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 CS J=7→6, HCN J=4→3, and HCO J=4→3 observations in 20 nearby star-forming galaxies with the Acatama Pathfinder EXperiment 12-m telescope. Combined with 4 CS, 4 HCN, and 3 HCO detections in literature, we probe the empirical link between the luminosity of molecular gas (L′gas) and that of infrared emission (LIR), up to the highest gas densities (106 108cm−3 ) that have been probed so far. For nearby galaxies with large radii, we measure the IR luminosity within the submm beam-size (14 –18) to match the molecular emission. We find linear slopes for L′CS J=7−6-LIR and L ′ HCN J=4−3-LIR, and a slightly super-linear slope for L′HCO+ J=4−3-LIR. The correlation of L ′ CS J=7−6-LIR even extends over eight orders of luminosity magnitude down to Galactic dense cores, with a fit of log(LIR)= 1.00(±0.01)×log(L′CSJ=7−6) +4.03(±0.04). Such linear correlations appear to hold for all densities > 104cm−3 , and indicate that star formation rate is not related to free-fall time scale for dense molecular gas. Subject headings: galaxies: evolution — galaxies: ISM — infrared: galaxies — ISM: molecules — radio lines: galaxies