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Most massive haloes with Gumbel statistics

Abstract : We present an analytical calculation of the extreme value statistics for dark matter haloes - i.e., the probability distribution of the most massive halo within some region of the universe of specified shape and size. Our calculation makes use of the counts-in-cells formalism for the correlation functions, and the halo bias derived from the Sheth-Tormen mass function.

We demonstrate the power of the method on spherical regions, comparing the results to measurements in a large cosmological dark matter simulation and achieving good agreement. Particularly good fits are obtained for the most likely value of the maximum mass and for the high-mass tail of the distribution, relevant in constraining cosmologies by observations of most massive clusters.

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O. Davis, J. Devriendt, S. Colombi, J. Silk, C. Pichon. Most massive haloes with Gumbel statistics. Monthly Notices of the Royal Astronomical Society, Oxford University Press (OUP): Policy P - Oxford Open Option A, 2011, 413, pp.2087-2092. ⟨10.1111/j.1365-2966.2011.18286.x⟩. ⟨insu-03645984⟩

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