Joint analysis of cluster number counts and weak lensing power spectrum to correct for the super-sample covariance

TL;DR

This paper demonstrates that combining cluster counts and weak lensing power spectrum measurements in the same survey can mitigate super-sample covariance effects, significantly improving the extraction of cosmological information.

Contribution

The authors derive the cross-correlation between cluster counts and weak lensing power spectrum, showing how joint analysis enhances information content by mitigating super-sample variance.

Findings

Adding cluster counts improves information content up to a factor of 2-4.

Super-sample covariance can be mitigated by joint analysis of counts and power spectrum.

Almost recovering Gaussian information up to lmax~1000 with known halo profiles.

Abstract

A coherent over- or under-density contrast across a finite survey volume causes an upward- or downward-fluctuation in the observed number of halos. This fluctuation in halo number adds a significant co-variant scatter in the observed amplitudes of weak lensing power spectrum at nonlinear, small scales -- the so-called super-sample variance or the halo sample variance. In this paper, we show that by measuring both the number counts of clusters and the power spectrum in the same survey region, we can mitigate this loss of information and significantly enhance the scientific return from the upcoming surveys. First, using the halo model approach, we derive the cross-correlation between the halo number counts and the weak lensing power spectrum, taking into account the super-sample covariance effect, which well matches the distributions measured from 1000 realizations for a Lambda-dominated cold dark matter model. Then we show that adding the observed number counts of massive halos with M> 10^14 Ms/h can significantly improve the information content of weak lensing power spectrum, almost recovering the Gaussian information up to lmax~1000, if the average mass profiles of the massive halos are known, which can be estimated from stacked lensing. When combined with the halo number counts for M > 3 or 1 x 10^14 Ms/h, the improvement is up to a factor of 1.4 or 2 at lmax~1000 --2000, equivalent to a factor 2 or 4 times larger survey volume, compared to the power spectrum measurement alone.