CMB lensing tomography with clustering estimation of lens redshift distributions

TL;DR

This paper introduces a clustering-based method for estimating lens redshift distributions in CMB lensing tomography, validated through cross-correlation measurements with radio galaxies and spectroscopic surveys, yielding results consistent with Planck data.

Contribution

It presents a novel clustering-based approach to reconstruct lensing kernel functions and predict CMB lensing-galaxy cross-correlations, demonstrated with real data.

Findings

Measured CMB lensing-galaxy cross-power spectrum using Planck and radio galaxies.

Estimated 16 109 for 186 109 consistent with Planck.

Validated the clustering-based redshift estimation method with real observational data.

Abstract

We develop a clustering-based redshift estimation approach for CMB lensing tomography, focusing on the kernel function of the lensing galaxies. Within a linear galaxy bias framework, we derive estimators for this kernel from two-point cross-correlations between lens mass and reference samples. The reconstructed kernel then enables a theoretical prediction for the angular cross-power spectrum \(C_{g\kappa}\) between CMB lensing convergence and lens galaxies. As a proof of concept, we measure \(C_{g\kappa}\) by correlating the \emph{Planck} PR4 convergence map with NVSS+SUMSS radio galaxies (\(0\lesssim z\lesssim 3\)). We estimate the radio-galaxy kernel by collectively cross-correlating their distribution with spectroscopic and photometric surveys (2MPZ, LOWZ-CMASS, eBOSS DR16 LRGs, and Gaia-unWISE QSOs). From the measured \(C_{g\kappa}\), we obtain \(\sigma_8 = 0.86^{+0.12}_{-0.09}\) when the density parameter is set to the {\it Planck} value of $\Omega_m = 0.315$; this is in good agreement with the \emph{Planck} normalisation of $\sigma_8 = 0.812$.