tokens: PO light cone output (Evrard et al. 2002 ), extracted from the DES_v1.02 mock galaxy catalog. 5 5 http://www.slac.stanford.edu/mbusha/mocks/catalogs.html ; provided by M. Busha R. Wechsler. The halos were identified directly on the dark matter light cone using a spherical overdensity halo finder. The algorithm defines spherical regions that are overdense with respect to the critical density . The halos mass M 200 is defined as the mass enclosed in a sphere of radius whose mean density is times the threshold density. Hence, the M 200 mass is given by 4.1. Mass Function Definition and Results in Simulations Since the theoretical models for the halo bias have been derived from the mass function (e.g., Mo White 1996 ; Sheth Tormen 1999 ), we first study the theoretical models of the halo abundance. The comoving number density of halos with mass between M and M + dM or the unconditional mass function can be written aswhere is the multiplicity function (the fraction of mass in collapsed objects) and is the mean comoving mass density. The height of the density peaks is defined aswhere is the critical density for spherical collapse and is the variance of matter density fluctuations on mass scale M . Sheth Tormen ( 1999 ) generalized the expression of the Press–Schechter mass function (Press Schechter 1974 ) and calibrated the free parameters using numerical simulations. It can be written as with p = 0.3, q = 0.707, and . Later, Tinker et al. ( 2008 ) also calibrate fitting functions for the mass function and bias using high-resolution simulations. They choose the formwhere , and d are the free parameters for each overdensity Δ value with respect to the mean density of the universe, . These parameters were calibrated in simulations at z = 0. They also provide redshift correction to match the mass function to simulations. In the DES light cone, the halo finder defines overdense regions with respect to the critical density instead of . So If we define an overdensity contrast as , we can use this functional form for any value of . The values of the parameters at z = 0 are calculated by spline interpolation as a function of , and then we calculate their redshift evolution. We compare the mass function measured in redshift bins of width using the dark matter halo simulation with a DES volume with the Sheth Tormen ( 1999 ) model with p and q fiducial values evaluated at the mean redshift. Since there is a high disagreement in all the mass ranges, we fit the parametric model to the halo catalog measurement. Our fitting method is a simple of the difference between the theoretical model and the measured counts in bins (e.g., Jenkins et al. 2001 ; Manera et al. 2010 and Manera Gaztañaga 2011 ). We also studied the accuracy of the fitting function for Δ overdensities of Tinker et al. ( 2008 ). Figure 1 shows the comparison of the systematic error with the statistical error σ for the two models. In all the redshift bins we found that the deviations, , increase
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