Covariance of CMB anomalies
  Several unexpected features are observed at large angular scales in the CMB
temperature anisotropy measurements by both WMAP and Planck. These include the
lack of both variance and correlation, alignment of the lowest multipole
moments with one another, hemispherical power asymmetry, and an odd-to-even
parity excess. In this work, we study the statistics of eight representative
large-angle CMB features in order to evaluate their covariance in LCDM. We do
so using two sets of simulated CMB temperature maps; an ensemble of 100,000
simple Gaussian simulations, and 1000 Full Focal Plane (FFP) simulations
provided by the Planck collaboration. In measuring feature probabilities, we
pay particular attention to analysis choices, making sure that we can reproduce
previous results in the literature, and explain differences where appropriate.
The covariance structure we find is consistent with expectations given that
many of the features studied are functions of the angular power spectrum.
Notably, we find significant differences in the covariance entries associated
with the quadrupole-octopole alignments derived from the Gaussian and FFP
simulations. We additionally perform a principal component analysis to
quantitatively gauge what combinations of features capture the most information
about how simulation measurements vary, and to provide an alternative
assessment of the ways in which the real sky is anomalous. The first four
principal components explain about 90\% of the simulations' variance, with the
first two roughly quantifying the lack of large-angle correlations, and the
next two quantifying the phase-dependent anomalies (multipole alignments and
power asymmetry). Though the results of this analysis are fairly unsurprising,
its comprehensive approach serves to tie together a number of previous results,
and will therefore provide context for future studies of large-angle anomalies.
