We present the results from VLT/X-shooter spectroscopic observations of 11 extremely strong intervening damped Lyman-alpha absorbers (ESDLAs) initially selected as high N(Hi) (i.e.>=5x10^21 cm-2) candidates from the Sloan Digital Sky Survey (SDSS). We confirm the high Hi column densities which we measure to be in the range log N(Hi) = 21.6-22.4. Molecular hydrogen is detected with high column densities (N(H_2)>=10^18 cm-2) in five out of eleven systems, three of which are reported here for the first time. We compare the chemical properties of this sample of ESDLAs, supplemented with literature measurements, to that of DLAs located at the redshift of long-duration gamma-ray bursts (GRB-DLAs). We confirm that the two populations are almost indistinguishable in terms of chemical enrichment, H_2 column density and gas kinematics. All this suggests that ESDLAs and GRB-DLAs probe similar galactic environments. We search for the galaxy counterparts of ESDLAs and find associated emission lines in three out of eleven systems, two of which are reported here for the first time (towards the quasars SDSS J002503.03+114547.80 and SDSS J114347.21+142021.60, respectively). The measured separations between the quasar sightlines and the emission associated with the ESDLA galaxy are all very small (rho < 3 kpc). While the small impact parameters are similar to what is observed for GRB-DLAs, the associated star-formation rates are on average lower than seen for GRB host galaxies. This is explained by long-duration GRBs being associated with the death of massive stars, hence pinpointing regions of active star formation in the GRB host galaxies. Our observations support the suggestion from the literature that ESDLAs could act as blind analogues of GRB-DLAs, probing high column density neutral gas in the heart of high-redshift galaxies, without any prior on the instantaneous star-formation rate.
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