The Lya emission has been observed from galaxies over a redshift span z ~ 0 - 8.6. However, the evolution of high-redshift Lya emitters (LAEs), and the link between these populations and local galaxies, remain poorly understood. Here, we investigate the Lya properties of progenitors of a local L* galaxy by combining cosmological hydrodynamic simulations with three-dimensional radiative transfer calculations using the new ART^2 code. We find that the main progenitor (the most massive one) of a Milky Way-like galaxy has a number of Lya properties close to those of observed LAEs at z ~ 2 - 6, but most of the fainter ones appear to fall below the detection limits of current surveys. The Lya photon escape fraction depends sensitively on a number of physical properties of the galaxy, such as mass, star formation rate, and metallicity, as well as galaxy morphology and orientation. Moreover, we find that high-redshift LAEs show blue-shifted Lya line profiles characteristic of gas inflow, and that the Lya emission by excitation cooling increases with redshift, and becomes dominant at z > 6. Our results suggest that some observed LAEs at z ~ 2-6 with luminosity of L_Lya ~ 10^{42-43} ergs/s may be similar to the main progenitor of the Milky Way at high redshift, and that they may evolve into present-day L* galaxies.
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