a continued story about the ecliptic pole and CMB dipole axes

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a continued story about the ecliptic pole and
CMB dipole axes
Questioning the statistical isotropy of the
cosmic microwave background
Dr Y. Wiaux, December 2006, FNRS contact group
Wavelet and Applications, Brussels
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Introduction

• (1) Cosmology
• Standard paradigm (k, ?b, ?m, H0, ns, )
• Laboratory microwave background (CMB)

• (2) Complex data processing
• High volume of data
• Distributed on non-trivial manifolds
• Scalar or tensor - valued

(3) Our subjecttesting the cosmological
principle in the CMB

• State of the art results N-point correlation
  functions, multipole vectors, etc.
• New method wavelet analysis

(4) Road map

• Complex data processing
• Wavelets on the sphere
• Fast direction correlation
• Cosmology
• Local CMB structures alignment
• Local CMB structures intensity
• Synthesis of synthesis

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I. Complex data processing
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I.1. Wavelets on the sphere

• Scale-space analysis

Directional correlation signal F projected on
the filter ?, dilated at each scale a 2 R,
rotated by ? 2 0,2?, and translated by ?0 2 S2
Correspondence principle wavelets ? built by
projection of planar wavelets ?
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I.2. Fast directional correlation

• Filter steerability
• Fast directional correlation algorithm

Definition any rotation of the filter ? by ?
reads as a M-terms linear combination of basis
filters ? m
Example second Gaussian derivative (2GD)
Asymptotic complexity at band limit L,
separation of variables and steerability reduce
the asymptotic complexity for the directional
correlation from O(L5) to O(L3)
Computation times for megapixels maps, reduced
from years to minutes!
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II. Cosmology
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(WMAP data pre-processing)

• WMAP data experimental map processing
• Simulations

• Foreground removal on Q, V, W WMAP frequency maps
  (template fits)
• Linear combination to enhance signal-to-noise
  ratio (co-added sum)
• Application of Kp0 mask to remove remaining
  foregrounds
• Monopole and dipole subtraction

Foreground cleaned WMAP co-added temperature map

• 10.000 best fit Gaussian and isotropic
  simulations produced at each frequency
• Same pre-processing procedure applied

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(Steerable wavelets -- analysis methods)

• Local structures morphology
• Local structures alignment

(1) Orientations Represents local structure
orientation
(2) Wavelet coefficients (intensity) Represents
local structure intensity ( sign)
(3) Elongations (2GD) Represents local structure
eccentricity
(4) Total weights (headless vectors) Represents
how much each direction ? is highlighted by local
structures
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II.1. Local structures alignment

• Total weights distribution in -3.3 ?, 6.1 ?
  WMAP 3

Scales between 8 and 10, second Gaussian
derivative. ? units at each point ?.
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alignment anomaly

• Total weights 99.865 anomalies WMAP 3
• Conclusion ecliptic and dipole synthesis (I) at
  98-99 C.L.

Scale between 8 and 10, second Gaussian
derivative. ? units at each point ?.

• Major cluster ecliptic poles axis, northern end
  at (60, 96)
• Two clusters plane orthogonal to CMB dipole
  axis, northern end at (42, 264)

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II.2. Local structures intensity

• Wavelet coefficients distribution in -2.9 ?,
  2.8 ? WMAP 3

Scales between 8 and 10, second Gaussian
derivative. ? units at each point ?.
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intensity anomaly

• Wavelet coefficients 99.865 anomalies WMAP 3
• Conclusion ecliptic and dipole synthesis (II) at
  98-99 C.L.

Scale between 8 and 10, second Gaussian
derivative. ? units at each point ?.

• Red cluster south ecliptic pole at (120, 276)
• Blue cluster 1 southern end of CMB dipole axis
  at (138, 84)
• Blue cluster 2 famous cold spot at (147, 209)

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II.3. Synthesis of synthesis

• Total weights distribution of the wavelet
  coefficient clusters
• Intuition confirmed by statistical analysis

Scale between 8 and 10, second Gaussian
derivative (not normalized to simulations).

• The red cluster of wavelet coefficients at the
  south ecliptic pole partially originates the
  total weights anomaly (98-99 total weights
  detection drops to 97 at scale 8, and to 88 at
  scale 10)
• The other two clusters of wavelet coefficients
  are completely independent of the total weights
  anomalies

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Conclusions
I. Statistical anisotropy of CMB data
Synthesis of synthesis 98-99 alignment anomaly
orthogonal to the CMB dipole axis, and
concentrated around the ecliptic pole
axis -partially- originating in the 98-99
intensity anomaly at south ecliptic
pole (structures scale 8-10)
Origin? Why ecliptic and dipole? Simple
violation of the cosmological principle
cosmological structures? Foregrounds?
Systematics?
PRL 96 (2006) 151303
II. Wavelets
Powerful complex signal processing tool
probing scale, position, orientation and other
morphological characteristics of local structures
of signals, beyond spectral analysis.
APJ 632 (2005) 15 APJ 652 (2006) 820
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Local structures alignment (WMAP 1)

• Total weights distribution in -3.5 ?, 7.4 ?
  WMAP 1

Scales between 8 and 10, second Gaussian
derivative. ? units at each point ?. Identical
pattern at each WMAP frequency (discarding
foreground origin).
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Local structures alignment (WMAP 1)

• Total weights 99.995 anomalies WMAP 1
• Conclusion ecliptic and dipole synthesis at
  99.99 C.L.

Scale between 8 and 10, second Gaussian
derivative. ? units at each point ?.

• Major cluster ecliptic poles axis, northern end
  at (60, 96)
• Two clusters plane orthogonal to CMB dipole
  axis, northern end at (42, 264)

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Local structures alignment (WMAP 3)

• Total weights 99.995 anomalies WMAP 3
• Conclusion ?

Scale between 8 and 10, second Gaussian
derivative. ? units at each point ?.
Reduced number of pixels loosing detection
significance relative to 1-year results!