The ESO UVES advanced data products quasar sample II. Cosmological evolution of the neutral gas mass density

Damped absorbers, seen in the spectra of background quasars, are unique probes to select Hi-rich galaxies. These galaxies allow one to estimate the neutral gas mass over cosmological scales. The neutral gas mass is a possible indicator of gas consumption as star formation proceeds. The damped Ly alpha absorbers (DLAs; N-HI >= 2 x 1020 cm(-2)) and sub-DLAs (1019 <= N-HI = 2 x 1020 cm(-2)) are believed to contain a large fraction of neutral gas mass in the Universe. In Paper I of the series, we presented the results of a search for DLAs and sub-DLAs in the European Southern Observatory (ESO) Ultraviolet Visual Echelle Spectrograph (UVES) advanced data products dataset of 250 quasars. Here we use an unbiased subsample of sub-DLAs from this dataset to derive their statistical properties. We built a subset of 122 quasars ranging from 1.5 < z(em) < 5.0, suitable for statistical analysis. The statistical sample was analyzed in conjunction with other sub-DLA samples from the literature. This resulted in a combined sample of 89 sub-DLAs over a redshift path of Delta z = 193. We derived the redshift evolution of the number density and the line density for sub-DLAs and compared them with the Lyman-limit systems (LLSs) and DLA measurements from the literature. The results indicate that these three classes of absorbers are evolving in the redshift interval 1.0 < z < 5.0. Thanks to the ESO UVES advanced data products data, we were able to determine the column density distribution, f(HI)(N, z), down to the sub-DLA limit. The flattening of fHI(N, z) in the sub-DLA regime is present in the observations. The redshift evolution of fHI(N, z) down to log NHI = 19.0 cm-2 is also presented, indicating that there are more sub-DLAs at high redshift than at low redshift. fHI(N, z) was also used to determine the neutral gas mass density, Omega(g), at 1.5 < z < 5.0. The complete sample shows that sub-DLAs contribute 8-20% to the total Omega(g) from 1.5 < z < 5.0. In agreement with previous studies, no evolution of Omega(g) was observed from low to high redshift (i.e., 1.5 < z < 5.0), suggesting that star formation alone cannot explain this non-evolution and replenishment of gas and that recombination of ionized gas is needed.