Molecular Star Formation Rate Indicators in Galaxies

We derive a physical model for the observed relations between star formation rate (SFR) and molecular line (CO and HCN) emission in galaxies, and show how these observed relations are reflective of the underlying star formation law. We do this by combining self-consistent 3D non-LTE radiative transfer calculations with hydrodynamic simulations of isolated disk galaxies and galaxy mergers. We demonstrate that the observed SFR-molecular line relations are not necessarily representative of a more direct tracer of the SFR. Rather, they are driven by the relationship between molecular line emission and gas density, and anchored by the index of the Schmidt law controlling the SFR in the galaxy. Lines with low critical densities (e.g. CO J=1-0) are typically thermalized and trace the gas density faithfully. In these cases, the SFR will be related to line luminosity with an index similar to the Schmidt law index. Lines with critical densities greater than the mean density of most of the emitting clouds in a galaxy (e.g. CO J=3-2, HCN J=1-0) will exhibit significant emission driven by subthermally excited gas which owes its excitation to line trapping. The contribution to the total line luminosity from subthermally excited gas along the line of sight causes the line luminosity to increase with mean gas density superlinearly. Consequently the SFR-line luminosity index is less than the Schmidt index. Our model for SFR-molecular line relations quantitatively reproduces the slopes of the observed SFRCO (J=1-0), CO (J=3-2) and HCN (J=1-0) relations when a Schmidt law with index of ∼1.5 describes the SFR. We use these results to make model distinguishing testable predictions for the SFR-molecular line relations of unobserved transitions. Subject headings: galaxies: ISM – galaxies: starburst – ISM: molecules – stars: formation – radio lines: galaxies – radio lines: ISM