We investigate the physical and morphological properties of LBGs at z ~2.5 to ~3.5, to determine if and how they depend on the nature and strength of the Lyalpha emission. We selected U-dropout galaxies from the z-detected GOODS MUSIC catalog, by adapting the classical Lyman Break criteria on the GOODS filter set. We kept only those galaxies with spectroscopic confirmation, mainly from VIMOS and FORS public observations. Using the full multi-wavelength 14-bands photometry, we determined the physical properties of the galaxies, through a standard spectral energy distribution fitting with the updated Charlot & Bruzual (2009) templates. We also added other relevant observations, i.e. the 24mu m observations from Spitzer/MIPS and the 2 MSec Chandra X-ray observations. Finally, using non parametric diagnostics (Gini, Concentration, Asymmetry, M_20 and ellipticity), we characterized the rest-frame UV morphology of the galaxies. We then analyzed how these physical and morphological properties correlate with the presence of the Lyalpha line in the optical spectra. We find that, unlike at higher redshift, the dependence of physical properties on the Lyalpha line is milder: galaxies without Lyalpha in emission tend to be more massive and dustier than the rest of the sample, but all other parameters, ages, SFRs, X-ray emission as well as UV morphology do not depend strongly on the presence of the line emission. A simple scenario where all LBGs have intrinsically high Lyalpha emission, but where dust and neutral hydrogen content (which shape the final appearance of the Lyalpha) depend on the mass of the galaxies, is able to reproduce the majority of the observed properties at z~3. Some modification might be needed to account for the observed evolution of these properties with cosmic epoch, which is also discussed.
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