H-2,C I, metallicity, and dust depletion in the z=2.34 damped Ly alpha absorption system toward QSO 1232+0815

We report the detection of strong molecular hydrogen (H-2) absorption lines in the z = 2.34 damped Ly alpha absorber (DLA) toward QSO 1232+0815. This is the second detection in our survey for high-redshift molecules. The new ultraviolet spectrum of the QSO 1232+0815 at 0.9 Angstrom resolution, taken with the Multiple Mirror Telescope Blue Channel Spectrograph, shows the v = 0-0 up to 10-0 Lyman bands and also the Werner v = 0-0 band of H-2 associ ated with the z = 2.34 DLA. We have estimated the total H-2 column density in this system. It ranges from approximate to3 x 10(19) cm(-2) to approxima te to3 x 10(17) cm(-2) depending on the Doppler parameters, b = 6 or 10 km s(-1). Based on the best fit b = 6 km s(-1), the estimated kinetic temperat ure is T-K approximate to 80 K. The measurements of the abundance of zinc a nd iron in the same DLA show that the metallicity measured by the relativel y undepleted element zinc is [Zn/H] = -0.85, while the relative abundance r atio [Fe/Zn] is -1.04, indicating dust depletion. Combining our work with p revious results on H-2 and relative heavy-element depletion, we find that t here is a correlation between them, which suggests that the formation of H- 2 on dust grains is perhaps the dominant formation process in high-redshift DLAs. Detections of strong absorption from the ground and excited states o f neutral carbon (C I) in the z = 2.34 DLA are also presented. The excitati on temperature between the two fine-structure levels of C I is 15.7 +/- 3.5 K, an upper limit for the cosmic microwave background radiation temperatur e at z = 2.34. This value is consistent with the prediction by the standard big bang cosmology.