Foreground Subtraction with an Internal Linear Combination Method: Application to the

Wilkinson Microwave Anisotropy Probe Data

Chan-Gyung Park (KIAS)

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Internal Linear Combination Method

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We finds five coefficients wi that minimizes the variance of the combined map. The variance is defined as

We linearly combine five WMAP maps (FWHM=1°, 22.8 – 93.5 GHz) to reduce the Galactic foregrounds (right figure).

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12 and 9 disjoint regions defined by the WMAP team & Tegmark et al. (2003)

Foreground cleaned maps obtained by applying ILC method for several disjoint regions separately.

Average of difference maps [MILC12 - true input CMB] for one hundred ILC simulations.

Previous Foreground Removal Methods: Applying ILC for several disjoint sky regions that are defined depending on the foreground intensities. WMA

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Tegmark et al. (2003)

Residual foregrounds are strong even at high Galactic latitude!

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We divide the whole sky into hundreds of groups with similar foreground spectral indexes over a range of WMAP frequencies.

(a) Intensity distribution of the Galactic foreground emission over WMAP frequency bands. MEM galaxy foreground maps derived by WMAP team are used.

(b) Spectral index distributions of the Galactic foregrounds estimated for K-Ka (dotted), Ka-Q (dashed), Q-V (long dashed), K-to-V (solid), V-W (dot-dashed) bands.

Spectral index maps for (a) K-to-V and (b) V-W bands. Spectral indexes are significantly different at positions and frequencies.

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We divide each spectral index map into 20 groups for each spectral index bin to have equal number of pixels (20 groups for both K-to-V and V-W spectral indexes). Finally, we obtain 20x20=400 groups of pixels with the similar foreground spectral properties.

Group Index

We apply the ILC method for each group of pixels to obtain a CMB map with foreground effectively reduced (MILC400).

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