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

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 & Thompson, we model emission for a set of common extragalactic lines from lognormal and power law density distributions. We consider the median density of gas that produces emission and the ability to predict density variations from observed line ratios. We emphasize line ratio variations because these do not require us to know the absolute abundance of our tracers. Patterns of line ratio variations have the potential 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 probability density function (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 adjustments to the underlying density distributions.