Physical constraints on the halo mass function

Abstract

We analyse the effect of two relevant physical constraints on the mass multiplicity function of dark matter halos in a Press--Schechter type algorithm. Considering the random--walk of linear Gaussian density fluctuations as a function of the smoothing scale, we simultaneously i) account for mass semi--positivity and ii) avoid the cloud--in--cloud problem. It is shown that the former constraint implies a severe cutoff of low--mass objects, balanced by an increase on larger mass scales. The analysis is performed both for scale--free power--spectra and for the standard cold dark matter model. Our approach shows that the well--known ``infrared" divergence of the standard Press--Schechter mass function is caused by unphysical, negative mass events which inevitably occur in a Gaussian distribution of density fluctuations.