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Star formation in high redshift galaxies including Supernova feedback: effect on stellar mass and luminosity functions

We present a semi-analytical model of high redshift galaxy formation. In our model the star formation inside a galaxy is regulated by the feedback from supernova (SNe) driven outflows. We derive a closed analytical form for star formation rate in a single galaxy taking account of the SNe feedback in a self-consistent manner. We show that our model can explain the observed correlation between the stellar mass and the circular velocity of galaxies from dwarf galaxies to massive galaxies of $10^{12} M_\odot$. For small mass dwarf galaxies additional feedback other than supernova feedback is needed to explain the spread in the observational data. Our models reproduce the observed 3-D fundamental correlation between the stellar mass, gas phase metallicity and star formation rate in galaxies establishing that the SNe feedback plays a major role in building this relation. Further, the observed UV luminosity functions of Lyman-Break galaxies (LBGs) are well explained by our feedback induced star formation model for a vast redshift range of $1.5 \le z \le 8$. In particular, the flattening of the luminosity functions at the low luminosity end naturally arises due to our explicit SNe feedback treatment.