UVES observations of QSO 0000-2620: Molecular hydrogen abundance in the damped Ly-alpha system at z_abs = 3.3901

We have discovered molecular hydrogen in a fourth quasar damped Ly-alpha system (hereafter DLA). The UVES spectrograph on the 8.2m ESO Kueyen telescope has allowed the detection of H2 in gas with low metallicity, Z/Z_solar ~= 10^{-2}, and high neutral hydrogen column density, N(HI) ~= 2.6*10^{21} cm^{-2}, at redshift z_abs = 3.3901 toward QSO 0000-2620. The measured H2 fractional abundance of f(H2) ~= 4*10^{-8} is lower than a typical value for Galactic interstellar clouds of high N(HI) column density by a factor of (2-3)*10^6. Since H2 molecules are formed efficiently on dust grains, it implies that the dust condensation in this DLA is negligible, and hence the abundances derived from metal absorption lines are the actual ones. The obtained f(H2) value leads to an estimate of the dust number density of _DLA ~= 10^{-3}*_ISM, which is consistent with the dust-to-gas ratio k <= 1.6 10^{-3} derived independently from the [Cr/Zn] and [Fe/Zn] ratios