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 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.
