Molecular Line Emission as a Tool for Galaxy Observations (LEGO). I. HCN as a tracer of moderate gas densities in molecular clouds and galaxies

Trends observed in galaxies, such as the Gao \& Solomon relation, suggest a linear relation between the star formation rate and the mass of dense gas available for star formation. Validation of such relations requires the establishment of reliable methods to trace the dense gas in galaxies. One frequent assumption is that the HCN ($J=1$--0) transition is unambiguously associated with gas at $\rm{}H_2$ densities $\gg{}10^4~\rm{}cm^{-3}$. If so, the mass of gas at densities $\gg{}10^4~\rm{}cm^{-3}$ could be inferred from the luminosity of this emission line, $L_{\rm{}HCN\,(1\text{--}0)}$. Here we use observations of the Orion~A molecular cloud to show that the HCN ($J=1$--0) line traces much lower densities $\sim{}10^3~\rm{}cm^{-3}$ in cold sections of this molecular cloud, corresponding to visual extinctions $A_V\approx{}6~\rm{}mag$. We also find that cold and dense gas in a cloud like Orion produces too little HCN emission to explain $L_{\rm{}HCN\,(1\text{--}0)}$ in star--forming galaxies, suggesting that galaxies might contain a hitherto unknown source of HCN emission. In our sample of molecules observed at frequencies near 100~GHz (also including $\rm{}^{12}CO$, $\rm{}^{13}CO$, $\rm{}C^{18}O$, CN, and CCH), $\rm{}N_2H^+$ is the only species clearly associated with rather dense gas.