Cleaned Three-Year WMAP CMB Map: Magnitude of the Quadrupole and Alignment of Large Scale Modes

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) (i) Accurate determination of cosmological parameters (ii) Flat, CDM- and Λ-dominated universe 2. Some peculiar aspects of the CMB (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 μK2ΛCDM Model: 1250 μK2 (iv) Alignment and planarity of l=2 and l=3 modes 3. What is the origin of the anomalies in the CMB? Cosmological? Due to the residual Galactic foreground emission?

3. Foreground Subtraction Methods from Multi-frequency CMB Data 1. Galactic Template Fitting Method (most popular) Model the Galactic emission as the weighted sum of foreground templates (synchrotron + free-free + dust emissions) [Bennett et al. 2003] 2. Internal Linear Combination (ILC) Method (i) Linearly combine five WMAP maps (FWHM=1°, 22.8 – 93.5 GHz) to reduce the Galactic foregrounds. Find five coefficients wi 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. Previous Foreground-Cleaned Maps 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. Hinshaw et al. (2006) Tegmark et al. (2003) Region Definition Maps de Oliveira-Costa & Tegmark (2006) Cleaned Maps

5. Improved ILC method (i) Combination weights [wi] 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. Sum of synchrotron, free-free, and dust emission maps derived by the Maximum Entropy Method (WMAP team; Hinshaw et al. 2006)

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

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

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

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

10. Large Scale Mode Statistics 1. Power spectrum (quadrupole and octopole powers) 2. Quadrupole and octopole direction (n2, n3), angular separation θ23(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) 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. SILC400has 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. Ngroup > 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 Difference Maps WMAP team’s ILC – SILC400 (This Work) This Work Tegmark Cleaned Map (3yr) – SILC400 (This Work)

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

19. Dependence of Statistics on Smoothing Scales

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