Mass functions from the excursion set model

¹ 1st Lyceum of Athens, Ipitou 15, Plaka, 10557 Athens, Greece
e-mail: hiotelis@ipta.demokritos.gr
² Institute of Modern Physics, Chinese Academy of Sciences Post Office Box 31, 730000 Lanzhou, PR China
³ Dipartimento di Fisica e Astronomia, University Of Catania, Viale Andrea Doria 6, 95125 Catania, Italy
⁴ INFN sezione di Catania, via S. Sofia 64, 95123 Catania, Italy

Received: 29 June 2017
Accepted: 11 September 2017

Abstract

Aims. We aim to study the stochastic evolution of the smoothed overdensity δ at scale S of the form δ(S) = ∫₀^S K(S,u)dW(u), where K is a kernel and dW is the usual Wiener process.

Methods. For a Gaussian density field, smoothed by the top-hat filter, in real space, we used a simple kernel that gives the correct correlation between scales. A Monte Carlo procedure was used to construct random walks and to calculate first crossing distributions and consequently mass functions for a constant barrier.

Results. We show that the evolution considered here improves the agreement with the results of N-body simulations relative to analytical approximations which have been proposed from the same problem by other authors. In fact, we show that an evolution which is fully consistent with the ideas of the excursion set model, describes accurately the mass function of dark matter haloes for values of ν ≤ 1 and underestimates the number of larger haloes. Finally, we show that a constant threshold of collapse, lower than it is usually used, it is able to produce a mass function which approximates the results of N-body simulations for a variety of redshifts and for a wide range of masses.

Conclusions. A mass function in good agreement with N-body simulations can be obtained analytically using a lower than usual constant collapse threshold.