2023MNRAS.523..498B

We compute a grid of photodissociation region (PDR) models. The varying parameters of the grid include effective temperature (T_eff) and luminosity (L) of the radiation source, density (n_H) of the nebula, PDR depth from the nebular ionization front (Δr_PDR), and densities of polycyclic aromatic hydrocarbon (PAH) molecules and amorphous carbon (AC) dust. The paradigm, including the range of the parameters used to calculate the models, corresponds to planetary nebulae (PNe). We study the heating and cooling rates, and the variation of gas kinetic temperature (T_K) along the PDR depth. We evaluate fluxes of fine structure lines: [O I] 63 $\mu$m, [C II] 158 $\mu$m, and [C I] 609 $\mu$m and flux ratios: [O I] 146/63 $\mu$m, [O I] 63/[C II] 158 $\mu$m, and [C I] 609/370 $\mu$m, and study their variation in the parameter space: T_eff, L, and n_H, for different composition of PAH and AC. We further study the distribution of [O I] 146/63 $\mu$m and [O I] 63/[C II] 158 $\mu$m ratios in the parameter spaces of n_H, Δr_PDR, T_eff, and L. We take the observed [O I] 146/63 $\mu$m and [O I] 63/[C II] 158 $\mu$m ratios for a number of PNe, and compare with these ratios obtained from our models. We verify that the correlation found between the [O I] 146/63 $\mu$m and [O I] 63/[C II] 158 $\mu$m ratios observed in real PNe is similar to that found from our PN model grid.