Molecular hydrogen in high-redshift Damped Lyman-alpha systems: The   VLT/UVES database
  We present the current status of ongoing searches for molecular hydrogen in high-redshift (1.8 < zabs <= 4.2) Damped Lyman-alpha systems (DLAs) capitalising on observations performed with the ESO Very Large Telescope (VLT) Ultraviolet and Visual Echelle Spectrograph (UVES). We identify 77 DLAs/strong sub-DLAs, with log N(HI) >= 20 and z_abs > 1.8, which have data that include redshifted H2 Lyman and/or Werner-band absorption lines. This sample of HI, H2 and metal line measurements, performed in an homogeneous manner, is more than twice as large as our previous sample (Ledoux et al. 2003) and considers every system in which searches for H2 could be completed so far, including all non-detections. H2 is detected in thirteen of the systems with molecular fractions of values between f=5x10^-7 and f=0.1, where f=2N(H2)/(2N(H2)+N(HI)). Upper limits are measured for the remaining 64 systems with detection limits of typically log N(H2)=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 H2 is detected -- regardless of the molecular fraction -- in 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 H2 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 H2 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). [truncated] 
P. Noterdaeme, C. Ledoux, P. Petitjean and R. Srianand