. 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) Collision term describing coupling between photons and baryons via electron scattering.

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

32. Photon Transport Equations f 2 =9/10 (no polarization), 3/4 (with polarization)  A = -h 00 /2,  H = h ii /2  C =Thomson scattering optical depth CONTINUITY EULER Photon-baryon coupling

33. Baryon Transport Cold Dark Matter

34. The Strong Coupling Regime SOUND WAVE!

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

36. 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 h 00 /2  h ij /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 C l.

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

38. Measuring Geometry Sound cross. length  

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

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

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

42. 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.

43. 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.

44. Polarization Mask f sky =0.743

45. 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-modeB-mode Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky, Stebbins (1997)

46. Polarized Light Filtered Polarized Light Un-filtered

47. 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. electron isotropic anisotropic no net polarization net polarization

48. Boltzmann 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) is not generated by Thomson scattering.

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

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

51. 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. z=1088,  ～ 1 z ～ 11,  ～ 0.1 First-star formation z=0 IONIZED REIONIZED NEUTRAL

52. 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

53. Polarization from Reioniazation “ Reionization Bump ”

54. 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

55. 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)

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

57. 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

58. 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.

59. What Should WMAP Say About Inflation Models? Hint for ns<1 Zero GW The 1-d marginalized constraint from WMAP alone is ns=0.95+-0.02. GW>0 The 2-d joint constraint still allows for ns=1.

60. 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.

61. 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.

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

63. 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

64. 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.

65. 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

66. 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

67. Constraints on  Tau is almost entirely determined by the EE data. –TE adds very little. Black Solid: TE+EE Cyan: EE only Dashed: Gaussian C l Dotted: TE+EE from KaQVW Shaded: Kogut et al.’s stand-alone tau analysis from C l TE Grey lines: 1-yr full analysis (Spergel et al. 2003)

68. Tau is Constrained by EE The EE data alone give –tau = 0.100 +- 0.029 The TE+EE data give –tau = 0.092 +- 0.029 The TT+TE+EE give –tau = 0.093 +- 0.029 This indicates that the EE data have exhausted most of the information on tau contained in the WMAP 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.

69. 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

70. 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.

71. Temperature Data: First Year

72. Three Year Significant improvement at the second and third peak.

73. “ WMAPext ”