Molecular hydrogen absorption systems in Sloan Digital Sky Survey

We present a systematic search for molecular hydrogen absorption systems at high redshift in quasar spectra from the Sloan Digital Sky Survey (SDSS) II Data Release 7 and SDSS-III Data Release 9. We have selected candidates using a modified profile fitting technique taking into account that the Ly$\alpha$ forest can effectively mimic H$_2$ absorption systems at the resolution of SDSS data. To estimate the confidence level of the detections, we use two methods: a Monte-Carlo sampling and an analysis of control samples. The analysis of control samples allows us to define regions of the spectral quality parameter space where H$_2$ absorption systems can be confidently identified. We find that H$_2$ absorption systems with column densities $\log {\rm N_{H_2}} > 19$ can be detected in only less than 3% of SDSS quasar spectra. We estimate the upper limit on the detection rate of saturated H$_2$ absorption systems ($\log {\rm N_{H_2}} > 19$) in Damped Ly-$\alpha$ (DLA) systems to be about 7%. We provide a sample of 23 confident H$_2$ absorption system candidates that would be interesting to follow up with high resolution spectrographs. There is a 1$\sigma$ $r-i$ color excess and non-significant $A_{\rm V}$ extinction excess in quasar spectra with an H$_2$ candidate compared to standard DLA-bearing quasar spectra. The equivalent widths (EWs) of C II, Si II and Al III (but not Fe II) absorptions associated with H$_2$ candidate DLAs are larger compared to standard DLAs. This is probably related to a larger spread in velocity of the absorption lines in the H$_2$ bearing sample.