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Early Results from GLASS-JWST XXIII: The transmission of Lyman-alpha from UV-faint z ~ 3-6 galaxies

Lyman-alpha (Ly$α$) emission from galaxies can be used to trace neutral hydrogen in the epoch of reionization, however, there is a degeneracy between the attenuation of Ly$α$ in the intergalactic medium (IGM) and the line profile emitted from the galaxy. Large shifts of Ly$α$ redward of systemic due to scattering in the interstellar medium can boost Ly$α$ transmission in the IGM during reionization. The relationship between Ly$α$ velocity offset from systemic and other galaxy properties is not well-established at high-redshift or low luminosities, due to the difficulty of observing emission lines which trace systemic redshift. Rest-frame optical spectroscopy with JWST/NIRSpec has opened a new window into understanding of Ly$α$ at z>3. We present a sample of 12 UV-faint galaxies ($-20 \lesssim$ MUV $\lesssim -16$) at $3 \lesssim z \lesssim 6$, with Ly$α$ velocity offsets, $Δv_{\mathrm{Ly}α}$, measured from VLT/MUSE and JWST/NIRSpec from the GLASS-JWST Early Release Program. We find median $Δv_{\mathrm{Ly}α}$ of 205 km s$^{-1}$ and standard deviation 75 km s$^{-1}$, compared to 320 and 170km s$^{-1}$ for MUV < -20 galaxies in the literature. Our new sample demonstrates the previously observed trend of decreasing Ly$α$ velocity offset with decreasing UV luminosity and optical line velocity dispersion, extends to MUV $\gtrsim$ -20, consistent with a picture where the Ly$α$ profile is shaped by gas close to the systemic redshift. Our results imply that during reionization Ly$α$ from UV-faint galaxies will be preferentially attenuated, but that detecting Ly$α$ with low $Δv_{\mathrm{Ly}α}$ can be an indicator of large ionized bubbles.