Comparison of Analytical Mass Functions with Numerical Simulations

Abstract

We present numerical testing results of our mass function derived in our previous paper, and compare the testing results with those of the popular Press-Schechter (PS) mass function. Two fiducial models are considered for the test: the scale-free power-law spectra P(k) \propto k^{n} with spectral indices n=-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 different output times: ten output times from two N-body realizations for the n=-1 power-law model; four outputs from one realization for the n=0 model. While for the 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 show that our mass function fits the numerical data in a much improved way over the PS one. Thus, we expect that our mass function can be a viable alternative of the PS mass function in applications to various areas.