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Lyman Alpha Emitters and Lyman Break Galaxies: dichotomous twins?

(Abridged) We extend our previous studies aimed at modeling Lyman Alpha Emitters (LAEs) to the second population of high redshift sources, Lyman Break Galaxies (LBGs), with the final goal of investigating the physical relationship between them at 6 < z <8. We use a set of large (~10^6 Mpc^3) cosmological SPH simulations that include a detailed treatment of star formation, feedback, metal enrichment and supernova dust production; these same simulations have already been shown to successfully reproduce a large number of observed properties of LAEs (Dayal et al. 2010). We identify LBGs as galaxies with an absolute ultraviolet (UV) magnitude M_{UV} <= -17, consistent with current observational criteria. With no further parameter tuning, the model reproduces the redshift evolution of the LBG UV luminosity function, stellar mass function, and star formation rate (SFR) density extremely well, compared to the data at z~6-8. It predicts a z-independent average beta value of about -2.2, consistent with the most recent observational results. The mean LBG specific SFR increases from 6.7 Gyr^-1 at z ~ 6 to 13.9 Gyr^-1 at z ~ 8, and is largest for the smallest LBGs. From a comparison of the simulated LAE and LBG populations, we find no appreciable differences between them in terms of the stellar masses, ages, SFR, and dust content; only the faintest LBGs with M_{UV} >= -18 (-19) at z ~ 6 (8) do not show an observable Lyman Alpha line. LAEs hence represent a luminous LBG subset, whose relative extent depends only on the adopted equivalent width (EW) selection criteria. Further, in line with current observations, we find that the fraction of LBGs showing a Lyman Alpha line decreases with increasing redshift due to the combined effects of dust and reionization. We conclude with a brief critical model discussion, which emphasizes the uncertainties inherent to theoretical EW determinations.