Toward optimal cluster power spectrum analysis
  The power spectrum of galaxy clusters is an important probe of the
cosmological model. In this paper we determine the optimal weighting scheme for
maximizing the signal-to-noise ratio for such measurements. We find a closed
form analytic expression for the optimal weights. Our expression takes into
account: cluster mass, finite survey volume effects, survey masking, and a flux
limit. The implementation of this weighting scheme requires knowledge of the
measured cluster masses, and analytic models for the bias and space-density of
clusters as a function of mass and redshift. Recent studies have suggested that
the optimal method for reconstruction of the matter density field from a set of
clusters is mass-weighting (Seljak et al 2009, Hamaus et al 2010, Cai et al
2011). We compare our optimal weighting scheme with this approach and also with
the original power spectrum scheme of Feldman et al (1994). We show that our
optimal weighting scheme outperforms these approaches for both volume- and
flux-limited cluster surveys. Finally, we present a new expression for the
Fisher information matrix for cluster power spectrum analysis. Our expression
shows that for an optimally weighted cluster survey the cosmological
information content is boosted, relative to the standard approach of Tegmark
(1997).
