The excursion set approach, and an improved model for the multiplicity function

¹ Dipartimento di Matematica, Università Statale di Bergamo, via dei Caniana 2, 24127 Bergamo, Italy
² Bo$\rm{\breve{g}azi}$çi University, Physics Department, 80815 Bebek, Istanbul, Turkey e-mail: antonino.delpopolo@boun.edu.tr
³ Istanbul Technical University, Ayazaga Campus, Faculty of Science and Letters, 34469 Maslak/Istanbul, Turkey

Received: 27 May 2005
Accepted: 18 October 2005

Abstract

I compare numerical multiplicity function with the theoretical multiplicity function obtained by means of the excursion set model and an improved version of the barrier shape which implicitly takes account of total angular momentum acquired by the proto-structure during evolution and of a non-zero cosmological constant. I describe the better agreement of the multiplicity function obtained in this paper with simulations of other previous models. While the theoretical multiplicity function of the present paper is in agreement with high resolution N-body simulations, the comparison of the theoretical multiplicity function of the present paper with the theoretical multiplicity function of several authors shows some discrepancies: e.g., the maximum value of the multiplicity function from simulations at is smaller, and its low mass tail is shallower when compared with the ST multiplicity function.
The multiplicity function of the present paper gives a good fit to simulations results and was obtained from a sound theoretical background.