Molecular-Cloud-Scale Chemical Composition III: Constraints of Average Physical Properties through Chemical Models

Abstract: It is important to understand the origin of molecular line intensities and chemical composition in the molecular-cloud scale in the Galactic sources because it serves as a benchmark to compare with the chemical compositions of extragalactic sources. Recent observations of the 3-mm spectra averaged over the 10-pc scale show similar spectral pattern among sources for molecular lines HCN, HCO$^+$, CCH, HNC, HNCO, c-C$3$H$_2$, CS, SO, N$_2$H$^+$, and CN. To constrain the average physical property emitting such spectral pattern, we model molecular spectra using a time-dependent gas-grain chemical model followed by a radiative transfer calculation. We use a grid of physical parameters such as the density $n=3 \times 10^2 - 3\times 10^4$ cm$^{-3}$, the temperature, $T=10-30$ K, the visual extinction $A{\rm V} = 2,4,10$ mag, the cosmic-ray ionization rate $\zeta = 10^{-17} - 10^{-16}$ s$^{-1}$, and the sulfur elemental abundance $S/H = 8\times 10^{-8} - 8\times 10^{-7}$. Comparison with the observed spectra indicates that spectra are well reproduced with the relatively low density of $n=(1-3) \times 10^3\,$cm$^{-3}$, $T=10\,$K, $\zeta = 10^{-17}$ s$^{-1}$, and the short chemistry timescale of $10^5$ yrs. This short chemistry timescale may indicate that molecular clouds are constantly affected by the turbulence, and exposed to low-density, low $A_{\rm V}$ regions that "refreshes" the chemical clock by UV radiation. The relatively low density obtained is orders of magnitude lower than the commonly-quoted critical density in the optically thin case. Meanwhile, this range of density is consistent with results from recent observational analysis of molecular-cloud-scale mapping.