Comparison of Analytical Mass Functions with Numerical Simulations

We present numerical testing results of our mass function derived in ourprevious paper, and compare the testing results with those of the popularPress-Schechter (PS) mass function. Two fiducial models are considered for thetest: the scale-free power-law spectra P(k) \propto k^{n} with spectral indicesn=-1, 0 and the standard cold dark matter (SCDM) model with Omega =1 and h=0.5.For the power-law models, we use numerical data averaged over several differentoutput times: ten output times from two N-body realizations for the n=-1power-law model; four outputs from one realization for the n=0 model. While forthe SCDM model, we consider four outputs separately at redshifts z = 0, 0.43,1.14 and 1.86 from one large N-body simulations. The comparison results showthat our mass function fits the numerical data in a much improved way over thePS one. Thus, we expect that our mass function can be a viable alternative ofthe PS mass function in applications to various areas.Comment: Revised version. Accepted by ApJ Letter. Significantly improved. Numerical test for the SCDM model included. 14 pages, Latex file, 2 psfig