Abstract
We have calculated 2448 interstellar cloud models to investigate the formation and destruction of high rotational level $H_2$ according to the combinations of five physical conditions: the input UV intensity, the $H_2$ column density, cloud temperature, total density, and the $H_2$ formation rate efficiency. The models include the populations of all the accessible states of $H_2$ with the rotational quantum number J < 16 as a function of depth through the model clouds, and assume that the abundance of $H_2$ is in a steady state governed primarily by the rate of formation on the grain surfaces and the rates of destruction by spontaneous fluorescent dissociation following absorption in the Lyman and Werner band systems. The high rotational levels J = 4 and J = 5 are both populated by direct formation into these levels of newly created molecules, and by pumping from J = 0 and J = 1, respectively The model results show that the high rotational level ratio N(4)/N(0) is proportional to the incident UV intensity, and is inversely proportional to the $H_2$ molecular fraction, as predicted in theory.
