Constraining cloud parameters using high density gas tracers in galaxies

¹ Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
e-mail: mher@strw.leidenuniv.nl
² Institute for Marine and Atmospheric research Utrecht, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
³ Dipartimento di Chimica, Universitá degli Studi di Bari, via Orabona 4, 70126 Bari, Italy
⁴ Kapteyn Astronomical Institute, PO Box 800, 9700 AV Groningen, The Netherlands

Received: 14 July 2014
Accepted: 24 May 2016

Abstract

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 < J ≤ 15−14 transitions of CO and ¹³CO , in addition to J ≤ 7−6 transitions of HCN, HNC, and HCO⁺ on galactic scales. We do this by re-sampling high density gas in a hydrodynamic model of a gas-rich disk galaxy, assuming that the density field of the ISM of the model galaxy follows the probability density function (PDF) inferred from the resolved low density scales. We find that in a narrow gas density PDF, with a mean density of ~10 cm^-3 and a dispersion σ = 2.1 in the log of the density, most of the emission of molecular lines, even of gas with critical densities >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.