We selected a sample of 76 Lya emitting galaxies from the VIMOS Ultra Deep Survey (VUDS) at 2<z<4. We estimated the velocity of the neutral gas flowing out of the interstellar medium as the velocity offset, Deltav, between the systemic redshift (zsys) and the center of low-ionization absorption line systems (LIS). To increase the SN of VUDS spectra, we stacked subsamples. We measured the systemic redshift from the rest-frame UV spectroscopic data using the CIII]1908 nebular emission line, and we considered SiII1526 as the highest signal-to-noise LIS line. We calculated the Lya peak shift with respect to the zsys, the EW(Lya), and the Lya spatial extension, Ext(Lya-C), from the profiles in the 2D stacked spectra. The galaxies that are faint in the rest-frame UV continuum, strong in Lya and CIII], with compact UV morphology, and localized in an underdense environment are characterized by outflow velocities of the order of a few hundreds of km/sec. The subsamples with smaller Deltav are characterized by larger Lya peak shifts, larger Ext(Lya-C), and smaller EW(Lya). In general we find that EW(Lya) anti-correlates with Ext(Lya-C) and Lya peak shift. We interpret these trends using a radiative-transfer shell model. The model predicts that an HI gas with a column density larger than 10^20/cm^2 is able to produce Lya peak shifts larger than >300km/sec. An ISM with this value of NHI would favour a large amount of scattering events, especially when the medium is static, so it can explain large values of Ext(Lya-C) and small EW(Lya). On the contrary, an ISM with a lower NHI, but large velocity outflows would lead to a Lya spatial profile peaked at the galaxy center (i.e. low values of Ext(Lya-C)) and to a large EW(Lya), as we see in our data. Our results and their interpretation via radiative-transfer models tell us that it is possible to use Lya to study the properties of the HI gas.
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