We study dwarf galaxy formation at high redshift ($zge5$) using a suite of high- resolution, cosmological hydrodynamic simulations and a semi-analytic model (SAM). We focus on gas accretion, cooling and star formation in this work by isolating the relevant process from reionization and supernova feedback, which will be further discussed in a companion paper. We apply the SAM to halo merger trees constructed from a collisionless N-body simulation sharing identical initial conditions to the hydrodynamic suite, and calibrate the free parameters against the stellar mass function predicted by the hydrodynamic simulations at z = 5. By making comparisons of the star formation history and gas components calculated by the two modelling techniques, we find that semi-analytic prescriptions that are commonly adopted in the literature of low-redshift galaxy formation do not accurately represent dwarf galaxy properties in the hydrodynamic simulation at earlier times. We propose 3 modifications to SAMs that will provide more accurate high-redshift simulations. These include 1) the halo mass and baryon fraction which are overestimated by collisionless N-body simulations; 2) the star formation efficiency which follows a different cosmic evolutionary path from the hydrodynamic simulation; and 3) the cooling rate which is not well defined for dwarf galaxies at high redshift. Accurate semi-analytic modelling of dwarf galaxy formation informed by detailed hydrodynamical modelling will facilitate reliable semi-analytic predictions over the large volumes needed for the study of reionization.
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