A cross-correlation analysis of CMB lensing and radio galaxy maps

We investigate the origin of the large clustering signal detected in the angular distribution of the radio sources in the TGSS catalog. To do so, we cross-correlate the angular position of the radio sources with the Cosmic Microwave Background (CMB) lensing maps from the Planck satellite, since cross-correlation is expected to be insensitive to source of possible systematic errors that may generate a spurious clustering signal. The amplitude of the angular cross-correlation spectrum of TGSS-CMB lensing turns out to be much smaller than that of the TGSS auto-spectrum and consistent with that of the NVSS-CMB lensing cross spectrum. A result that confirms the spurious origin of the TGSS large scale clustering signal. We further compare the two cross-spectra with theoretical predictions that use various prescriptions from the literature, for the redshift counts of the radio sources, $N(z)$, and their bias $b(z)$. These models, that assume a $\Lambda$CDM cosmology and that were proposed to fit the NVSS auto-spectrum, fail to match the cross-spectra on large scale, though not by far. When the bias relation is let free to vary (model predictions are rather insensitive to the choice of the N(z)) the quality of the fit improves but a large bias ($ b_g = 2.53 \pm 0.11$) is required, which does not seem to be consistent with the observed clustering amplitude of the radio sources in the local universe. Whether this large cross-correlation amplitude represents a problem for the radio sources models, or for the $\Lambda$CDM framework itself, can only be clarified using next generation datasets featuring large number of objects. What our analysis does show is the possibility to remove the $N(z)$ and $b(z)$ degeneracy by combining angular and cross-correlation analyses.