Millimeter-Wave Line Ratios and Sub-beam Volume Density Distributions

TL;DR

This paper investigates how millimeter-wave emission line ratios can be used to infer the distribution of molecular gas densities in external galaxies, accounting for complex sub-beam density variations.

Contribution

It introduces a modeling framework for interpreting mm-wave line ratios considering diverse density distributions, highlighting the importance of distribution shape knowledge.

Findings

Line ratio variations can reveal the high-end shape of the density distribution.

Different density distribution models lead to significantly different line ratio predictions.

Correcting for sub-beam density variations is crucial for accurate dense gas studies.

Abstract

We explore the use of mm-wave emission line ratios to trace molecular gas density when observations integrate over a wide range of volume densities within a single telescope beam. For observations targeting external galaxies, this case is unavoidable. Using a framework similar to that of Krumholz and Thompson (2007), we model emission for a set of common extragalactic lines from lognormal and power law density distributions. We consider the median density of gas producing emission and the ability to predict density variations from observed line ratios. We emphasize line ratio variations, because these do not require knowing the absolute abundance of our tracers. Patterns of line ratio variations have the prospect to illuminate the high-end shape of the density distribution, and to capture changes in the dense gas fraction and median volume density. Our results with and without a high density power law tail differ appreciably; we highlight better knowledge of the PDF shape as an important area. We also show the implications of sub-beam density distributions for isotopologue studies targeting dense gas tracers. Differential excitation often implies a significant correction to the naive case. We provide tabulated versions of many of our results, which can be used to interpret changes in mm-wave line ratios in terms of changes in the underlying density distributions.