Dense Gas Tracers and Star Formation Laws in Active Galaxies: Apex Survey of HCN J = 4 → 3, Hco + J = 4 → 3, and Cs J = 7 → 6

We report HCN J = 4 → 3, HCO^+ J = 4 → 3, and CS J = 7 → 6 observations in 20 nearby star-forming galaxies with the Atacama Pathfinder EXperiment 12 m telescope. Combined with four HCN, three HCO^+, and four CS detections from the literature, we probe the empirical link between the luminosity of molecular gas L'gas and that of infrared emission (L_ (IR), up to the highest gas densities (~10⁶ cm^ (–3) ) that have been probed so far. For nearby galaxies with large radii, we measure the IR luminosity within the submillimeter beam size (14"-18") to match the molecular emission. We find linear slopes for L'_ (CSJ=7-6) -L_ (IR) and L'_ (HCNJ=4-3) -L_ (IR), and a slightly super-linear slope for L'_ (HCO^+J=4-3) -L_ (IR). The correlation of L'_ (CSJ=7-6) -L_ (IR) even extends over eight orders of luminosity magnitude down to Galactic dense cores, with a fit of log (L_ (IR) ) =1. 00 (± 0. 01) ×log L'_ (CSJ=7-6) + 4. 03 (± 0. 04). Such linear correlations appear to hold for all densities >10⁴ cm^ (–3), and indicate that star formation rate is not related to the free-fall timescale for dense molecular gas.