Most massive halos with Gumbel Statistics

TL;DR

This paper develops an analytical method to predict the distribution of the most massive dark matter halos in a given region, validated against simulations, aiding cosmological constraints from massive cluster observations.

Contribution

It introduces an analytical approach using counts-in-cells and halo bias to calculate extreme value statistics for dark matter halos, validated with simulations.

Findings

Good agreement with simulation data for maximum halo mass distribution

Accurate predictions for the high-mass tail relevant to cosmology

Method applicable to spherical regions of various sizes

Abstract

We present an analytical calculation of the extreme value statistics for dark matter halos - that is, 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.