Julien Devriendt

Abstract:

We consider the Gumbel or extreme value statistics describing the distribution function p_G(x_max) of the maximum values of a random field x within patches of fixed size. We present, for smooth Gaussian random fields in two and three dimensions, an analytical estimate of p_G which is expected to hold in a regime where local maxima of the field are moderately high and weakly clustered. When the patch size becomes sufficiently large, the negative of the logarithm of the cumulative extreme value distribution is simply equal to the average of the Euler Characteristic of the field in the excursion x > x_max inside the patches. The Gumbel statistics therefore represents an interesting alternative probe of the genus as a test of non Gaussianity, e.g. in cosmic microwave background temperature maps or in three-dimensional galaxy catalogs. It can be approximated, except in the remote positive tail, by a negative Weibull type form, converging slowly to the expected Gumbel type form for infinitely large patch size. Convergence is facilitated when large scale correlations are weaker. We compare the analytic predictions to numerical experiments for the case of a scale-free Gaussian field in two dimensions, achieving impressive agreement between approximate theory and measurements. We also discuss the generalization of our formalism to non-Gaussian fields.

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.

Abstract:

We use sub-parsec resolution hydrodynamic resimulations of a Milky Way (MW) like galaxy at high redshift to investigate the formation of the MW satellite galaxies. More specifically, we assess the impact of supernova feedback on the dwarf progenitors of these satellite, and the efficiency of a simple instantaneous reionisation scenario in suppressing star formation at the low-mass end of this dwarf distribution. Identifying galaxies in our high redshift simulation and tracking them to z=0 using a dark matter halo merger tree, we compare our results to present-day observations and determine the epoch at which we deem satellite galaxy formation must be completed. We find that only the low-mass end of the population of luminous subhalos of the Milky-Way like galaxy is not complete before redshift 8, and that although supernovae feedback reduces the stellar mass of the low-mass subhalos (log(M/Msolar) < 9), the number of surviving satellites around the Milky-Way like galaxy at z = 0 is the same in the run with or without supernova feedback. If a luminous halo is able to avoid accretion by the Milky-Way progenitor before redshift 3, then it is likely to survive as a MW satellite to redshift 0.