We present the results of cosmological hydrodynamic simulations with zoom-in initial conditions, and investigate the formation of the first galaxies and their evolution towards observable galaxies at $z sim 6$. We focus on three different galaxies which end up in halos with masses $M_{h} = 2.4 times10^{10}~h^{-1}; M_{odot}$ (Halo-10), $1.6 times10^{11}~h^{-1}; M_{odot}$ (Halo-11) and $0.7 times10^{12}~h^{-1} M_{odot}$ (Halo-12) at z=6. Our simulations also probe impacts of different sub-grid assumptions, i.e., SF efficiency and cosmic reionization, on SF histories in the first galaxies. We find that star formation occurs intermittently due to supernova (SN) feedback at z > 10, and then it proceeds more smoothly as the halo mass grows at lower redshifts. Galactic disks are destroyed due to SN feedback, while galaxies in simulations with no-feedback or lower SF efficiency models can sustain galactic disk for long periods > 10 Myr. The expulsion of gas at the galactic center also affects the inner dark matter density profile. However, SN feedback does not seem to keep the shallow profile of dark matter for a long period. Our simulated galaxies in Halo-11 and Halo-12 reproduce the star formation rates (SFR) and stellar masses of observed Lyman-$alpha$ emitters (LAEs) at z = 7-8 fairly well given observational uncertainties. In addition, we investigate the effect of UV background radiation on star formation as an external feedback source, and find that earlier reionization extends the quenching time of star formation due to photo-ionization heating, but does not affect the stellar mass at z=6.
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