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An independent analysis of the molecular hydrogen absorption system at z =2.059 in the spectrum of the quasar J2123-0050 is presented. The H_2 systemconsists of two components (A and B) with column densities log N^A(H_2) =17.94+/-0.01 and log N^B(H_2) = 15.16+/-0.02. The spectrum exhibits the linesof HD molecules (log N^A(HD) = 13.87+/-0.06) and the neutral species C I and ClI associated with the H_2 absorption system. For the molecular hydrogen linesnear the quasar's Ly_beta and O VI emission lines, we detect a nonzero residualflux, ~3% of the total flux, caused by the effect of partial coverage of thequasar's broad-line region by an H_2 cloud. The uniqueness of the system beinginvestigated is manifested in a high abundance of the neutral species H_2 and CI at the lowest H I column density, log N(H I) = 19.18+/-0.15, among the highredshift systems. The N(HD)/2N(H_2) ratio for component A has turned out to bealso unusually high, (4.26+/-0.60)x10^{-5}. We have investigated the physicalconditions in components A and B. Component A represents the optically thickcase; the gas has a low number density (n~30 cm^{-3}) and a temperature T~140K. In component B, the medium is optically thin with n<100 cm^{-3} and T<100 K.The ultraviolet (UV) background intensity in the clouds exceeds the meanintensity in our Galaxy by almost an order of magnitude. A high gas ionizationfraction, n(H+)/n(H)~10^{-2}, which can be the result of partial shielding ofthe system from hard UV radiation, is needed to describe the high HD and C Icolumn densities. Using our simulations with the PDR Meudon code, we canreconstruct the observed column densities of the species within the model witha constant density n(H)=40 cm^{-3}. A high H_2 formation rate (higher than themean Galactic value by a factor of 10-40) and high gas ionization fraction andUV background intensity are needed in this case.

Estimation of physical conditions in the cold phase of the ISM in the sub-DLA system at z = 2.06 in the spectrum of the quasar J2123-0050