A reassessment of the evidence of the Integrated Sachs-Wolfe effect through the WMAP-NVSS correlation

We reassess the estimate of the cross-correlation of the spatial distribution of the NRAO VLA Sky Survey (NVSS) radio sources with that of Cosmic Microwave Background (CMB) anisotropies from the Wilkinson Microwave Anisotropy Probe (WMAP). This re-analysis is motivated by the fact that most previous studies adopted a redshift distribution of NVSS sources inconsistent with recent data. We find that the constraints on the bias-weighted redshift distribution, b(z) × N (z), of NVSS sources, set by the observed angular correlation function, w(θ), or, equivalently, by the power spectrum of their spatial distribution, strongly mitigate the effect of the choice of N (z). If such constraints are met, even highly discrepant redshift distributions yield NVSS–WMAP cross-correlation functions consistent with each other within statistical errors. The models favoured by recent data imply a bias factor, b(z), decreasing with increasing z, rather than constant, as assumed by most previous analyses. As a consequence, the function b(z) × N (z) has more weight at z < 1, i.e. in the redshift range yielding the maximum contribution to the ISW in a standard ΛCDM cosmology. On the whole, the NVSS turns out to be better suited for ISW studies than generally believed, even in the absence of an observational determination of the redshift distribution. The systematics introducing spurious power in the angular correlation function on scales of several degrees are strongly reduced restricting the analysis to the sub-sample brighter than 10 mJy. Even though this sub-sample comprises less than one third of the NVSS sources, it yields a slightly more significant detection of the ISW effect than the full sample (3σ rather than 2.5σ). The NVSS–WMAP cross-correlation function is found to be fully consistent with the prediction of the standard ΛCDM cosmology.