Molecular Hydrogen in the Damped Ly alpha Absorber of Q1331+170
  We used HST/STIS to obtain the spectrum of molecular hydrogen associated with the damped Ly$\alpha$ system at $z_{\rm abs}=1.7765$ toward the quasar Q1331+170 at $z_{\rm em}=2.084$. Strong ${\rm H}_2$ absorption was detected, with a total ${\rm H}_2$ column density of $N({\rm H}_2)=(4.45\pm 0.36)\times 10^{19} {\rm cm^{-2}}$.The molecular hydrogen fraction is $f_{{\rm H}_2}=\frac{2N_{\rm H_2}}{N_{\rm HI}+2N_{\rm H_2}}=(5.6\pm 0.7)%$, which is the greatest value reported so far in any redshifted damped Ly$\alpha$ system. This results from the combined effect of a relatively high dust-to-gas ratio, a low gas temperature, and an extremely low ambient UV radiation field. Based on the observed population of $J$ states, we estimate the photo-absorption rate to be $R_{\rm abs}=(7.6\pm 2.4)\times 10^{-13} {\rm s^{-1}}$, corresponding to a local UV radiation field of $J(1000{\rm \AA})\approx 2.1\times 10^{-3} J_{1000{\rm \AA},\odot}$, where $J_{1000{\rm \AA},\odot}$ is the UV intensity at $1000 \AA$ in the solar neighborhood. This is comparable with the metagalactic UV background intensity at this redshift, and implies an extremely low star formation rate in the absorber's environment. The observed CO-to-H$_2$ column density ratio is $\frac{N_{\rm CO}}{N_{\rm H_2}}<2.5\times 10^{-7}$, which is similar to the value measured for diffuse molecular clouds in the Galactic ISM. Finally, applying the inferred physical conditions to the observed C I fine structure excitation (Songaila {\it et al.} 1994), we estimate the cosmic microwave background temperature to be $T_{\rm CMB}=(7.2\pm 0.8) {\rm K}$ at $z=1.77654$, consistent with the predicted value of $7.566 {\rm K}$ from the standard cosmology. 
Jun Cui, Jill Bechtold, Jian Ge, David M. Meyer