Non-Gaussian scatter in cluster scaling relations

Abstract

We investigate the impact of non-Gaussian scatter in the cluster mass-observable scaling relation on the mass and redshift distribution of clusters detected by wide area surveys. We parameterize non-Gaussian scatter by incorporating the third and fourth moments (skewness and kurtosis) into the distribution P(Mobs|M). We demonstrate that the effect of the higher order moments becomes important when the product of the standard deviation of P(Mobs|M) and the slope of the mass function is greater than unity. For high scatter mass indicators it is therefore necessary for the survey, limiting mass threshold to be less than 1014 h-1 M ⊙, to prevent the skewness from having a significant impact on the observed number counts, particularly at high redshift. We also show that an unknown level of non-Gaussianity in the scatter is equivalent to an additional uncertainty on the variance in P(Mobs|M) and thus may limit the constraints that can be placed on σ8 and the dark energy equation of state parameter w. © 2010 The American Astronomical Society.