Molecular hydrogen in high-redshift damped Lyman-α systems:: the VLT/UVES database

Aims. We present the current status of ongoing searches for molecular hydrogen in high-redshift (1.8 z(abs) = 4.2) Damped Lyman-alpha systems (DLAs) capitalising on observations performed with the ESO Very Large Telescope (VLT) Ultraviolet and Visual Echelle Spectrograph (UVES). Methods. We identify 77 DLAs/strong sub-DLAs, with log N(HI) = 20 and zabs > 1.8, which have data that include redshifted H-2 Lyman and/or Werner-band absorption lines. This sample of hi, H-2 and metal line measurements, performed in an homogeneous manner, is more than twice as large as our previous sample (Ledoux et al. 2003) considering every system in which searches for H-2 could be completed so far, including all non-detections. Results. H-2 is detected in thirteen of the systems, which have molecular fractions of values between f similar or equal to 5 x 10(-7) and f similar or equal to 0.1, where f = 2N(H-2)/(2N(H-2) + N(hi)). Upper limits are measured for the remaining 64 systems with detection limits of typically log N(H-2) similar to 14.3, corresponding to log f -5. We find that about 35% of the DLAs with metallicities relative to solar [X/H] >= -1.3 (i.e., 1/20th solar), with X = Zn, S or Si, have molecular fractions log f > -4.5, while H-2 is detected - regardless of the molecular fraction - in similar to 50% of them. In contrast, only about 4% of the [X/H] -1.3 DLAs have log f > -4.5. We show that the presence of H-2 does not strongly depend on the total neutral hydrogen column density, although the probability of finding log f > -4.5 is higher for log N(HI) = 20.8 than below this limit (19% and 7% respectively). The overall H-2 detection rate in log N(HI) = 20 DLAs is found to be about 16% (10% considering only log f > -4.5 detections) after correction for a slight bias towards large N(HI). There is a strong preference for H-2-bearing DLAs to have significant depletion factors, [X/Fe] > 0.4. In addition, all H-2-bearing DLAs have column densities of iron into dust grains larger than log N(Fe)(dust) similar to 14.7, and about 40% of the DLAs above this limit have detected H-2 lines with log f > -4.5. This demonstrates the importance of dust in governing the detectability of H-2 in DLAs. Our extended sample supports neither the redshift evolution of the detection fraction of H-2-bearing DLAs nor that of the molecular fraction in systems with H-2 detections over the redshift range 1.8 < z(abs) = 3.