Isotropy statistics of CMB hot and cold spots
  Statistical Isotropy of the Cosmic Microwave Background (CMB) radiation has
been studied and debated extensively in recent years. Under this assumption,
the hot spots and cold spots of the CMB are expected to be uniformly
distributed over a 2-sphere. We use the orientation matrix and associated shape
and strength parameters, first proposed by Watson, to analyse whether the
placements of hot and cold spots of the CMB temperature anisotropy field are
uniformly distributed. We demonstrate the usefulness of our estimators by using
simulated toy models containing non-uniform data. We apply our method on
several foreground minimised CMB maps observed by WMAP and Planck over large
angular scales. The shape and strength parameters constrain geometric features
of possible deviations from uniformity (isotropy) and the power of the
anomalous signal. We find that distributions of hot or cold spots in cleaned
maps show no unusual signature of clustering or girdling. Instead, we notice a
strikingly uniform distribution of hot spots over the full sky. The signal
remains robust with respect to the four cleaned maps used and presence or
absence of the non-Gaussian cold spot (NGCS). On the partial sky with WMAP KQ75
and Planck U73 masks we find unusual uniformity for cold spots which is found
to be robust with respect to various cleaning methods, masks applied,
instruments, frequencies, and the presence or absence of the NGCS.
