Petitjean, PatrickSrianand, R.Ledoux, C.2012-03-122012-03-122000-12-14http://hdl.handle.net/11007/1268We report results from our mini-survey for molecular hydrogen in eight high-redshift damped Lyman- α (DLA) systems using the ESO Ultra-violet and Visible Spectrograph on the VLT. In addition, we investigate two systems using ESO public data. We include in the sam- ple the only system where H2 was previously detected and studied at high-spectral resolution. Altogether our sample consists of eleven absorbers with 1.85 < zabs < 3.4. We confirm the presence of H2 in the zabs = 2.3377, metal-poor ([Si/H] = −1.20), system toward PKS 1232+082. The derived molecular fraction, f = 2N(H2)/(2N(H2)+N(H i)) = 4×10−4, is two orders of magnitude less than what has been claimed previ- ously from low-resolution data. The physical conditions within the cloud can be constrained directly from ob- servation. The kinetic temperature and particle density are in the ranges, respectively, 100 < T < 300 K and 30 < nH < 50 cm−3. In addition, UV pumping is of the same order of magnitude than in our Galaxy. The upper limits on the molecular fraction derived in nine of the systems are in the range 1.2×10−7−1.6×10−5. There is no evidence in this sample for any correlation be- tween H2 abundance and relative heavy element depletion into dust grains. This should be investigated using a larger sample however. The molecular abundance in a few DLA systems (and in particular in the two systems where H2 is detected) is consistent with what is seen in the Magel- lanic clouds. But most of the DLA measurements are well below these values. This is probably partly due to small amounts of dust and/or high UV flux. We argue however that the lack of molecules is a direct consequence of high kinetic temperature (T > 3000 K) implying a low forma- tion rate of H2 onto dust grains. Therefore, most of the DLA systems arise in warm and diffuse neutral gas.enH2 moleculesMolecular hydrogenDamped Lyman-alpha systemsPreprint