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

Abstract

Determining the atomic and molecular content of the interstellar medium (ISM) as a function of environmental parameters is of fundamental importance to understand the star-formation process across the epochs. Although there exist various three-dimensional hydro-chemical codes modelling the ISM at different scales and redshifts, 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 ($A_{\mathrm{V},\mathrm{eff}}$) and the observed ($A_{\mathrm{V},\mathrm{obs}}$) visual extinctions, and the local number density, $n_{\mathrm{H}}$, with probability density functions (PDF) of $A_{\mathrm{V},\mathrm{obs}}$ on cloud scales typically tens-to-hundreds of pc as an input. For any given $A_{\mathrm{V},\mathrm{obs}}$-PDF, sampled with thousands of clouds, the algorithm instantly computes the average abundances of the most important species (HI, H${}_2$, CII, CI, CO, OH, OH${}^{+}$, H${}_2$O${}^{+}$, CH, HCO${}^{+}$) and performs radiative transfer calculations to estimate the average emission of the most commonly observed lines ([CII]~$158\mu$m, both [CI] fine-structure lines and the first five rotational transitions of ${}^{12}$CO). We examine two $A_{\mathrm{V},\mathrm{obs}}$-PDFs corresponding to a non star-forming and a star-forming ISM region, under a variety of environmental parameters combinations. These cover FUV intensities in the range of $\chi /{\chi }_0=10^{-1}-10^3$, cosmic-ray ionization rates in the range of ${\zeta }_{\mathrm{CR}}=10^{-17}-10^{-13}{\mathrm{s}}^{-1}$ and metallicities in the range of $Z=0.1-2{\mathrm{Z}}_{\odot }$. PDFchem is fast, easy to use, reproduces the PDR quantities of the time-consuming hydrodynamical models and can be used directly with observed data to understand the evolution of the cold ISM chemistry.

33 pages, 27 figures. Accepted in MNRAS. The algorithm can be found in: https://github.com/tbisbas/PDFchem. Comments welcome!

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