Ultraviolet excited high-j molecular hydrogen in photodissociation regions

We have calculated synthetic interstellar cloud models to investigate the formation and destruction of high-J molecular hydrogen in photodissociation regions. The effects of five physical parameters (the incident ultraviolet [UV] intensity, H₂ column density, cloud temperature, total density, and H₂ formation rate coefficient) on the populations of H₂ rotational levels are explored. We have found that N(4)/N(0) is proportional to the incident UV intensity I_UV and the H₂ molecular fraction f is simply related to the ratio of I_UV and the hydrogen density n_H, implying a new method to derive I_UV and n _H with the observational parameters N(4)/N(0) and f, assuming an H₂ formation rate R. High-resolution FUSE spectra of H₂ toward three translucent sight lines (HD 110432, HD 192639, and HD 185418) in the Milky Way and 24 diffuse sight lines in the SMC and LMC are referenced to obtain N(4)N(0) and f. Using our method, we are able to derive I_UV ∼ 10-40 for the translucent sight lines, when R is assumed to be 10 times higher than the Galactic value. Synthetic models for the Magellanic sight lines suggest that I_UV ≥ 10, n_H ≤ 100 cm^-3, and R ∼ 3 × 10^-16 for the low H₂ column density sight lines (N[H₂] ≤ 10¹⁸ cm^-2) and I _UV ≥ 10, n_H ≤ 1000 cm^-3, and R ∼ 3 × 10^-17 for the high H₂ column density sight lines (N[H₂] ≥ 10¹⁹ cm^-2).