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 (similar to 10(6) 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'(CS J=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'(CS J=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)xlog(L'(CS J=7-6)) + 4.03(+/-0.04). Such linear correlations appear to hold for all densities >10(4) cm(-3), and indicate that star formation rate is not related to the free-fall timescale for dense molecular gas.