Clustering of Local Extrema in Planck CMB maps

Abstract

The clustering of local extrema will be exploited to examine Gaussianity, asymmetry, and the footprint of the cosmic-string network on the CMB observed by Planck. The number density of local extrema ($n_{\mathrm{pk}}$ for peak and $n_{\mathrm{tr}}$ for trough) and sharp clipping ($n_{\mathrm{pix}}$) statistics support the Gaussianity hypothesis for all component separations. However, the pixel at the threshold reveals a more consistent treatment with respect to end-to-end simulations. A very tiny deviation from associated simulations in the context of trough density, in the threshold range $\theta \in [-2-0]$ for NILC and CR component separations, are detected. The unweighted two-point correlation function, of the local extrema, illustrates good consistency between different component separations and corresponding Gaussian simulations for almost all available thresholds. However, for high thresholds, a small deficit in the clustering of peaks is observed with respect to the Planck fiducial $\Lambda$CDM model. To put a significant constraint on the amplitude of the mass function based on the value of $\Psi$ around the Doppler peak ($\theta \approx 70-75$ arcmin), we should consider $\vartheta \lesssim 0.0$. The scale-independent bias factors for the peak above a threshold for large separation angle and high threshold level are in agreement with the value expected for a pure Gaussian CMB. Applying the $n_{\mathrm{pk}}$, $n_{\mathrm{tr}}$, ${\Psi }_{\mathrm{pk}-\mathrm{pk}}$ and ${\Psi }_{\mathrm{tr}-\mathrm{tr}}$ measures on the tessellated CMB map with patches of $7.5^2$ deg${}^2$ size prove statistical isotropy in the Planck maps. The peak clustering analysis puts the upper bound on the cosmic-string tension, $G{\mu }^{(\mathrm{up})}\lesssim 5.59\times 10^{-7}$, in SMICA.

arXiv comment17 pages, 7 figures, and 3 tables. Including major revision and matched to the accepted version that appeared in MNRAS

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