The detectability of mm-wave molecular rotational transitions

Abstract

Elaborating on a formalism that was first expressed some 40 years ago, we consider the brightness of low-lying mm-wave rotational lines of strongly polar molecules at the threshold of detectability. We derive a simple expression relating the brightness to the line of sight integral of the product of the total gas and molecular number densities and a suitably-defined temperature-dependent excitation rate into the upper level of the transition. Detectability of a line is contingent only on the ability of a molecule to channel enough of the ambient thermal energy into the line and the excitation can be computed in bulk by summing over rates without solving the multi-level rate equations or computing optical depths and excitation temperatures. Results for \hcop, HNC and CS are compared with escape-probability solutions of the rate equations using closed-form expressions for the expected range of validity of our {\it ansatz}, with the result that gas number densities as high as $10^4 \pccc$ or optical depths as high as 100 can be accommodated in some cases. For densities below a well-defined upper bound, the range of validity of the discussion can be cast as an upper bound on the line brightness which is 0.3 K for the J=1-0 lines and 0.8 - 1.7 K for the J=2-1 lines of these species. The discussion casts new light on interpretation of line brightnesses under conditions of weak excitation, simplifies derivation of physical parameters and eliminates the need to construct grids of numerical solutions of the rate equations.

Accepted for ApJ

References in corpus (5)

• The Critical Density and the Effective Excitation Density of Commonly Observed Molecular Dense Gas Tracers
• The Chemical Evolution of Helium
• Formation, fractionation and excitation of carbon monoxide in diffuse clouds
• Electron-impact rotational and hyperfine excitation of HCN, HNC, DCN and DNC
• Low energy H+CO scattering revisited: CO rotational excitation with new potential surfaces

Cited by in corpus (18)

• The anatomy of the Orion B Giant Molecular Cloud: A local template for studies of nearby galaxies
• EMPIRE: The IRAM 30-m Dense Gas Survey of Nearby Galaxies
• Turbulence and star formation efficiency in molecular clouds: solenoidal versus compressive motions in Orion B
• Star Formation Occurs in Dense Gas, but What Does "Dense" Mean?
• Clustering the Orion B giant molecular cloud based on its molecular emission
• Chemical complexity in local diffuse and translucent clouds: ubiquitous l-C3H and CH3CN, a detection of HC3N and an upper limit on the abundance of CH2CN
• Tracers of the ionization fraction in dense and translucent gas: I. Automated exploitation of massive astrochemical model grids
• Small-scale physical and chemical structure of diffuse and translucent molecular clouds along the line of sight to Sgr B2
• Chemical evolution along the circumnuclear ring of M83
• Molecular Gas and Dark Neutral Medium in the Outskirts of Chamaeleon
• HCN emission from translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of Orion B GMC: Revisiting its role as tracer of the dense gas reservoir for star formation
• Formation and Fractionation of CO (carbon monoxide) in diffuse clouds observed at optical and radio wavelengths
• ALMA hints at the existence of an unseen reservoir of diffuse molecular gas in the Galactic bulge
• H2CO and CS in diffuse clouds: Excitation and abundance
• An imaging line survey of OMC-1 to OMC-3
• CO emission and CO hotspots in diffuse molecular gas
• Predicting HCN, HCO + , multi-transition CO, and dust emission of star-forming galaxies: Constraining the properties of resolved gas and dust disks of local spiral galaxies
• Rethinking Habitability using Biogenic Precursors: Formaldehyde in Millimeter Molecular Clouds of the Inner Galaxy