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

摘要

A coherent over- or under-density contrast across a finite survey volumecauses an upward- or downward-fluctuation in the observed number of halos. Thisfluctuation in halo number adds a significant co-variant scatter in theobserved amplitudes of weak lensing power spectrum at nonlinear, small scales-- the so-called super-sample variance or the halo sample variance. In thispaper, we show that by measuring both the number counts of clusters and thepower spectrum in the same survey region, we can mitigate this loss ofinformation and significantly enhance the scientific return from the upcomingsurveys. First, using the halo model approach, we derive the cross-correlation betweenthe halo number counts and the weak lensing power spectrum, taking into accountthe super-sample covariance effect, which well matches the distributionsmeasured 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 lensingpower spectrum, almost recovering the Gaussian information up to lmax~1000, ifthe average mass profiles of the massive halos are known, which can beestimated 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 atlmax~1000 --2000, equivalent to a factor 2 or 4 times larger survey volume,compared to the power spectrum measurement alone.