Primordial Non-Gaussianity and Extreme-Value Statistics of Galaxy Clusters

Abstract

What is the size of the most massive object one expects to find in a survey of a given volume? In this paper, we present a solution to this problem using Extreme-Value Statistics, taking into account primordial non-Gaussianity and its effects on the abundance and the clustering of rare objects. We calculate the probability density function (pdf) of extreme-mass clusters in a survey volume, and show how primordial non-Gaussianity shifts the peak of this pdf. We also study the sensitivity of the extreme-value pdfs to changes in the mass functions, survey volume, redshift coverage and the normalization of the matter power spectrum, σ_8. For 'local' non-Gaussianity parametrized by f_NL, our correction for the extreme-value pdf due to the bias is important when f_NL > O(100), and becomes more significant for wider and deeper surveys. Applying our formalism to the massive high-redshift cluster XMMUJ0044.0-2-33, we find that its existence is consistent with f_NL = 0, although the conclusion is sensitive to the assumed values of the survey area and σ_8. We also discuss the convergence of the extreme-value distribution to one of the three possible asymptotic forms, and argue that the convergence is insensitive to the presence of non-Gaussianity.

Revised version, 20 pages, 10 figures. Major improvement in the treatment of non-Gaussian bias. Previous claim of large f_NL associated with the cluster is no longer supported

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