Sample Variance Considerations for Cluster Surveys

We present a general statistical framework for describing the effect of sample variance in the number counts of virialized objects and examine its effect on cosmological parameter estimation. Specifically, we consider effects of sample variance on the power spectrum normalization and properties of dark energy extracted from current and future local and high-redshift samples of clusters. We show that for future surveys that probe ever lower cluster masses and temperatures, sample variance is generally comparable to or greater than shot noise and thus cannot be neglected in deriving precision cosmological constraints. For example, sample variance is usually more important than shot variance in constraints on the equation of state of the dark energy from z < 1 clusters. Although we found that effects of sample variance on the sigma₈-Omegaₘ constraints from the current flux and temperature limited X-ray surveys are not significant, they may be important for future studies utilizing the shape of the temperature function to break the sigma₈-Omegaₘ degeneracy. We also present numerical tests clarifying the definition of cluster mass employed in cosmological modelling and accurate fitting formula for the conversion between different definitions of halo mass (e. g. , virial vs. fixed overdensity).