A Homogeneous Sample of Sub-DLAs II: Statistical, Kinematic and Chemical Properties

Damped Ly-alpha Systems (DLAs), with N(HI)>2*10^20 cm^{-2}, observed in quasars have allowed us to quantify the chemical content of the Universe over cosmological scales. Such studies can be extended to lower N(HI), in the sub-DLA range (10^19<N(HI)<2*10^20 cm^{-2}), which are systems believed to contain a large fraction of the neutral hydrogen at z>3.5. In this paper, we use a homogeneous sample of sub-DLAs from the ESO UVES archives presented in Paper I (Dessauges-Zavadsky et al. 2003), to observationally determine for the first time the column density distribution, f(N), down to N(HI)=10^19 cm^{-2}. The results are in good agreement with the predictions from Peroux et al. (2003). We present the kinematic and clustering properties of this survey. We compare low- and high-ionization transition widths and find that the sub-DLAs properties roughly span the parameter space of DLAs. We analyse the chemical content of this sample in conjunction with abundances from 72 DLAs taken from the literature. We compute the HI column density-weighted mean abundance which is believed to be an indicator of the Universe's metallicity. Although the number statistics is limited, the results suggest a slightly stronger evolution in the sub-DLA range. The evolution we probe is not due to their lower dust content. Therefore these systems might be associated with a different class of objects which better trace the overall chemical evolution of the Universe. Finally, we present abundance ratios of [Si/Fe], [O/Fe], [C/Fe] and [Al/Fe], but it is difficult to decipher whether the observed values are the effect of nucleosynthesis or are due to differential dust depletion. The metallicities are compared with two different sets of models of galaxy evolution in order to provide constraints on the morphology of the absorbers [abridged].