Structure of stationary photodissociation fronts

The structure of stationary photodissociation fronts is revisited. H₂ self-shielding is discussed, including the effects of line overlap. We find that line overlap is important for N(H₂) ≳ 10²⁰ cm^-2, with a factor-of-2 suppression of pumping rates at column densities N(H₂) ≈ 3 × 10²⁰ cm^-2. We compute multiline UV pumping models and compare these with simple analytic approximations for the effects of self-shielding. The overall fluorescent efficiency of the photodissociation front is obtained for different ratios of χ/n_H (where χ characterizes the intensity of the illuminating ultraviolet radiation) and different dust extinction laws. The dust optical depth τ_pdr to the point where 50% of the H is molecular is found to be a simple function of a dimensionless quantity φ₀ depending on χ/n_H the rate coefficient R(T) for H₂ formation on grains, and the UV dust opacity. The fluorescent efficiency of the photodissocation region (PDR) also depends primarily on φ₀ for χ ≲ 3000 and n_H ≲ 10⁴ cm^-3; for stronger radiation fields and higher densities, radiative and collisional depopulation of vibrationally excited levels interferes with the radiative cascade. We show that the emission spectrum from the PDR is essentially independent of the color temperature τ_color of the illuminating radiation for 10⁴ K ≲ T_color but shows some sensitivity to the rotationvibration distribution of newly formed H₂. The 1-0 S(1)/2-1 S(1) and 2-1 S(1)/6-4 Q(1) intensity ratios, the ortho/para ratio, and the rotational temperature in the v = 1 and v = 2 levels are computed as functions of the temperature and density for different values of χ/n_H. We apply our models to the reflection nebula NGC 2023. Apparent inconsistencies between published K-band and far-red spectroscopy of this object are discussed; we adjust the two sets of observations for consistency. We are able to reproduce approximately the (adjusted) observations with models having χ = 5000, n_H = 10⁵ cm^-3, and a reasonable viewing angle. Further observations of NGC 2023 will be valuable to clarify the uncertain spatial structure of the emission.