Revisiting the WMAP - NVSS angular cross correlation. A skeptic's view
  In the context of the study of the ISW, we revisit the angular cross
correlation of WMAP CMB data with the NVSS radio survey. We compute 2-point
cross functions between the two surveys in real and in Fourier space, paying
particular attention on the dependence of results on the flux of NVSS radio
sources, the angular scales where correlations arise and the comparison with
theoretical expectations. We reproduce previous results that claim an excess of
correlation in the angular correlation function (ACF), and we also find some
(low significance) similarity between the CMB and radio galaxy data in the
multipole range $\el \in $ [10, 25]. However, the S/N in the ACFs increases
with higher flux thresholds for NVSS sources, but drops a $\sim$ 30 - 50% in
separations of the order of a pixel size, suggesting some residual point source
contribution. When restricting our analyses to multipoles $\el \gt $60, we fail
to find any evidence for cross correlation in the range $\el \in [2,10]$, where
according to the model predictions and our simulations $\sim$ 50% of the S/N is
supposed to arise. Also, the accumulated S/N for $\el \lt $60 is below 1, far
from the theoretical expectation of S/N$\sim 5$. Part of this disagreement may
be caused by an inaccurate modeling of the NVSS source population: as in
previous works, we find a level of large scale ($\el \lt $70) clustering in the
NVSS catalog that seems incompatible with a high redshift population. This is
unlikely to be caused by contaminants or systematics, since it is independent
of flux threshold, and hence present for the brightest ($\gt 30 \sigma$) NVSS
sources. Either our NVSS catalogs are not probing the high redshift, large
scale gravitational potential wells, or there is a clear mismatch between the
ISW component present in WMAP data and theoretical expectations.
