The Critical Density and the Effective Excitation Density of Commonly Observed Molecular Dense Gas Tracers

TL;DR

This paper provides tables of critical and effective excitation densities for 12 dense gas tracers, analyzing their dependence on physical conditions and highlighting their differences for various molecules in molecular clouds.

Contribution

It introduces comprehensive tabulations of critical and effective excitation densities for common dense gas tracers and compares their applicability under different physical assumptions.

Findings

Critical densities are 1-2 orders of magnitude higher than effective excitation densities.

Effective excitation density better characterizes the density traced by various molecules.

Limitations of effective excitation density include undefined cases for certain transitions.

Abstract

The optically thin critical densities and the effective excitation densities to produce a 1 K km/s (or 0.818 Jy km/s $(\frac{\nu_{jk}}{100 \rm{GHz}})^2 \, (\frac{\theta_{beam}}{10^{\prime\prime}})^2$) spectral line are tabulated for 12 commonly observed dense gas molecular tracers. The dependence of the critical density and effective excitation density on physical assumptions (i.e. gas kinetic temperature and molecular column density) is analyzed. Critical densities for commonly observed dense gas transitions in molecular clouds (i.e. HCN $1-0$, HCO$^+$ $1-0$, N$_2$H$^+$ $1-0$) are typically $1 - 2$ orders of magnitude larger than effective excitation densities because the standard definitions of critical density do not account for radiative trapping and 1 K km/s lines are typically produced when radiative rates out of the upper energy level of the transition are faster than collisional depopulation. The use of effective excitation density has a distinct advantage over the use of critical density in characterizing the differences in density traced by species such as NH$_3$, HCO$^+$, N$_2$H$^+$, and HCN as well as their isotpologues; but, the effective excitation density has the disadvantage that it is undefined for transitions when $E_u/k \gg T_k$, for low molecular column densities, and for heavy molecules with complex spectra (i.e. CH$_3$CHO).