Physical conditions in high-redshift GRB-DLA absorbers observed with VLT/UVES: implications for molecular hydrogen searches

Aims. We aim to understand the nature of the absorbing neutral gas in the galaxies hosting high-redshift long-duration gamma-ray bursts (GRBs) and to determine their physical conditions. Methods. A detailed analysis of high-quality VLT/UVES spectra of the optical afterglow of GRB 050730 and other Swift-era bursts is presented. Results. We report the detection of a significant number of previously unidentified allowed transition lines of Fe + , involving the fine structure of the ground term ( 6 D7/2, 6 D5/2, 6 D3/2, 6 D1/2) and that of other excited levels ( 4 F9/2, 4 F7/2, 4 F5/2, 4 F3/2, 4 D7/2, 4 D5/2), from the zabs = 3.969, log N(H 0 ) = 22.10, damped Lyman-α (DLA) system located in the host galaxy of GRB 050730. No molecular hydrogen (H2) is detected down to a molecular fraction of log f < −8.0. We derive accurate metal abundances for Fe + ,S + ,N 0 , Ni + , and, for the first time in this system, Si + and Ar 0 . The absorption lines are best-fit as a single narrow velocity component at zabs = 3.96857. The time-dependent evolution of the observed Fe + energy-level populations is modelled by assuming the excitation