2023MNRAS.519..729B

Determining the atomic and molecular content of the interstellar medium (ISM) is of fundamental importance to understand the star-formation process. Although there exist various three-dimensional hydro-chemical codes modelling the ISM, they are computationally expensive and inefficient for studies over a large parameter space. Building on our earlier approach, we present PDFCHEM, a novel algorithm that models the cold ISM at moderate and large scales using functions connecting the quantities of the local (A_V, eff_) and the observed (A_V, obs_) visual extinctions, and the local number density, n_H, with probability density functions (PDF) of A_V, obs_ on cloud scales typically tens-to-hundreds of pc as an input. For any given A_V, obs_-PDF, the algorithm instantly computes the average abundances of the most important species (H I, H₂, C II, C I, CO, OH, OH⁺, H₂O⁺, CH, HCO⁺) and performs radiative transfer calculations to estimate the average emission of the most commonly observed lines ([C II] 158$\mu$m, both [C I] fine-structure lines and the first five rotational transitions of ¹²CO). We examine two A_V, obs_-PDFs corresponding to a non-star-forming and a star-forming ISM region, under a variety of environmental parameters combinations. These cover far-ultraviolet intensities in the range of χ/χ₀ = 10^–1 - 10³, cosmic ray ionization rates in the range of $\zeta _{\rm CR}=10^{-17}-10^{-13}\, {\rm s}^{-1}$ and metallicities in the range of $Z=0.1-2\, {\rm Z}_{\odot }$. PDFCHEM is fast, easy to use, reproduces the PDR quantities of the hydrodynamical models, and can be used directly with observed data of the cold ISM.