Cross-correlating radio continuum surveys and CMB lensing: constraining redshift distributions, galaxy bias, and cosmology

We measure the harmonic-space auto-power spectrum of the galaxy overdensity in the LOFAR Two-metre Sky Survey (LoTSS) first data release and its cross-correlation with the map of the lensing convergence of the cosmic microwave background (CMB) from the Planck collaboration. We report a similar to 5 sigma detection of the cross-correlation. We show that the combination of the clustering power spectrum and CMB lensing cross-correlation allows us to place constraints on the high-redshift tail of the redshift distribution, one of the largest sources of uncertainty in the use of continuum surveys for cosmology. Our analysis shows a preference for a broader redshift tail than that predicted by the photometric redshifts contained in the LoTSS value-added catalogue, as expected, and more compatible with predictions from simulations and spectroscopic data. Although the ability of CMB lensing to constrain the width and tail of the redshift distribution could also be valuable for the analysis of current and future photometric weak lensing surveys, we show that its performance relies strongly on the redshift evolution of the galaxy bias. Assuming the redshift distribution predicted by the Square Kilometre Array Design simulations, we use our measurements to place constraints on the linear bias of radio galaxies and the amplitude of matter inhomogeneities sigma(8), finding sigma(8) = 0.69(-0.21)(+0.14) assuming the galaxy bias scales with the inverse of the linear growth factor, and sigma(8) = 0.79(-0.32)(+0.17) assuming a constant bias.