We aim to constrain the average star formation associated with neutral hydrogen gas reservoirs at cosmic noon. We used a unprecedented sample of 1716 high-column-density, damped Ly-alpha absorbers (DLAs) from the Sloan Digital Sky Survey with log($N$(H i $) ge 21. This allowed us to generate the average Ly-alpha emission spectrum associated to DLAs, free from any emission coming from the background quasar. We measured the Lyalpha emission at $> 5.8 level with a luminosity of $8.95 erg s $ (corresponding to about 0.02 L$^ star $ at $z 2-3) in systems with average i $) of approx 21.2 and at a median redshift of $z 2.64. The peak of the Lyalpha emission is apparently redshifted by sim 300 $ relative to the absorption redshift, which appears to be due to suppression of blue Ly-alpha photons by radiative transfer through expanding gas. We infer that DLAs form stars with an average rate of (0.08 pm 0.01)/$ f esc M odot yr $; namely, $ M odot yr $ for a typical escape fraction ($ f esc =0.15$) of Lyman-alpha emitting galaxies. DLA galaxies follow the main sequence of star-forming galaxies at high redshift, suggesting that the DLA population is dominated by the lower mass end of Lyman-alpha emitting galaxies.
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