Molecular fraction limits in damped Lyman-alpha absorption systems

We have used the Green Bank Telescope (GBT) and Berkeley-Illinois-Maryland Association (BIMA) array to search for redshifted millimetre absorption in a sample of damped Lyman-alpha absorption systems (DLAs). This brings the number of published systems searched from 18 to 30. In 17 cases we reach $3\sigma$ limits of $\tau\leq0.1$, which is a significant improvement over the previous searches and more than sufficient to detect the 4 known redshifted millimetre absorbers ($\tau\gapp1$). While the CO rotational (millimetre) column density limits obtained are weaker than the electronic (optical) limits, they may provide useful limits below the atmospheric cut-off for the Lyman and Werner \MOLH-bands in the UV ($z_{\rm abs}\lapp1.8$). Using a model for the DLA metallicity evolution combined with assumed HCO$^+$/\MOLH ~and CO/\MOLH \~conversion ratios, we use the molecular column density limits to calculate plausible \MOLH ~molecular fraction limits. Finally, we use these results to discuss the feasibility of detecting rotational CO transitions in DLAs with the next generation of large radio telescopes.