Constraining cloud parameters using high density gas tracers in galaxies

Far-infrared molecular emission is an important tool used to understand the excitation mechanisms of the gas in the interstellar medium (ISM) of star-forming galaxies. In the present work, we model the emission from rotational transitions with critical densities n ≳ 104 cm-3. We include 4−3 104 cm-3, emanates from the 10–1000 cm-3 part of the PDF. We construct synthetic emission maps for the central 2 kpc of the galaxy and fit the line ratios of CO and 13CO up to J = 15−14, as well as HCN, HNC, and HCO+ up to J = 7−6, using one photo-dissociation region (PDR) model. We attribute the goodness of the one component fits for our model galaxy to the fact that the distribution of the luminosity, as a function of density, is peaked at gas densities between 10 and 1000 cm-3, with negligible contribution from denser gas. Specifically, the Mach number, ℳ, of the model galaxy is ~10. We explore the impact of different log-normal density PDFs on the distribution of the line-luminosity as a function of density, and we show that it is necessary to have a broad dispersion, corresponding to Mach numbers ≳30 in order to obtain significant (>10%) emission from n> 104 cm-3 gas. Such Mach numbers are expected in star-forming galaxies, luminous infrared galaxies (LIRGS), and ultra-luminous infrared galaxies (ULIRGS). This method provides a way to constrain the global PDF of the ISM of galaxies from observations of molecular line emission. As an example, by fitting line ratios of HCN(1−0), HNC(1−0), and HCO+ (1−0) for a sample of LIRGS and ULIRGS using mechanically heated PDRs, we constrain the Mach number of these galaxies to 29 < ℳ < 77