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Statistical Isotropy of the Cosmic Microwave Background (CMB) radiation hasbeen studied and debated extensively in recent years. Under this assumption,the hot spots and cold spots of the CMB are expected to be uniformlydistributed over a 2-sphere. We use the orientation matrix, first proposed byWatson (1965) and Scheidegger (1965) and associated shape and strengthparameters (Woodcock, 1977) to analyse whether the hot and cold spots of theobserved CMB temperature anisotropy field are uniformly placed. We demonstratethe usefulness of our estimators by using simulated toy models containingnon-uniform data. We apply our method on several foreground minimized CMB mapsobserved by WMAP and Planck over large angular scales. The shape and strengthparameters constrain geometric features of possible deviations from uniformity(isotropy) and the power of the anomalous signal. We find that distributions ofhot or cold spots in cleaned maps show no unusual signature of clustering orgirdling. Instead, we notice a strikingly uniform distribution of hot spotsover the full sky. The signal remains robust with respect to the four cleanedmaps used and presence or absence of the non-Gaussian cold spot (NGCS). On thepartial sky with WMAP KQ75 and Planck U73 masks we find anomalously lowstrength of non-uniformity for cold spots which is found to be robust withrespect to various cleaning methods, masks applied, instruments, frequencies,and the presence or absence of the NGCS. Interestingly we find that the signalof anomalously weak non-uniformity could be due to contributions from thequadrupole and octupole and may be related with the low CMB temperaturevariance anomaly.

Isotropy statistics of CMB hot and cold spots