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

A coherent over- or under-density contrast across a finite survey volume causes an upward- or downward fluctuation in the observed number of haloes. This fluctuation in halo number adds a significant co-variant scatter in the observed amplitudes of weak lensing power spectrum at non-linear, 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 {n-ary logical and}-dominated cold dark matter model. Then we showthat adding the observed number counts of massive haloes withM≳10¹⁴M⊙/h can significantly improve the information content of weak lensing power spectrum, almost recovering the Gaussian information up to l_max ≃ 1000, if the average mass profiles of the massive haloes are known, which can be estimated from stacked lensing. When combined with the halo number counts for M > 3 or 1 × 10¹⁴M⊙ h^-1, the improvement is up to a factor of 1.4 or 2 at l_max ≃ 1000-2000, equivalent to a factor of 2 or 4 times larger survey volume, compared to the power spectrum measurement alone.