PDFCHEM: A new fast method to determine ISM properties and infer environmental parameters using probability distributions

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.