The Halo Mass Function from the Excursion Set Method. Ii. the Diffusing Barrier

This paper is the second of a series of three where we study the mass function of virialized dark matter halos using the excursion set method. Motivated by recent large-scale N-body simulations determining the relation between the density threshold for gravitational collapse and the variance of the linear density field for regions that collapse to form halos by the present epoch, we deduce that the critical value for collapse is a stochastic variable. Within the excursion set method, the computation of the halo mass function can then be mapped into a first-passage time process in the presence of a barrier whose height evolves according to a diffusion equation (“diffusing barrier”). We show that the resulting halo mass function is in remarkable agreement with the existing N-body simulations without any need of introducing ad hoc coefficients. Two main physical effects concur to this agreement: 1) the presence of a diffusing barrier implies that the excursion takes place with an effective diffusion coefficient larger than one, thus increasing the halo mass function in the high-mass limit with respect to the (extended) Press-Schechter theory and 2) the non-markovian effects arising from the use of the tophat filter in real space, computed in paper I of this series, suitably decrease the halo mass function in the low-mass range with respect to the (extended) PS result. Subject headings: cosmology:theory — dark matter:halos — large scale structure of the universe