Simulating the atomic and molecular content of molecular clouds using probability distributions of physical parameters

Modern observations of the interstellar medium (ISM) in galaxies detect a variety of atomic and molecular species. The goal is to connect these observations to the astrochemical properties of the ISM. 3D hydro-chemical simulations attempt this but due to extreme computational cost, they have to rely on simplified chemical networks and are bound to individual case studies. We present an alternative approach which models the ISM at larger scales by an ensemble of pre-calculated 1D thermo-chemical photodissociation region (PDR) calculations that determine the abundance and excitation of atomic and molecular species. We adopt lognormal distributions of column density (\avpdf s) for which each column density is linked to a volume density as derived by hydrodynamical simulations. We consider two lognormal {\avpdf}s: a diffuse, low density medium with average visual extinction of $\overline{{\rm A}_V}=0.75\,{\rm mag}$ and dispersion of $\sigma=0.5$ and a denser giant molecular cloud with $\overline{{\rm A}_V}=4\,{\rm mag}$ and $\sigma=0.8$. We treat the UV radiation field, cosmic-ray ionization rate and metallicity as free parameters. We find that the low density medium remains fully HI- and CII-dominated under all explored conditions. The denser cloud remains almost always molecular (i.e. H$_2$-dominated) while its carbon phase (CO, CI and CII) is sensitive to the above free parameters, implying that existing methods of tracing H$_2$-rich gas may require adjustments depending on environment. Our numerical framework can be used to estimate the PDR properties of large ISM regions and quantify trends with different environmental parameters as it is fast, covers wide parameter space, and is flexible for extensions.