The Magellan Uniform Survey of Damped Lyman alpha Systems II: Paucity of Strong Molecular Hydrogen Absorption

We present the first large, blind and uniformly selected survey for molecular hydrogen (H_2) in damped Lyman alpha systems (DLAs) with moderate-to-high resolution spectra. 86 DLAs were searched for absorption in the many Lyman and Werner H_2 transitions, with approximately 79% completeness for H_2 column densities above N(H_2)=10^17.5 cm^-2 for an assumed Doppler broadening parameter b=2 km s^-1. Only a single strong H_2 absorber was found -- a system detected previously in VLT/UVES spectra. Given our distribution of N(H_2) upper limits, this ~1% detection rate is smaller than expected from previous surveys at 99.8% confidence. Assuming the N(H_2) distribution shape from previous surveys, our detection rate implies a covering factor of ~1% for N(H_2) >= 10^17.5 cm^-2 gas in DLAs (<6% at 95% confidence). We obtained new Magellan/MagE spectra for 53 DLAs; 8 km s^-1 -resolution spectra were available for 27 DLAs. MagE's moderate resolution (~71 km s^-1) yields weaker N(H_2) upper limits and makes them dependent on the assumed Doppler parameter. For example, half the (relevant) previous H_2 detections have N(H_2) >= 10^18.1 cm^-2, a factor of just 3 higher than our median upper limit. Nevertheless, several tests suggest our upper limits are accurate, and they would need to be increased by 1.8 dex to bring our detection rate within 95% confidence of previous surveys.