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-α absorbers (DLAs) from the Sloan Digital Sky Survey with log(N(H I)/cm‑2) ≥ 21. This allowed us to generate the average Ly-α emission spectrum associated to DLAs, free from any emission coming from the background quasar. We measured the Lyα emission at > 5.8σ level with a luminosity of 8.95 ± 1.54 × 1040 erg s‑1 (corresponding to about 0.02 L⋆ at z ∼ 2 ‑ 3) in systems with average log(N(H I) /cm‑2) of ≈21.2 and at a median redshift of z ∼ 2.64. The peak of the Lyα emission is apparently redshifted by ∼300 km s‑1 relative to the absorption redshift, which appears to be due to suppression of blue Ly-α photons by radiative transfer through expanding gas. We infer that DLAs form stars with an average rate of (0.08 ± 0.01)/fescM⊙ yr‑1; namely, ≈ (0.54 ± 0.09) M⊙ yr‑1 for a typical escape fraction (fesc = 0.15) of Lyman-α 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-α emitting galaxies.

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