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Reliability of merger tree realizations of dark halos in the Monte-Carlo modeling of galaxy formation

We examine the reliability of the merger trees generated for the Monte-Carlo modeling of galaxy formation. In particular we focus on the cold gas fraction predicted from the merger trees with different assumptions on the progenitor distribution function, the timestep, and the mass resolution. We show that the cold gas fraction is sensitive to the accuracy of the merger trees at small-mass scales of progenitors at high redshifts. One can reproduce the Press-Schechter prediction to a reasonable degree by adopting a fairly large number of redshift bins, N_{step} ~ 1000 in generating merger trees, which is a factor of ten larger than the canonical value used in previous literature.