Planck 2015 results. XVI. Isotropy and statistics of the CMB

TL;DR

Planck 2015 results XVI systematically tests the CMB for statistical isotropy and Gaussianity using full-mission temperature data and limited polarization, employing a diverse suite of statistics (moments, N-point functions, Minkowski functionals, and multiscale analyses) across four component-separated maps and FFP8 simulations. Across these methods, the data are largely consistent with a statistically isotropic Gaussian random field, reinforcing the standard cosmological model, while reaffirming several large-scale anomalies (e.g., low large-angle power, Cold Spot, hemispherical asymmetry, parity effects) whose significance is tempered by look-elsewhere considerations and polarization limitations. Tight constraints on quadrupolar modulation further limit statistically anisotropic inflationary scenarios. Polarization analyses, though limited by systematics, show morphologies compatible with isotropy when stacked, supporting Planck’s comprehensive characterization of CMB fluctuations to date.

Abstract

We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect our studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The "Cold Spot" is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.

Figures (27)

• Figure 1: Variance, skewness, and kurtosis for the four different component-separation methods --- Commander (red), NILC (orange), SEVEM (green), and SMICA (blue) --- compared to the distributions derived from 1000 Monte Carlo simulations.
• Figure 2: $N$-point correlation functions determined from the $N_{\mathrm{side}}=64$Planck CMB 2015 temperature maps. Results are shown for the 2-point, pseudo-collapsed 3-point (upper left and right panels, respectively), equilateral 3-point, and connected rhombic 4-point functions (lower left and right panels, respectively). The red dot-dot-dot-dashed, orange dashed, green dot-dashed, and blue long dashed lines correspond to the Commander, NILC, SEVEM, and SMICA maps, respectively. Note that the lines lie on top of each other. The black solid line indicates the mean determined from 1000 SMICA simulations. The shaded dark and light grey regions indicate the corresponding 68% and 95% confidence regions, respectively. See Sect. \ref{['sec:npoint_correlation']} for the definition of the separation angle $\theta$.
• Figure 3: Needlet space MFs for Planck 2015 data using the four component-separated maps, Commander (red), NILC (orange), SEVEM (green), and SMICA (blue); the grey regions, from dark to light, correspond, respectively, to 1, 2, and $3\sigma$ confidence regions estimated from the 1000 FFP8 simulations processed by the Commander method. The columns from left to right correspond to the needlet parameters $j=4, 6,$ and $8$, respectively; the $j$th needlet parameter has compact support over multipole ranges $[2^{j-1}, 2^{j+1}]$. The $\ell_c=2^j$ value indicates the central multipole of the corresponding needlet map. Note that to have the same range at all the needlet scales, the vertical axis has been multiplied by a factor that takes into account the steady decrease of the variance of the MFs as a function of scale.
• Figure 4: Histograms of $\chi^2$ for the Planck 2015 Commander (red), NILC (orange), SEVEM (green), and SMICA (blue) foreground-cleaned maps analysed with the common mask. The $\chi^2$ is obtained by combining the three MFs in needlet space with an appropiate covariance matrix. The histograms are for the FFP8 simulations, while the vertical lines are for the data. The figures from left to right are for the needlet scales $j=4, 6,$ and $8$, with the central multipoles $\ell_\mathrm{c}=2^j$ shown in each panel.
• Figure 5: Comparison of the window functions (normalized to have equal area) for the SMHW (blue), GAUSS (yellow), and SSG84 (magenta) filters. The scales shown are 25 $^{\prime}$ (top) and 250 $^{\prime}$ (bottom).