Velocity Dispersion of Excited H2

We present a study of the high rotational bands (J > 2) of H2 toward 4 early type galactic stars: HD 73882, HD 192639, HD 206267, and HD 207538. In each case, the velocity dispersion - characterized by the spectrum fitting parameter b - increases with the level of excitation, a phenomenon that has previously been detected by the Copernicus and IMAPS observatories. In particular, we show with 4 sigma confidence that for HD 192639 it is not possible to fit all J levels with a single b value, and that higher b values are needed for the higher levels. The amplitude of the line broadening, which can be as high as 10 km s^-1, makes explanations such as inhomogeneous spatial distribution unlikely. We investigate a mechanism in which the broadening is due to the molecules that are rotationally excited through the excess energy acquired after their formation on a grain (H2-formation pumping). We show that different dispersions would be a natural consequence of this mechanism. We note however that such process would require a formation rate 10 times higher then what was inferred from other observations. In view of the difficulty to account for the velocity dispersion as thermal broadening (T would be around 10,000 K), we conclude then that we are most certainly observing some highly turbulent warm layer associated with the cold diffuse cloud. Embedded in a magnetic field, it could be responsible for the high quantities of CH+ measured in the cold neutral medium.