A cross-correlation analysis of CMB lensing and radio galaxy maps
Authors: Piccirilli G. , Migliaccio M. , Branchini E. , Dolfi A. 
Published: December 2022

Aims. The goal of this work is to clarify the origin of the seemingly anomalously large clustering signal detected at large angular separation in the wide TGSS radio survey and, in so doing, to investigate the nature and the clustering properties of the sources that populate the radio sky in the [0.15, 1.4] GHz frequency range.
Methods. To achieve this goal, we cross-correlated the angular position of the radio sources in the TGSS and NVSS samples with the cosmic microwave background (CMB) lensing maps from the Planck satellite. A cross-correlation between two different tracers of the underlying mass density field has the advantage of being quite insensitive to possible systematic errors that may affect the two observables, provided that they are not correlated, which seems unlikely in our case. The cross-correlation analysis was performed in harmonic space and limited to relatively modest multipoles. These choices, together with that of binning the measured spectra, minimize the correlation among the errors in the measured spectra and allowed us to adopt the Gaussian hypothesis to perform the statistical analysis. Finally, we decided to consider the auto-angular power spectrum on top of the cross-spectrum since a joint analysis has the potential to improve the constraints on the radio source properties by lifting the degeneracy between the redshift distribution, N(z), and the bias evolution, b(z).
Results. The angular cross-correlation analysis does not present the power excess at large scales for TGSS and provides a TGSS–CMB lensing cross-spectrum that is in agreement with the one measured using the NVSS catalog. This result strongly suggests that the excess found in TGSS clustering analyses can be due to uncorrected systematic effects in the data. However, we considered several cross-spectra models that rely on physically motivated combinations of N(z) and b(z) prescriptions for the radio sources and find that they all underestimate the amplitude of the measured cross-spectra on the largest angular scales considered in our analysis, ∼10°. This result is robust to the various potential sources of systematic errors, both of observational and theoretical nature, that may affect our analysis, including the uncertainties in the N(z) model. Having assessed the robustness of the results to the choice of N(z), we repeated the analysis using simpler bias models specified by a single free parameter, bg, namely, the value of the effective bias of the radio sources at redshift zero. This improves the goodness of the fit, although not even the best model, which assumes a non-evolving bias, quite matches the amplitude of the cross-spectrum at small multipoles. Moreover, the best fitting bias parameter, bg = 2.53 ± 0.11, appears to be somewhat large considering that it represents the effective bias of a sample that is locally dominated by mildly clustered star-forming galaxies and Fanaroff-Riley class I sources. Interestingly, it is the addition of the angular auto-spectrum that favors the constant bias model over the evolving one.
Conclusions. The nature of the large cross-correlation signal between the radio sources and the CMB lensing maps found in our analysis at large angular scales is not clear. It probably indicates some limitation in the modeling of the radio sources, namely the relative abundance of the various populations, their clustering properties, and how these evolve with redshift. What our analysis does show is the importance of combining the auto-spectrum with the cross-spectrum, preferably obtained with unbiased tracers of the large-scale structure, such as CMB lensing, for answering these questions.