1. Cleaned Three-Year WMAP CMB Map: Magnitude of the Quadrupole and Alignment of Large Scale Modes Chan-Gyung Park, Changbom Park (KIAS), J. Richard Gott III (Princeton Univ.)

2. Research Background 1. WMAP 3yr data analysis (Hinshaw et al. 2006, Spergel et al. 2006, Page et al. 2006) 2. Some peculiar aspects of the CMB 3. What is the origin of the anomalies in the CMB? Cosmological? Due to the residual Galactic foreground emission? (i) Accurate determination of cosmological parameters (ii) Flat, CDM- and Λ-dominated universe (i) Many reports of detection of non-Gaussianity (ii) Asymmetry between North & South hemispheres (Park 2004; Eriksen et al. 2004) (iii) Low CMB quadrupole power Cut-sky analysis : 211 μK 2 ΛCDM Model: 1250 μK 2 (iv) Alignment and planarity of l =2 and l =3 modes

3. Foreground Subtraction Methods from Multi-frequency CMB Data 1. Galactic Template Fitting Method (most popular) 2. Internal Linear Combination (ILC) Method Model the Galactic emission as the weighted sum of foreground templates (synchrotron + free-free + dust emissions) [Bennett et al. 2003] (i) Linearly combine five WMAP maps (FWHM=1°, 22.8 – 93.5 GHz) to reduce the Galactic foregrounds. Find five coefficients w i that minimizes the variance of the combined map T(p). (ii) WMAP 3-year (Hinshaw et al. 2006): Weights are obtained by Largrange multiplier method (Eriksen et al 2004), bias correction for the residual foreground emission (iii) Tegmark et al. (2003), de Oliveira-Costa & Tegmark (2006): a variant of ILC method (linear combinations in the harmonic space) – high resolution CMB map

4. Hinshaw et al. (2006)Tegmark et al. (2003) de Oliveira-Costa & Tegmark (2006) Foreground removal methods have been applied to several disjoint sky regions that contain map-pixels with similar properties. Otherwise, the efficiency of the ILC method becomes very low, leaving significant residual foregrounds. Previous Foreground-Cleaned Maps Region Definition Maps Cleaned Maps

5. Sum of synchrotron, free-free, and dust emission maps derived by the Maximum Entropy Method (WMAP team; Hinshaw et al. 2006) Improved ILC method (i ) Combination weights [w i ] from the constraint of minimum variance (ii ) Definition of pixel groups with common foreground spectral properties The foreground reduction of ILC will be successful when the ILC is performed at a region where the foreground characteristic is most homogeneous.

6. Galactic emission intensities Spectral index histogram 22-61 GHz 61-94 GHz 20 Spectral Index of Galactic Foreground Intensities [22-61 GHz] [61-94 GHz] The spectral index is a sensitive function of both frequency and direction.

7. Divides each histogram into 20 bins that contain equal number of pixels (~157,300) Definition of Pixel Groups Defines 400 groups of pixels with similar spectral properties 400 = 20 (Low) x 20 (Hi freq.) 22-61 GHz 61-94 GHz Group Index

8. Foreground-Cleaned CMB Map Temperature Applies ILC method to each pixel group. SILC400 CMB map (FWHM=1º)

9. Bias Due to Residual Galactic Emission (from 200 simulations) [SILC400 Mock – True Input CMB] Mean Std On the SILC400, we performs bias correction for the effects of residual Galactic emission Two hundred simulations that mimic the WMAP data and analyze them in the same way that SILC400 is made.

10. Large Scale Mode Statistics 1. Power spectrum (quadrupole and octopole powers) 2. Quadrupole and octopole direction ( n 2, n 3 ), angular separation θ 23 (de Oliveira-Costa et al. 2004) Find a direction n that maximizes angular momentum dispersion.

11. Magnitude of Quadrupole ( l =2) Strong alignment of Quadrupole and Octopole ( l =3) l =2 Power p l =3 Power( l 2, b 2 ), ( l 3, b 3 )Ang. sep. p Cut Sky Analysis (WMAP 3-yr) 211 μK 2 2.6% 1041 μK 2 ΛCDM Model1250 μK 2 1143 μK 2 WMAP team’s ILC 249 μK 2 3.7% 1051 μK 2 (235º,68º),(237º,63º)5.8 deg 0.52% Eriksen et al. (2004) 351 μK 2 7.6% 1090 μK 2 (248º,62º),(233º,63º)6.9 deg 0.72% de Oliveira & Tegmark (2006) 210 μK 2 2.5% 1038 μK 2 (224º,77º),(237º,64º)13.2 deg 2.65% SILC400 5.7%4.29% p value denotes the probability of finding a lower quadrupole (or angular sep.) than the measured value if the concordance ΛCDM model is correct.

12. Comparison of Angular Power Spectra Power Spectrum of SILC400 is very similar to measurements of WMAP and other teams up to l =35 Due to instrument and reconstruction noises, all ILC maps give higher amplitude with increasing l. SILC400 has lower amplitude than those of WMAP team ILC and Tegmark ILC, which indicates that our ILC method better satisfies the minimum variance constraint.

13. Dependence of Statistics on Number of Pixel-Groups We investigate whether the measured statistics depend on the number of pixel- groups. N group > a few hundred, all statistics become very stable. Pole directions Standard deviations Quadrupole and Octopole powers Angular separation between l=2 and 3

14. Discussion 1. We have derived a new foreground-reduced CMB map from the WMAP 3- year data by applying improved internal linear combination method where the information of the spectral properties of the Galactic foreground emission has been used. 2. The low quadrupole power, and strong alignment between quadrupole and octopole have been identified (consistent with previous measurements). 3. The known large-scale anomalies are only marginally significant with p values around 4-6%. 4. Actually, there exists correlations between all ILC maps and the Galactic emission maps. Whether the residual foreground strongly affects the measured statistics or not is not clear. Need further investigations.

15. Thanks

16. Linear Combination Weights (step 4) Minimizing for each group of pixels

17. Comparison with Other ILC Maps WMAP team’s ILC – SILC400 (This Work) Tegmark Cleaned Map (3yr) – SILC400 (This Work) Difference Maps WMAP teamRe[a lm ]Im[a lm ] l=2,m=0 11.48 0.00 m=1 -0.054.86 m=2 -14.41-18.80 Tegmark Clean Map Re[a lm ]Im[a lm ] l=2,m=0 3.34 0.00 m=1 0.264.88 m=2 -14.88-17.26 This Work

18. Quadrupole and Octopole Pole Directions SILC400 Tegmark 3yr WMAP Eriksen X X : Octopole

19. Dependence of Statistics on Smoothing Scales

20. Genus of North and South Hemispheres (WMAP 3yr) Genus curves expected from the best-fit ΛCDM model (200 simulations, red) Asymmetry in temperature fluctuations between north & south (filled and open circles)