Bias and Conditional Mass Function of Dark Halos Based on the Nonspherical Collapse Model

Nonspherical collapse is modelled, under the Zeldovich approximation, bysix-dimensional random walks of the initial deformation tensor field. Thecollapse boundary adopted here is a slightly-modified version of that proposedby Chiueh and Lee (2001). Not only the mass function agrees with the fittingformula of Sheth and Tormen (1999), but the bias function and conditional massfunction constructed by this model are also found to agree reasonably well withthe simulation results of Jing (1998) and Somerville et al. (2000),respectively. In particular, by introducing a small mass gap, we find a fittingformula for the conditional mass function, which works well even at small timeintervals between parent and progenitor halos during the merging history.Comment: 28 pages, 11 figures, section 3.2 complemented, Fig.1 and Fig. 4 modified, version accepted for publication in Ap