Planck 2013 results. XXIII. Isotropy and statistics of the CMB

Planck 2013 results

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Table 23

Probabilities of obtaining values of the χ² statistic for the Planck fiducial model at least as large as the observed values of the statistic for the PlanckSMICA map with resolution parameter N_side = 64 and removed multipoles of order ℓ ≤ 3 (columns denoted as “ℓ > 3”) or order ℓ ≤ 5 (columns denoted as “ℓ > 5”) .

	Probability

	Ecl.		Gal.		DB		DM		PA
Hemisphere	ℓ > 3	ℓ > 5	ℓ > 3	ℓ > 5	ℓ > 3	ℓ > 5	ℓ > 3	ℓ > 5	ℓ > 3	ℓ > 5

Two-point function
Negative .......	0.886	0.951	0.875	0.957	0.344	0.509	0.746	0.869	0.745	0.819
Positive .......	0.609	0.906	0.123	0.330	0.824	0.973	0.811	0.979	0.756	0.947
Pseudo-collapsed 3-point function
Negative .......	0.985	0.999	0.981	0.978	0.965	0.879	0.966	0.948	0.986	0.872
Positive .......	0.262	0.643	0.468	0.789	0.807	0.989	0.132	0.390	0.224	0.516
Equilateral 3-point function
Negative .......	0.984	0.997	0.963	0.952	0.531	0.790	0.945	0.998	0.536	0.943
Positive .......	0.776	0.790	0.347	0.727	0.966	0.991	0.358	0.694	0.485	0.649
Rhombic 4-point function
Negative .......	0.951	>0.999	0.998	0.992	0.482	0.842	0.991	0.997	0.929	0.989
Positive .......	0.677	0.584	0.746	0.870	0.994	0.966	0.334	0.368	0.314	0.359

Notes. The probabilities were computed for hemispheres determined in the ecliptic, Galactic, Doppler boost (DB), dipole modulation (DM), and power asymmetry (PA) frames.

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