Toward optimal cluster power spectrum analysis

TL;DR

This paper derives an optimal weighting scheme for galaxy cluster power spectrum analysis that maximizes the signal-to-noise ratio, outperforming previous methods and enhancing cosmological information extraction.

Contribution

It provides a closed-form analytic expression for optimal weights considering survey effects, and compares its performance with existing methods, demonstrating improved results.

Findings

Optimal weights improve signal-to-noise ratio in cluster power spectrum measurements.

The new scheme outperforms mass-weighting and Feldman et al. (1994) methods.

Enhanced Fisher information boosts cosmological parameter constraints.

Abstract

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).