We explore the properties of high-redshift Lyman-alpha emitters (LAE), and their link with the Lyman-Break galaxy population (LBG), using a semi-analytic model of galaxy formation that takes into account resonant scattering of Lya photons in gas outflows. We can reasonably reproduce the abundances of LAEs and LBGs from redshift 3 to 7, as well as most UV LFs of LAEs. The stronger dust attenuation for (resonant) Lya photons compared to UV continuum photons in bright LBGs provides a natural interpretation to the increase of the LAE fraction in LBG samples, X_LAE, towards fainter magnitudes. The redshift evolution of X_LAE seems however very sensitive to UV magnitudes limits and EW cuts. In spite of the apparent good match between the statistical properties predicted by the model and the observations, we find that the tail of the Lya equivalent width distribution (EW > 100 A) cannot be explained by our model, and we need to invoke additional mechanisms. We find that LAEs and LBGs span a very similar dynamical range, but bright LAEs are about 4 times rarer than LBGs in massive halos. Moreover, massive halos mainly contain weak LAEs in our model, which might introduce a bias towards low-mass halos in surveys which select sources with high EW cuts. Overall, our results are consistent with the idea that LAEs and LBGs make a very similar galaxy population. Their apparent differences seem mainly due to EW selections, UV detection limits, and a decreasing Lya-to-UV escape fraction ratio in high SFR galaxies.
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